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Profit and Loss Questions in English
Competitive Exam Quantitative Aptitude · Profit and Loss · Profit and Loss
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51
DifficultMCQ
Sanjay purchased a chair marked at $Rs. 800$ at $2$ successive discounts of $10 \%$ and $15 \%$ respectively. He spent $Rs. 28$ on transportation and sold the chair for $Rs. 800$. How much is his gain percentage (in $\%$)?
A
$14$
B
$30$
C
$25$
D
$40$
Solution
(C) Marked Price $(MP)$ of the chair $= Rs. 800$.
After applying successive discounts of $10 \%$ and $15 \%$, the purchase price for Sanjay is calculated as:
$CP_{initial} = 800 \times (1 - 0.10) \times (1 - 0.15) = 800 \times 0.90 \times 0.85 = Rs. 612$.
Total Cost Price $(CP)$ including transportation cost $= 612 + 28 = Rs. 640$.
Selling Price $(SP) = Rs. 800$.
Profit $= SP - \text{Total } CP = 800 - 640 = Rs. 160$.
Gain percentage $= (\text{Profit} / \text{Total } CP) \times 100 = (160 / 640) \times 100 = (1 / 4) \times 100 = 25 \%$.
After applying successive discounts of $10 \%$ and $15 \%$, the purchase price for Sanjay is calculated as:
$CP_{initial} = 800 \times (1 - 0.10) \times (1 - 0.15) = 800 \times 0.90 \times 0.85 = Rs. 612$.
Total Cost Price $(CP)$ including transportation cost $= 612 + 28 = Rs. 640$.
Selling Price $(SP) = Rs. 800$.
Profit $= SP - \text{Total } CP = 800 - 640 = Rs. 160$.
Gain percentage $= (\text{Profit} / \text{Total } CP) \times 100 = (160 / 640) \times 100 = (1 / 4) \times 100 = 25 \%$.
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View Solution52
MediumMCQ
When a book is sold at its Marked Price,it gives a profit of $40 \%$. What percentage of profit or loss will occur if it is sold at half the Marked Price?
A
$30 \% \text{ profit}$
B
$25 \% \text{ loss}$
C
$30 \% \text{ loss}$
D
$40 \% \text{ profit}$
Solution
(C) Let the Cost Price $(CP)$ of the book be $Rs. 100$.
Since selling the book at the Marked Price $(MP)$ gives a profit of $40 \%$,the $MP$ is $100 + 40 = Rs. 140$.
If the book is sold at half the Marked Price,the new Selling Price $(SP)$ is $\frac{140}{2} = Rs. 70$.
Now,we compare the new $SP$ with the $CP$: $SP = Rs. 70$ and $CP = Rs. 100$.
Since $SP < CP$,there is a loss.
$\text{Loss} = CP - SP = 100 - 70 = Rs. 30$.
$\text{Loss percentage} = \frac{\text{Loss}}{CP} \times 100 = \frac{30}{100} \times 100 = 30 \%$.
Therefore,there is a $30 \% \text{ loss}$.
Since selling the book at the Marked Price $(MP)$ gives a profit of $40 \%$,the $MP$ is $100 + 40 = Rs. 140$.
If the book is sold at half the Marked Price,the new Selling Price $(SP)$ is $\frac{140}{2} = Rs. 70$.
Now,we compare the new $SP$ with the $CP$: $SP = Rs. 70$ and $CP = Rs. 100$.
Since $SP < CP$,there is a loss.
$\text{Loss} = CP - SP = 100 - 70 = Rs. 30$.
$\text{Loss percentage} = \frac{\text{Loss}}{CP} \times 100 = \frac{30}{100} \times 100 = 30 \%$.
Therefore,there is a $30 \% \text{ loss}$.
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View Solution53
MediumMCQ
Aditya purchased $14$ shirts and $25$ pants at $Rs. 45$ and $Rs. 55$ respectively. What should be the approximate overall average selling price of a shirt and a pant so that a $40\%$ profit is earned?
A
$72.5$
B
$71$
C
$72$
D
$70$
Solution
(C) Total cost price of $14$ shirts $= 14 \times 45 = Rs. 630$.
Total cost price of $25$ pants $= 25 \times 55 = Rs. 1375$.
Total cost price of $39$ items $= 630 + 1375 = Rs. 2005$.
To earn a $40\%$ profit,the total selling price must be $2005 \times 1.40 = Rs. 2807$.
The average selling price per item $= \frac{2807}{39} \approx Rs. 71.97$.
Rounding to the nearest whole number,the approximate average selling price is $Rs. 72$.
Total cost price of $25$ pants $= 25 \times 55 = Rs. 1375$.
Total cost price of $39$ items $= 630 + 1375 = Rs. 2005$.
To earn a $40\%$ profit,the total selling price must be $2005 \times 1.40 = Rs. 2807$.
The average selling price per item $= \frac{2807}{39} \approx Rs. 71.97$.
Rounding to the nearest whole number,the approximate average selling price is $Rs. 72$.
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View Solution54
MediumMCQ
$A$ person sells $36$ apples per rupee and suffers a loss of $4 \%$. Find how many apples per rupee should be sold to have a gain of $8 \%$.
A
$32$
B
$16$
C
$4$
D
$15$
Solution
$(A)$ Let the cost price $(CP)$ of $1$ rupee worth of apples be $C$.
Since the $CP$ is constant, we use the relationship: $\frac{SP_1}{100 - \text{Loss}\%} = \frac{SP_2}{100 + \text{Gain}\%}$.
Given, $SP_1 = \frac{1}{36}$ rupees per apple, $\text{Loss} = 4\%$, and $\text{Gain} = 8\%$.
Substituting the values: $\frac{1/36}{100 - 4} = \frac{SP_2}{100 + 8}$.
$\frac{1}{36 \times 96} = \frac{SP_2}{108}$.
$SP_2 = \frac{108}{36 \times 96} = \frac{3}{96} = \frac{1}{32}$.
Thus, the person should sell $32$ apples per rupee to gain $8\%$.
Since the $CP$ is constant, we use the relationship: $\frac{SP_1}{100 - \text{Loss}\%} = \frac{SP_2}{100 + \text{Gain}\%}$.
Given, $SP_1 = \frac{1}{36}$ rupees per apple, $\text{Loss} = 4\%$, and $\text{Gain} = 8\%$.
Substituting the values: $\frac{1/36}{100 - 4} = \frac{SP_2}{100 + 8}$.
$\frac{1}{36 \times 96} = \frac{SP_2}{108}$.
$SP_2 = \frac{108}{36 \times 96} = \frac{3}{96} = \frac{1}{32}$.
Thus, the person should sell $32$ apples per rupee to gain $8\%$.
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View Solution55
MediumMCQ
Ram sells an article to Girish at a gain of $20 \%$,Girish sells it to Sanjay at a gain of $10 \%$,and Sanjay sells it to Aditya at a gain of $12 \frac{1}{2} \%$. If Aditya pays $Rs. 59.40$,what did it cost Ram in $Rs.$?
A
$40$
B
$22$
C
$24$
D
$18$
Solution
(A) Let the initial cost price for Ram be $Rs. x$.
Ram sells the article to Girish at a gain of $20 \%$,so the selling price for Ram is $x \times (1 + 0.20) = 1.2x$.
Girish sells it to Sanjay at a gain of $10 \%$,so the selling price for Girish is $1.2x \times (1 + 0.10) = 1.2x \times 1.1 = 1.32x$.
Sanjay sells it to Aditya at a gain of $12 \frac{1}{2} \% = 12.5 \%$,so the selling price for Sanjay is $1.32x \times (1 + 0.125) = 1.32x \times 1.125 = 1.485x$.
Given that Aditya pays $Rs. 59.40$,we have the equation:
$1.485x = 59.40$
Solving for $x$:
$x = \frac{59.40}{1.485} = 40$
Therefore,the cost price for Ram was $Rs. 40$.
Ram sells the article to Girish at a gain of $20 \%$,so the selling price for Ram is $x \times (1 + 0.20) = 1.2x$.
Girish sells it to Sanjay at a gain of $10 \%$,so the selling price for Girish is $1.2x \times (1 + 0.10) = 1.2x \times 1.1 = 1.32x$.
Sanjay sells it to Aditya at a gain of $12 \frac{1}{2} \% = 12.5 \%$,so the selling price for Sanjay is $1.32x \times (1 + 0.125) = 1.32x \times 1.125 = 1.485x$.
Given that Aditya pays $Rs. 59.40$,we have the equation:
$1.485x = 59.40$
Solving for $x$:
$x = \frac{59.40}{1.485} = 40$
Therefore,the cost price for Ram was $Rs. 40$.
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View Solution56
DifficultMCQ
$A$ fruit seller sells $\frac{3}{5}$ th part of fruit at a profit of $10 \%$ and the remaining at a loss of $5 \%$. If the total profit is $Rs. 1500$,then what is the total cost price of the fruit in $Rs.$?
A
$37500$
B
$37000$
C
$36500$
D
$36000$
Solution
(A) Let the total cost price $(CP)$ of the fruit be $A$.
The seller sells $\frac{3}{5}$ of the fruit at $10 \%$ profit and the remaining $\frac{2}{5}$ of the fruit at $5 \%$ loss.
The total profit is given by:
$Profit = (\frac{3}{5} \times A \times \frac{10}{100}) - (\frac{2}{5} \times A \times \frac{5}{100})$
Given that the total profit is $Rs. 1500$,we have:
$1500 = \frac{30A}{500} - \frac{10A}{500}$
$1500 = \frac{20A}{500}$
$1500 = \frac{A}{25}$
$A = 1500 \times 25$
$A = 37500$
Therefore,the total cost price of the fruit is $Rs. 37,500$.
The seller sells $\frac{3}{5}$ of the fruit at $10 \%$ profit and the remaining $\frac{2}{5}$ of the fruit at $5 \%$ loss.
The total profit is given by:
$Profit = (\frac{3}{5} \times A \times \frac{10}{100}) - (\frac{2}{5} \times A \times \frac{5}{100})$
Given that the total profit is $Rs. 1500$,we have:
$1500 = \frac{30A}{500} - \frac{10A}{500}$
$1500 = \frac{20A}{500}$
$1500 = \frac{A}{25}$
$A = 1500 \times 25$
$A = 37500$
Therefore,the total cost price of the fruit is $Rs. 37,500$.
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View Solution57
DifficultMCQ
$A$ shopkeeper buys a toy at $Rs. 100$ and sells it at $Rs. 125$. Another shopkeeper buys the same toy at $Rs. 125$ but sells it at $Rs. 100$. What are the respective profit and loss percentages for the two shopkeepers?
A
$20 \%, 20 \%$
B
$25 \%, 20 \%$
C
$25 \%, 25 \%$
D
$25 \%, 16.67 \%$
Solution
(B) Case $-1$: For the first shopkeeper,Cost Price $(CP)$ = $Rs. 100$ and Selling Price $(SP)$ = $Rs. 125$.
Profit = $SP - CP = 125 - 100 = Rs. 25$.
Profit percentage = $\left(\frac{\text{Profit}}{CP}\right) \times 100 = \left(\frac{25}{100}\right) \times 100 = 25\%$.
Case $-2$: For the second shopkeeper,Cost Price $(CP)$ = $Rs. 125$ and Selling Price $(SP)$ = $Rs. 100$.
Loss = $CP - SP = 125 - 100 = Rs. 25$.
Loss percentage = $\left(\frac{\text{Loss}}{CP}\right) \times 100 = \left(\frac{25}{125}\right) \times 100 = \left(\frac{1}{5}\right) \times 100 = 20\%$.
Thus,the profit and loss percentages are $25\%$ and $20\%$ respectively.
Profit = $SP - CP = 125 - 100 = Rs. 25$.
Profit percentage = $\left(\frac{\text{Profit}}{CP}\right) \times 100 = \left(\frac{25}{100}\right) \times 100 = 25\%$.
Case $-2$: For the second shopkeeper,Cost Price $(CP)$ = $Rs. 125$ and Selling Price $(SP)$ = $Rs. 100$.
Loss = $CP - SP = 125 - 100 = Rs. 25$.
Loss percentage = $\left(\frac{\text{Loss}}{CP}\right) \times 100 = \left(\frac{25}{125}\right) \times 100 = \left(\frac{1}{5}\right) \times 100 = 20\%$.
Thus,the profit and loss percentages are $25\%$ and $20\%$ respectively.
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View Solution58
MediumMCQ
The marked price of a bed is $Rs. 2400$. The shopkeeper gives successive discounts of $10 \%$ and $X \%$ to the customer. If the customer pays $Rs. 1836$ for the bed,then find the value of $X$ in $\%$.
A
$15$
B
$18$
C
$12$
D
$10$
Solution
(A) The marked price of the bed is $Rs. 2400$.
After the first discount of $10 \%$,the price becomes $2400 \times (1 - 0.10) = 2400 \times 0.9 = 2160$.
Let the second discount be $X \%$. The final price paid is $2160 \times (1 - \frac{X}{100}) = 1836$.
Dividing both sides by $2160$,we get $(1 - \frac{X}{100}) = \frac{1836}{2160} = 0.85$.
Therefore,$\frac{X}{100} = 1 - 0.85 = 0.15$.
Thus,$X = 15 \%$.
After the first discount of $10 \%$,the price becomes $2400 \times (1 - 0.10) = 2400 \times 0.9 = 2160$.
Let the second discount be $X \%$. The final price paid is $2160 \times (1 - \frac{X}{100}) = 1836$.
Dividing both sides by $2160$,we get $(1 - \frac{X}{100}) = \frac{1836}{2160} = 0.85$.
Therefore,$\frac{X}{100} = 1 - 0.85 = 0.15$.
Thus,$X = 15 \%$.
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View Solution59
MediumMCQ
Three successive discounts of $10 \%$,$12 \%$,and $15 \%$ are equivalent to a single discount of what percentage (in $\%$)?
A
$36.28$
B
$32.68$
C
$34.68$
D
$37$
Solution
(B) To find the equivalent single discount for three successive discounts of $x \%$,$y \%$,and $z \%$,we use the formula:
$\text{Equivalent Discount} = \left[ x + y + z - \frac{xy + yz + zx}{100} + \frac{xyz}{100^2} \right] \%$
Given $x = 10$,$y = 12$,and $z = 15$:
$1. \text{ Sum of discounts} = 10 + 12 + 15 = 37$
$2. \text{ Sum of products taken two at a time} = (10 \times 12) + (12 \times 15) + (15 \times 10) = 120 + 180 + 150 = 450$
$3. \text{ Product of all three} = 10 \times 12 \times 15 = 1800$
Substituting these values into the formula:
$\text{Equivalent Discount} = \left[ 37 - \frac{450}{100} + \frac{1800}{10000} \right] \%$
$= [37 - 4.5 + 0.18] \%$
$= 32.68 \%$
$\text{Equivalent Discount} = \left[ x + y + z - \frac{xy + yz + zx}{100} + \frac{xyz}{100^2} \right] \%$
Given $x = 10$,$y = 12$,and $z = 15$:
$1. \text{ Sum of discounts} = 10 + 12 + 15 = 37$
$2. \text{ Sum of products taken two at a time} = (10 \times 12) + (12 \times 15) + (15 \times 10) = 120 + 180 + 150 = 450$
$3. \text{ Product of all three} = 10 \times 12 \times 15 = 1800$
Substituting these values into the formula:
$\text{Equivalent Discount} = \left[ 37 - \frac{450}{100} + \frac{1800}{10000} \right] \%$
$= [37 - 4.5 + 0.18] \%$
$= 32.68 \%$
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View Solution60
DifficultMCQ
$A$ loss of $19 \%$ gets converted into a profit of $17 \%$ when the selling price is increased by $Rs. 162$. Find the cost price of the article in $Rs.$
A
$300$
B
$350$
C
$400$
D
$450$
Solution
(D) Let the cost price of the article be $Rs. x$.
Initially,there is a loss of $19 \%$,so the selling price $(SP_1)$ is $x - 0.19x = 0.81x$.
After increasing the selling price by $Rs. 162$,there is a profit of $17 \%$,so the new selling price $(SP_2)$ is $x + 0.17x = 1.17x$.
According to the problem,the difference between the two selling prices is $Rs. 162$:
$SP_2 - SP_1 = 162$
$1.17x - 0.81x = 162$
$0.36x = 162$
$x = \frac{162}{0.36} = 450$.
Therefore,the cost price of the article is $Rs. 450$.
Initially,there is a loss of $19 \%$,so the selling price $(SP_1)$ is $x - 0.19x = 0.81x$.
After increasing the selling price by $Rs. 162$,there is a profit of $17 \%$,so the new selling price $(SP_2)$ is $x + 0.17x = 1.17x$.
According to the problem,the difference between the two selling prices is $Rs. 162$:
$SP_2 - SP_1 = 162$
$1.17x - 0.81x = 162$
$0.36x = 162$
$x = \frac{162}{0.36} = 450$.
Therefore,the cost price of the article is $Rs. 450$.
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View Solution61
MediumMCQ
$A$ shopkeeper sold an article offering a discount of $5 \%$ and earned a profit of $23.5 \%$. What would have been the percentage of profit earned if no discount had been offered?
A
$23 \%$
B
$30 \%$
C
$33 \%$
D
Cannot be determined
Solution
(B) Let the Cost Price $(CP)$ be $Rs. 100$.
Since the profit earned is $23.5 \%$,the Selling Price $(SP)$ is $Rs. 123.50$.
Let the Marked Price $(MP)$ be $x$.
Given that a discount of $5 \%$ is offered on the $MP$,the $SP$ is $95 \%$ of $MP$.
So,$0.95x = 123.50$.
$x = \frac{123.50}{0.95} = 130$.
If no discount is offered,the article would be sold at its Marked Price,which is $Rs. 130$.
Profit in this case $= SP - CP = 130 - 100 = 30$.
Profit percentage $= \frac{30}{100} \times 100 = 30 \%$.
Since the profit earned is $23.5 \%$,the Selling Price $(SP)$ is $Rs. 123.50$.
Let the Marked Price $(MP)$ be $x$.
Given that a discount of $5 \%$ is offered on the $MP$,the $SP$ is $95 \%$ of $MP$.
So,$0.95x = 123.50$.
$x = \frac{123.50}{0.95} = 130$.
If no discount is offered,the article would be sold at its Marked Price,which is $Rs. 130$.
Profit in this case $= SP - CP = 130 - 100 = 30$.
Profit percentage $= \frac{30}{100} \times 100 = 30 \%$.
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View Solution62
DifficultMCQ
If Aditya sells an article to Nutan at $10 \%$ gain,while Nutan sells it to Manish at $20 \%$ gain at $Rs. 1914$,then what is the Cost Price in $Rs.$?
A
$1450$
B
$1340$
C
$1560$
D
$1780$
Solution
(A) Let the original cost price for Aditya be $Rs. 100$.
Aditya sells the article to Nutan at a $10 \%$ gain:
Selling Price for Aditya = $100 + (10 \% \text{ of } 100) = 110$.
Nutan sells the article to Manish at a $20 \%$ gain:
Selling Price for Nutan = $110 + (20 \% \text{ of } 110) = 110 + 22 = 132$.
If the final selling price (Manish's cost price) is $Rs. 132$,the initial cost price is $Rs. 100$.
Given that Manish bought the article at $Rs. 1914$,we can set up the proportion:
$\text{Initial Cost Price} = \left( \frac{100}{132} \times 1914 \right)$.
Calculating the value:
$\frac{191400}{132} = 1450$.
Therefore,the original cost price is $Rs. 1450$.
Aditya sells the article to Nutan at a $10 \%$ gain:
Selling Price for Aditya = $100 + (10 \% \text{ of } 100) = 110$.
Nutan sells the article to Manish at a $20 \%$ gain:
Selling Price for Nutan = $110 + (20 \% \text{ of } 110) = 110 + 22 = 132$.
If the final selling price (Manish's cost price) is $Rs. 132$,the initial cost price is $Rs. 100$.
Given that Manish bought the article at $Rs. 1914$,we can set up the proportion:
$\text{Initial Cost Price} = \left( \frac{100}{132} \times 1914 \right)$.
Calculating the value:
$\frac{191400}{132} = 1450$.
Therefore,the original cost price is $Rs. 1450$.
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View Solution63
DifficultMCQ
Rita buys an article for $Rs. 9600$. She sold it at $12\%$ loss and gets some money,and from that money,she again buys an article and this time she gets $12\%$ profit. What was the profit or loss she got from this transaction in $Rs.$?
A
$130$
B
$138$
C
$138.24$
D
$138.42$
Solution
(C) Initial $CP = Rs. 9600$.
Selling Price $(SP)$ after selling it at $12\%$ loss:
$SP_1 = 9600 \times (1 - 0.12) = 9600 \times 0.88 = Rs. 8448$.
Now,she buys another article with this money,so the new $CP = Rs. 8448$.
Final $SP$ after selling this article at $12\%$ profit:
$SP_2 = 8448 \times (1 + 0.12) = 8448 \times 1.12 = Rs. 9461.76$.
Total loss incurred in the transaction = Initial $CP - Final SP$.
Total loss $= 9600 - 9461.76 = Rs. 138.24$.
Alternatively,using the net percentage change formula for successive profit and loss of $x\%$:
Net change $= -x^2 / 100 = -(12)^2 / 100 = -144 / 100 = -1.44\%$.
Loss $= 1.44\% \text{ of } 9600 = (1.44 / 100) \times 9600 = 1.44 \times 96 = Rs. 138.24$.
Selling Price $(SP)$ after selling it at $12\%$ loss:
$SP_1 = 9600 \times (1 - 0.12) = 9600 \times 0.88 = Rs. 8448$.
Now,she buys another article with this money,so the new $CP = Rs. 8448$.
Final $SP$ after selling this article at $12\%$ profit:
$SP_2 = 8448 \times (1 + 0.12) = 8448 \times 1.12 = Rs. 9461.76$.
Total loss incurred in the transaction = Initial $CP - Final SP$.
Total loss $= 9600 - 9461.76 = Rs. 138.24$.
Alternatively,using the net percentage change formula for successive profit and loss of $x\%$:
Net change $= -x^2 / 100 = -(12)^2 / 100 = -144 / 100 = -1.44\%$.
Loss $= 1.44\% \text{ of } 9600 = (1.44 / 100) \times 9600 = 1.44 \times 96 = Rs. 138.24$.
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View Solution64
MediumMCQ
Nutan bought $30$ dozens of oranges for her juice stall in the school fair. She paid $Rs. 8$ per dozen of oranges. She also had to pay $Rs. 500$ as the stall fee to the school authorities. She calculated that each glass of juice would need $3$ oranges. How much should she charge per glass of juice so as to make $20 \%$ profit in $Rs$?
A
$7.20$
B
$7.40$
C
$7.60$
D
$7.80$
Solution
(B) Total Cost Price $(CP)$ = (Cost of $30$ dozen oranges) + (Stall fee)
Total $CP = (30 \times 8) + 500 = 240 + 500 = Rs. 740$.
Total number of oranges = $30 \times 12 = 360$ oranges.
Since each glass requires $3$ oranges,the total number of glasses of juice = $360 / 3 = 120$ glasses.
To make a $20 \%$ profit,the total Selling Price $(SP)$ must be $120 \%$ of the total $CP$.
Total $SP = 740 \times 1.20 = Rs. 888$.
Selling Price per glass = (Total $SP$) / (Total number of glasses) = $888 / 120 = Rs. 7.40$.
Total $CP = (30 \times 8) + 500 = 240 + 500 = Rs. 740$.
Total number of oranges = $30 \times 12 = 360$ oranges.
Since each glass requires $3$ oranges,the total number of glasses of juice = $360 / 3 = 120$ glasses.
To make a $20 \%$ profit,the total Selling Price $(SP)$ must be $120 \%$ of the total $CP$.
Total $SP = 740 \times 1.20 = Rs. 888$.
Selling Price per glass = (Total $SP$) / (Total number of glasses) = $888 / 120 = Rs. 7.40$.
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View Solution65
DifficultMCQ
Aditya bought a scooter for a certain sum of money. He spent $15 \%$ of the cost price on repairs and sold it for a profit of $Rs. 1104$. What did he spend on repairs if the profit he earned was $20 \%$?
A
$600$
B
$720$
C
$800$
D
$900$
Solution
(B) Let the original cost price $(CP)$ be $100x$.
Repair cost is $15 \%$ of $CP$,so repair cost $= 15x$.
Total $CP$ after repair $= 100x + 15x = 115x$.
Profit earned is $20 \%$ on the total $CP$.
Profit amount $= 20 \% \text{ of } 115x = 0.20 \times 115x = 23x$.
Given that the profit is $Rs. 1104$,we have $23x = 1104$.
$x = \frac{1104}{23} = 48$.
Since the repair cost is $15x$,the actual repair cost $= 15 \times 48 = Rs. 720$.
Repair cost is $15 \%$ of $CP$,so repair cost $= 15x$.
Total $CP$ after repair $= 100x + 15x = 115x$.
Profit earned is $20 \%$ on the total $CP$.
Profit amount $= 20 \% \text{ of } 115x = 0.20 \times 115x = 23x$.
Given that the profit is $Rs. 1104$,we have $23x = 1104$.
$x = \frac{1104}{23} = 48$.
Since the repair cost is $15x$,the actual repair cost $= 15 \times 48 = Rs. 720$.
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View Solution66
MediumMCQ
In a certain store,the profit is $320 \%$ of the cost. If the cost increases by $25 \%$ but the selling price remains constant,approximately what percentage of the selling price is the profit?
A
$30$
B
$70$
C
$100$
D
$250$
Solution
(B) Let the original cost price $(CP_1)$ be $Rs. 100$.
Since the profit is $320 \%$ of the cost,the profit is $Rs. 320$.
Therefore,the selling price $(SP)$ is $CP_1 + \text{Profit} = 100 + 320 = Rs. 420$.
If the cost increases by $25 \%$,the new cost price $(CP_2)$ becomes $100 + 25 \% \text{ of } 100 = Rs. 125$.
The selling price remains constant at $Rs. 420$.
The new profit is $SP - CP_2 = 420 - 125 = Rs. 295$.
To find the profit as a percentage of the selling price,we calculate: $\frac{\text{New Profit}}{SP} \times 100 = \frac{295}{420} \times 100$.
$\frac{295}{420} \times 100 \approx 70.23 \%$.
Thus,the profit is approximately $70 \%$ of the selling price.
Since the profit is $320 \%$ of the cost,the profit is $Rs. 320$.
Therefore,the selling price $(SP)$ is $CP_1 + \text{Profit} = 100 + 320 = Rs. 420$.
If the cost increases by $25 \%$,the new cost price $(CP_2)$ becomes $100 + 25 \% \text{ of } 100 = Rs. 125$.
The selling price remains constant at $Rs. 420$.
The new profit is $SP - CP_2 = 420 - 125 = Rs. 295$.
To find the profit as a percentage of the selling price,we calculate: $\frac{\text{New Profit}}{SP} \times 100 = \frac{295}{420} \times 100$.
$\frac{295}{420} \times 100 \approx 70.23 \%$.
Thus,the profit is approximately $70 \%$ of the selling price.
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View Solution67
DifficultMCQ
$A$ shopkeeper sells one transistor for $Rs.\, 840$ at a gain of $20 \%$ and another for $Rs.\, 960$ at a loss of $4 \%$. His total gain or loss percent is
A
$5 \frac{15}{17} \% \text{ loss}$
B
$5 \frac{15}{17} \% \text{ gain}$
C
$6 \frac{2}{3} \% \text{ gain}$
D
$6 \frac{1}{2} \% \text{ loss}$
Solution
(B) Cost Price $(CP)$ of the $1^{\text{st}}$ transistor $= \frac{840}{1 + 0.20} = \frac{840}{1.2} = Rs.\, 700$ (at $20 \%$ gain).
Cost Price $(CP)$ of the $2^{\text{nd}}$ transistor $= \frac{960}{1 - 0.04} = \frac{960}{0.96} = Rs.\, 1000$ (at $4 \%$ loss).
Total Cost Price $(CP)$ $= 700 + 1000 = Rs.\, 1700$.
Total Selling Price $(SP)$ $= 840 + 960 = Rs.\, 1800$.
Since $SP > CP$,there is a gain.
Gain $= SP - CP = 1800 - 1700 = Rs.\, 100$.
Gain percentage $= \left( \frac{\text{Gain}}{CP} \right) \times 100 = \left( \frac{100}{1700} \right) \times 100 = \frac{100}{17} = 5 \frac{15}{17} \%$ gain.
Cost Price $(CP)$ of the $2^{\text{nd}}$ transistor $= \frac{960}{1 - 0.04} = \frac{960}{0.96} = Rs.\, 1000$ (at $4 \%$ loss).
Total Cost Price $(CP)$ $= 700 + 1000 = Rs.\, 1700$.
Total Selling Price $(SP)$ $= 840 + 960 = Rs.\, 1800$.
Since $SP > CP$,there is a gain.
Gain $= SP - CP = 1800 - 1700 = Rs.\, 100$.
Gain percentage $= \left( \frac{\text{Gain}}{CP} \right) \times 100 = \left( \frac{100}{1700} \right) \times 100 = \frac{100}{17} = 5 \frac{15}{17} \%$ gain.
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View Solution68
MediumMCQ
$A$ dealer buys a table listed at $Rs. 600$ and gets successive discounts of $10\%$ and $20\%$. What is his profit or loss percent if he sells it at $Rs. 540$?
A
$25\%$
B
$20\%$
C
$15\%$
D
$17 \frac{1}{2}\%$
Solution
(A) Given,Marked Price $(MP)$ = $Rs. 600$.
Successive discounts are $10\%$ and $20\%$.
The Cost Price $(CP)$ for the dealer is calculated as:
$CP = 600 \times (1 - 0.10) \times (1 - 0.20) = 600 \times 0.90 \times 0.80 = 600 \times 0.72 = Rs. 432$.
The Selling Price $(SP)$ is given as $Rs. 540$.
Since $SP > CP$,the dealer makes a profit.
Profit = $SP - CP = 540 - 432 = Rs. 108$.
Profit Percent = $\frac{\text{Profit}}{CP} \times 100 = \frac{108}{432} \times 100 = \frac{1}{4} \times 100 = 25\%$.
Successive discounts are $10\%$ and $20\%$.
The Cost Price $(CP)$ for the dealer is calculated as:
$CP = 600 \times (1 - 0.10) \times (1 - 0.20) = 600 \times 0.90 \times 0.80 = 600 \times 0.72 = Rs. 432$.
The Selling Price $(SP)$ is given as $Rs. 540$.
Since $SP > CP$,the dealer makes a profit.
Profit = $SP - CP = 540 - 432 = Rs. 108$.
Profit Percent = $\frac{\text{Profit}}{CP} \times 100 = \frac{108}{432} \times 100 = \frac{1}{4} \times 100 = 25\%$.
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View Solution69
DifficultMCQ
Sonal buys mangoes at the rate of $3 \, \text{kg}$ for $Rs. 21$ and sells them at $5 \, \text{kg}$ for $Rs. 50$. To earn a profit of $Rs. 102$, he must sell how many mangoes in $\text{kg}$?
A
$34$
B
$52$
C
$26$
D
$32$
Solution
(A) Cost Price $(CP)$ of $1 \, \text{kg}$ mango $= \frac{21}{3} = Rs. 7$.
Selling Price $(SP)$ of $1 \, \text{kg}$ mango $= \frac{50}{5} = Rs. 10$.
Profit per $\text{kg} = SP - CP = 10 - 7 = Rs. 3$.
To earn a total profit of $Rs. 102$, the quantity of mangoes to be sold is calculated as:
Quantity $= \frac{\text{Total Profit}}{\text{Profit per kg}} = \frac{102}{3} = 34 \, \text{kg}$.
Selling Price $(SP)$ of $1 \, \text{kg}$ mango $= \frac{50}{5} = Rs. 10$.
Profit per $\text{kg} = SP - CP = 10 - 7 = Rs. 3$.
To earn a total profit of $Rs. 102$, the quantity of mangoes to be sold is calculated as:
Quantity $= \frac{\text{Total Profit}}{\text{Profit per kg}} = \frac{102}{3} = 34 \, \text{kg}$.
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View Solution70
MediumMCQ
An electric pump was sold at a profit of $15 \%$. Had it been sold for $Rs. 600$, the profit would have been $20 \%$. What was the former selling price in $Rs.$?
A
$500$
B
$540$
C
$575$
D
$600$
Solution
(C) Let the Cost Price $(CP)$ of the electric pump be $x$.
According to the first condition, the profit is $15 \%$, so the first selling price $(SP)_1 = x + 0.15x = 1.15x$.
According to the second condition, if the selling price $(SP)_2$ is $Rs. 600$, the profit is $20 \%$.
Using the formula: $SP = CP \times (1 + \text{Profit } \%)$
$600 = x \times (1 + 0.20)$
$600 = 1.20x$
$x = \frac{600}{1.20} = 500$.
So, the Cost Price $(CP)$ is $Rs. 500$.
Now, calculate the former selling price $(SP)_1$:
$(SP)_1 = 1.15 \times 500 = 575$.
Therefore, the former selling price was $Rs. 575$.
According to the first condition, the profit is $15 \%$, so the first selling price $(SP)_1 = x + 0.15x = 1.15x$.
According to the second condition, if the selling price $(SP)_2$ is $Rs. 600$, the profit is $20 \%$.
Using the formula: $SP = CP \times (1 + \text{Profit } \%)$
$600 = x \times (1 + 0.20)$
$600 = 1.20x$
$x = \frac{600}{1.20} = 500$.
So, the Cost Price $(CP)$ is $Rs. 500$.
Now, calculate the former selling price $(SP)_1$:
$(SP)_1 = 1.15 \times 500 = 575$.
Therefore, the former selling price was $Rs. 575$.
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View Solution71
DifficultMCQ
On a $Rs. 10,000$ payment order,a person has a choice between three successive discounts of $10\%, 10\%$ and $30\%$ and three successive discounts of $40\%, 5\%$ and $5\%$. By choosing the better offer,how much can he save in $Rs.$?
A
$200$
B
$225$
C
$400$
D
$255$
Solution
(D) Let the initial amount be $Rs. 100$.
Case-$1$: Successive discounts of $10\%, 10\%, 30\%$.
The final amount after discounts is $100 \times (1 - 0.10) \times (1 - 0.10) \times (1 - 0.30) = 100 \times 0.9 \times 0.9 \times 0.7 = Rs. 56.7$.
Case-$2$: Successive discounts of $40\%, 5\%, 5\%$.
The final amount after discounts is $100 \times (1 - 0.40) \times (1 - 0.05) \times (1 - 0.05) = 100 \times 0.6 \times 0.95 \times 0.95 = Rs. 54.15$.
Difference in savings for $Rs. 100$ is $56.7 - 54.15 = Rs. 2.55$.
For a payment order of $Rs. 10,000$,the total savings will be $\frac{2.55}{100} \times 10,000 = Rs. 255$.
Case-$1$: Successive discounts of $10\%, 10\%, 30\%$.
The final amount after discounts is $100 \times (1 - 0.10) \times (1 - 0.10) \times (1 - 0.30) = 100 \times 0.9 \times 0.9 \times 0.7 = Rs. 56.7$.
Case-$2$: Successive discounts of $40\%, 5\%, 5\%$.
The final amount after discounts is $100 \times (1 - 0.40) \times (1 - 0.05) \times (1 - 0.05) = 100 \times 0.6 \times 0.95 \times 0.95 = Rs. 54.15$.
Difference in savings for $Rs. 100$ is $56.7 - 54.15 = Rs. 2.55$.
For a payment order of $Rs. 10,000$,the total savings will be $\frac{2.55}{100} \times 10,000 = Rs. 255$.
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View Solution72
MediumMCQ
$A$ man sells each of his $2$ articles for $Rs. 99$. On one he gains $10 \%$ and on the other he incurs a loss of $1 \%$. What is his total gain in $\%$ in the entire transaction?
A
$9$
B
$4 \frac{4}{19}$
C
$4.5$
D
$5.5$
Solution
(B) Cost Price $(CP)$ of the $1$st article $= \frac{99}{1 + 0.10} = \frac{99}{1.10} = Rs. 90$ (Profit of $10 \%$).
Cost Price $(CP)$ of the $2$nd article $= \frac{99}{1 - 0.01} = \frac{99}{0.99} = Rs. 100$ (Loss of $1 \%$).
Total $CP$ of both articles $= 90 + 100 = Rs. 190$.
Total Selling Price $(SP)$ of both articles $= 99 + 99 = Rs. 198$.
Total Profit $= 198 - 190 = Rs. 8$.
Profit $\%$ $= \left( \frac{\text{Total Profit}}{\text{Total } CP} \right) \times 100 = \left( \frac{8}{190} \right) \times 100 = \frac{80}{19} = 4 \frac{4}{19} \%$.
Cost Price $(CP)$ of the $2$nd article $= \frac{99}{1 - 0.01} = \frac{99}{0.99} = Rs. 100$ (Loss of $1 \%$).
Total $CP$ of both articles $= 90 + 100 = Rs. 190$.
Total Selling Price $(SP)$ of both articles $= 99 + 99 = Rs. 198$.
Total Profit $= 198 - 190 = Rs. 8$.
Profit $\%$ $= \left( \frac{\text{Total Profit}}{\text{Total } CP} \right) \times 100 = \left( \frac{8}{190} \right) \times 100 = \frac{80}{19} = 4 \frac{4}{19} \%$.
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View Solution73
MediumMCQ
The market price of an article is $Rs. 100$. If the article is sold at a discount of $10 \%$,then $35 \%$ profit is realized. How much loss or profit will be made if it is sold for $Rs. 30$ less than the market price?
A
$5 \% \text{ loss}$
B
$8 \% \text{ gain}$
C
$5 \% \text{ gain}$
D
$8 \% \text{ loss}$
Solution
(C) Given,Market Price $(MP) = Rs. 100$.
Discount $= 10 \% \text{ of } 100 = Rs. 10$.
Selling Price $(SP_1) = 100 - 10 = Rs. 90$.
Profit $= 35 \%$,so $SP_1 = CP \times (1 + 0.35) = 1.35 \times CP$.
$1.35 \times CP = 90 \Rightarrow CP = \frac{90}{1.35} = \frac{9000}{135} = Rs. \frac{200}{3}$.
If the article is sold for $Rs. 30$ less than the market price,the new Selling Price $(SP_2) = 100 - 30 = Rs. 70$.
Profit $= SP_2 - CP = 70 - \frac{200}{3} = \frac{210 - 200}{3} = Rs. \frac{10}{3}$.
Profit $\% = \left( \frac{\text{Profit}}{CP} \right) \times 100 = \left( \frac{10/3}{200/3} \right) \times 100 = \frac{10}{200} \times 100 = 5 \% \text{ gain}$.
Discount $= 10 \% \text{ of } 100 = Rs. 10$.
Selling Price $(SP_1) = 100 - 10 = Rs. 90$.
Profit $= 35 \%$,so $SP_1 = CP \times (1 + 0.35) = 1.35 \times CP$.
$1.35 \times CP = 90 \Rightarrow CP = \frac{90}{1.35} = \frac{9000}{135} = Rs. \frac{200}{3}$.
If the article is sold for $Rs. 30$ less than the market price,the new Selling Price $(SP_2) = 100 - 30 = Rs. 70$.
Profit $= SP_2 - CP = 70 - \frac{200}{3} = \frac{210 - 200}{3} = Rs. \frac{10}{3}$.
Profit $\% = \left( \frac{\text{Profit}}{CP} \right) \times 100 = \left( \frac{10/3}{200/3} \right) \times 100 = \frac{10}{200} \times 100 = 5 \% \text{ gain}$.
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View Solution74
DifficultMCQ
$A$ shopkeeper sold an article offering a discount of $24 \%$ and earned a profit of $23.5 \%$. What would have been the percentage of profit earned if no discount had been offered?
A
$63$
B
$62.50$
C
$60$
D
Cannot be determined
Solution
(B) Let the Cost Price $(CP)$ be $Rs. 100$.
Since the profit earned is $23.5 \%$,the Selling Price $(SP)$ is $Rs. 123.50$.
Let the Marked Price $(MP)$ be $x$.
Given that a discount of $24 \%$ is offered on the $MP$,the $SP$ is $76 \%$ of $MP$.
So,$0.76 \times x = 123.50$.
$x = \frac{123.50}{0.76} = 162.50$.
If no discount is offered,the article would be sold at the Marked Price $(MP = Rs. 162.50)$.
Profit = $MP - CP = 162.50 - 100 = 62.50$.
Profit percentage = $\frac{62.50}{100} \times 100 = 62.50 \%$.
Since the profit earned is $23.5 \%$,the Selling Price $(SP)$ is $Rs. 123.50$.
Let the Marked Price $(MP)$ be $x$.
Given that a discount of $24 \%$ is offered on the $MP$,the $SP$ is $76 \%$ of $MP$.
So,$0.76 \times x = 123.50$.
$x = \frac{123.50}{0.76} = 162.50$.
If no discount is offered,the article would be sold at the Marked Price $(MP = Rs. 162.50)$.
Profit = $MP - CP = 162.50 - 100 = 62.50$.
Profit percentage = $\frac{62.50}{100} \times 100 = 62.50 \%$.
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View Solution75
EasyMCQ
On selling an article for $Rs. 500$,the loss incurred is $20 \%$. To make a profit of $20 \%$,the article must be sold at what price in $Rs.$?
A
$700$
B
$750$
C
$800$
D
$900$
Solution
(B) Let the Cost Price $(CP)$ of the article be $x$.
Given that the selling price $(SP_1)$ is $Rs. 500$ and the loss is $20 \%$.
Loss percentage formula: $Loss \% = \frac{CP - SP}{CP} \times 100$.
$20 = \frac{x - 500}{x} \times 100$.
$0.20x = x - 500$.
$0.80x = 500$.
$x = \frac{500}{0.8} = 625$.
So,the Cost Price $(CP)$ is $Rs. 625$.
Now,to make a profit of $20 \%$,the new Selling Price $(SP_2)$ should be:
$SP_2 = CP \times (1 + \text{Profit} \%)$.
$SP_2 = 625 \times (1 + 0.20) = 625 \times 1.2 = 750$.
Therefore,the article must be sold at $Rs. 750$ to gain a $20 \%$ profit.
Given that the selling price $(SP_1)$ is $Rs. 500$ and the loss is $20 \%$.
Loss percentage formula: $Loss \% = \frac{CP - SP}{CP} \times 100$.
$20 = \frac{x - 500}{x} \times 100$.
$0.20x = x - 500$.
$0.80x = 500$.
$x = \frac{500}{0.8} = 625$.
So,the Cost Price $(CP)$ is $Rs. 625$.
Now,to make a profit of $20 \%$,the new Selling Price $(SP_2)$ should be:
$SP_2 = CP \times (1 + \text{Profit} \%)$.
$SP_2 = 625 \times (1 + 0.20) = 625 \times 1.2 = 750$.
Therefore,the article must be sold at $Rs. 750$ to gain a $20 \%$ profit.
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View Solution76
MediumMCQ
The $CP$ of $19$ articles is equal to the selling price $(SP)$ of $15$ articles. What is the gain percentage?
A
$26\%$
B
$26 \frac{1}{3}\%$
C
$12\%$
D
$26 \frac{2}{3}\%$
Solution
(D) Given that the $CP$ of $19$ articles is equal to the $SP$ of $15$ articles.
Let the $CP$ of $1$ article be $x$.
Then,$CP$ of $19$ articles $= 19x$.
$SP$ of $15$ articles $= 19x$.
$SP$ of $1$ article $= \frac{19x}{15}$.
Gain $= SP - CP = \frac{19x}{15} - x = \frac{4x}{15}$.
Gain $\% = \left( \frac{\text{Gain}}{CP} \times 100 \right) = \left( \frac{4x/15}{x} \times 100 \right) = \frac{4}{15} \times 100 = \frac{400}{15} = \frac{80}{3} = 26 \frac{2}{3}\%$.
Let the $CP$ of $1$ article be $x$.
Then,$CP$ of $19$ articles $= 19x$.
$SP$ of $15$ articles $= 19x$.
$SP$ of $1$ article $= \frac{19x}{15}$.
Gain $= SP - CP = \frac{19x}{15} - x = \frac{4x}{15}$.
Gain $\% = \left( \frac{\text{Gain}}{CP} \times 100 \right) = \left( \frac{4x/15}{x} \times 100 \right) = \frac{4}{15} \times 100 = \frac{400}{15} = \frac{80}{3} = 26 \frac{2}{3}\%$.
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View Solution77
MediumMCQ
The cash difference between the selling price of an article at a profit of $4 \%$ and $6 \%$ is $Rs. 3$. The ratio of the $2$ selling prices is?
A
$50:53$
B
$51:52$
C
$51:53$
D
$52:53$
Solution
(D) Let the cost price of the article be $CP = x$.
Selling price at $4 \%$ profit is $(SP)_1 = x + 0.04x = 1.04x$.
Selling price at $6 \%$ profit is $(SP)_2 = x + 0.06x = 1.06x$.
The ratio of the two selling prices is $\frac{(SP)_1}{(SP)_2} = \frac{1.04x}{1.06x}$.
Multiplying both numerator and denominator by $100$,we get $\frac{104}{106}$.
Simplifying the fraction by dividing by $2$,we get $\frac{52}{53}$.
Thus,the ratio is $52:53$.
Selling price at $4 \%$ profit is $(SP)_1 = x + 0.04x = 1.04x$.
Selling price at $6 \%$ profit is $(SP)_2 = x + 0.06x = 1.06x$.
The ratio of the two selling prices is $\frac{(SP)_1}{(SP)_2} = \frac{1.04x}{1.06x}$.
Multiplying both numerator and denominator by $100$,we get $\frac{104}{106}$.
Simplifying the fraction by dividing by $2$,we get $\frac{52}{53}$.
Thus,the ratio is $52:53$.
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View Solution78
DifficultMCQ
$A$ shopkeeper has to sell $24 \text{ kg}$ of sugar. He sells a part of these at a gain of $20 \%$ and the rest at a loss of $5 \%$. If on the whole he earns a profit of $10 \%$,what is the quantity of sugar (in $\text{kg}$) sold at a loss?
A
$7.5$
B
$9.6$
C
$10$
D
Cannot be determined
Solution
(B) Let the quantity of sugar sold at a loss be $x \text{ kg}$.
Then,the quantity of sugar sold at a gain is $(24 - x) \text{ kg}$.
Let the cost price $(CP)$ per $\text{kg}$ be $Rs. 1$.
Total $CP = 24 \times 1 = Rs. 24$.
Total profit required is $10 \%$,so total selling price $(SP)$ = $110 \% \text{ of } 24 = 1.1 \times 24 = Rs. 26.4$.
Selling price of the part sold at $20 \% \text{ gain} = (24 - x) \times 1.20$.
Selling price of the part sold at $5 \% \text{ loss} = x \times 0.95$.
Equating the total $SP$: $1.20(24 - x) + 0.95x = 26.4$.
$28.8 - 1.20x + 0.95x = 26.4$.
$28.8 - 0.25x = 26.4$.
$0.25x = 28.8 - 26.4 = 2.4$.
$x = \frac{2.4}{0.25} = 9.6 \text{ kg}$.
Then,the quantity of sugar sold at a gain is $(24 - x) \text{ kg}$.
Let the cost price $(CP)$ per $\text{kg}$ be $Rs. 1$.
Total $CP = 24 \times 1 = Rs. 24$.
Total profit required is $10 \%$,so total selling price $(SP)$ = $110 \% \text{ of } 24 = 1.1 \times 24 = Rs. 26.4$.
Selling price of the part sold at $20 \% \text{ gain} = (24 - x) \times 1.20$.
Selling price of the part sold at $5 \% \text{ loss} = x \times 0.95$.
Equating the total $SP$: $1.20(24 - x) + 0.95x = 26.4$.
$28.8 - 1.20x + 0.95x = 26.4$.
$28.8 - 0.25x = 26.4$.
$0.25x = 28.8 - 26.4 = 2.4$.
$x = \frac{2.4}{0.25} = 9.6 \text{ kg}$.
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View Solution79
MediumMCQ
If a shopkeeper sells $25$ articles at $Rs. 45$ per article after giving $10 \%$ discount and earns $50 \%$ profit. If the discount is not given,what is the profit percentage gained?
A
$30$
B
$32$
C
$35$
D
$66.67$
Solution
(D) Let the Marked Price $(MP)$ of one article be $Rs. 100$.
After giving a $10 \%$ discount,the Selling Price $(SP)$ becomes $Rs. 90$.
Since the shopkeeper earns a $50 \%$ profit,we use the formula $SP = CP \times (1 + \text{Profit} \%)$.
$90 = CP \times 1.50 \Rightarrow CP = \frac{90}{1.50} = Rs. 60$.
If no discount is given,the Selling Price $(SP_{new})$ will be equal to the Marked Price $(MP)$,which is $Rs. 100$.
The new profit is $SP_{new} - CP = 100 - 60 = Rs. 40$.
The profit percentage is $\frac{\text{Profit}}{CP} \times 100 = \frac{40}{60} \times 100 = \frac{2}{3} \times 100 = 66.67 \%$.
After giving a $10 \%$ discount,the Selling Price $(SP)$ becomes $Rs. 90$.
Since the shopkeeper earns a $50 \%$ profit,we use the formula $SP = CP \times (1 + \text{Profit} \%)$.
$90 = CP \times 1.50 \Rightarrow CP = \frac{90}{1.50} = Rs. 60$.
If no discount is given,the Selling Price $(SP_{new})$ will be equal to the Marked Price $(MP)$,which is $Rs. 100$.
The new profit is $SP_{new} - CP = 100 - 60 = Rs. 40$.
The profit percentage is $\frac{\text{Profit}}{CP} \times 100 = \frac{40}{60} \times 100 = \frac{2}{3} \times 100 = 66.67 \%$.
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View Solution80
MediumMCQ
The price of a $TV$ is $Rs. 10,000$. If successive discounts of $15\%$,$10\%$,and $5\%$ are allowed,then at what price does a customer buy it in $Rs.$?
A
$7267.50$
B
$7000$
C
$7200$
D
Cannot be determined
Solution
(A) The initial price of the $TV$ is $Rs. 10,000$.
Successive discounts are $15\%$,$10\%$,and $5\%$.
The price after the first discount of $15\%$ is $10000 \times (1 - 0.15) = 10000 \times 0.85 = 8500$.
The price after the second discount of $10\%$ is $8500 \times (1 - 0.10) = 8500 \times 0.90 = 7650$.
The price after the third discount of $5\%$ is $7650 \times (1 - 0.05) = 7650 \times 0.95 = 7267.50$.
Therefore,the final price the customer pays is $Rs. 7267.50$.
Successive discounts are $15\%$,$10\%$,and $5\%$.
The price after the first discount of $15\%$ is $10000 \times (1 - 0.15) = 10000 \times 0.85 = 8500$.
The price after the second discount of $10\%$ is $8500 \times (1 - 0.10) = 8500 \times 0.90 = 7650$.
The price after the third discount of $5\%$ is $7650 \times (1 - 0.05) = 7650 \times 0.95 = 7267.50$.
Therefore,the final price the customer pays is $Rs. 7267.50$.
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View Solution81
DifficultMCQ
Sarita sells a phone at a profit of $20 \%$. If she had bought it at $20 \%$ less and sold it for $Rs. 180$ less, she would have gained $25 \%$. Find the cost price of the phone in $Rs.$
A
$800$
B
$850$
C
$900$
D
$1000$
Solution
(C) Let the original cost price $(CP_1)$ of the phone be $100x$.
Since she sells it at a profit of $20 \%$, the selling price $(SP_1)$ is $100x + 20x = 120x$.
If she had bought it at $20 \%$ less, the new cost price $(CP_2)$ would be $100x - 20x = 80x$.
She would have gained $25 \%$ on this new cost price, so the new selling price $(SP_2)$ is $80x + (25 \% \text{ of } 80x) = 80x + 20x = 100x$.
The difference between the two selling prices is $SP_1 - SP_2 = 120x - 100x = 20x$.
According to the problem, this difference is $Rs. 180$, so $20x = 180$, which means $x = 9$.
The original cost price was $100x = 100 \times 9 = Rs. 900$.
Since she sells it at a profit of $20 \%$, the selling price $(SP_1)$ is $100x + 20x = 120x$.
If she had bought it at $20 \%$ less, the new cost price $(CP_2)$ would be $100x - 20x = 80x$.
She would have gained $25 \%$ on this new cost price, so the new selling price $(SP_2)$ is $80x + (25 \% \text{ of } 80x) = 80x + 20x = 100x$.
The difference between the two selling prices is $SP_1 - SP_2 = 120x - 100x = 20x$.
According to the problem, this difference is $Rs. 180$, so $20x = 180$, which means $x = 9$.
The original cost price was $100x = 100 \times 9 = Rs. 900$.
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View Solution82
DifficultMCQ
Ravi purchases $90$ pens and sells $40$ pens at a gain of $10 \%$ and $50$ pens at a gain of $20 \%$. Had he sold all of them at a uniform profit of $15 \%$,he would have got $Rs. 40$ less. Find the cost price of each pen in $Rs$.
A
$80$
B
$75$
C
$90$
D
$100$
Solution
(A) Let the $CP$ of each pen be $Rs. 100$.
At a profit of $10 \%$,the $SP$ of $40$ pens $= (100 + 10) \times 40 = Rs. 4400$.
At a profit of $20 \%$,the $SP$ of $50$ pens $= (100 + 20) \times 50 = Rs. 6000$.
Total $SP$ of $90$ pens $= Rs. (4400 + 6000) = Rs. 10400$.
Total $CP$ of $90$ pens $= Rs. (90 \times 100) = Rs. 9000$.
If sold at a uniform profit of $15 \%$,the $SP$ of $90$ pens $= Rs. (90 \times 115) = Rs. 10350$.
Difference in $SP = Rs. (10400 - 10350) = Rs. 50$.
If the difference is $Rs. 50$,the assumed $CP$ of each pen is $Rs. 100$.
If the difference is $Rs. 40$,the actual $CP$ of each pen $= \frac{100 \times 40}{50} = Rs. 80$.
Hence,the cost price of each pen is $Rs. 80$.
At a profit of $10 \%$,the $SP$ of $40$ pens $= (100 + 10) \times 40 = Rs. 4400$.
At a profit of $20 \%$,the $SP$ of $50$ pens $= (100 + 20) \times 50 = Rs. 6000$.
Total $SP$ of $90$ pens $= Rs. (4400 + 6000) = Rs. 10400$.
Total $CP$ of $90$ pens $= Rs. (90 \times 100) = Rs. 9000$.
If sold at a uniform profit of $15 \%$,the $SP$ of $90$ pens $= Rs. (90 \times 115) = Rs. 10350$.
Difference in $SP = Rs. (10400 - 10350) = Rs. 50$.
If the difference is $Rs. 50$,the assumed $CP$ of each pen is $Rs. 100$.
If the difference is $Rs. 40$,the actual $CP$ of each pen $= \frac{100 \times 40}{50} = Rs. 80$.
Hence,the cost price of each pen is $Rs. 80$.
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View Solution83
DifficultMCQ
Savita buys $5$ shirts and $10$ pants for $Rs. 1600$. She sells shirts at a profit of $15\%$ and pants at a loss of $10\%$. If her overall profit was $Rs. 90$,what was the cost price of a shirt and a pant in $Rs.$?
A
$175, 50$
B
$200, 50$
C
$200, 60$
D
Cannot be determined
Solution
(C) Let $p$ be the cost price of a shirt and $q$ be the cost price of a pant in $Rs.$
Given that the total cost price of $5$ shirts and $10$ pants is $Rs. 1600$,we have:
$5p + 10q = 1600$ --- $(i)$
Profit on $5$ shirts at $15\%$ is $\frac{15}{100} \times 5p = 0.75p$.
Loss on $10$ pants at $10\%$ is $\frac{10}{100} \times 10q = q$.
Given the overall profit is $Rs. 90$:
$0.75p - q = 90$ --- $(ii)$
From $(ii)$,$q = 0.75p - 90$.
Substitute this into $(i)$:
$5p + 10(0.75p - 90) = 1600$
$5p + 7.5p - 900 = 1600$
$12.5p = 2500$
$p = \frac{2500}{12.5} = 200$.
Now,find $q$:
$q = 0.75(200) - 90 = 150 - 90 = 60$.
Thus,the cost price of a shirt is $Rs. 200$ and a pant is $Rs. 60$.
Given that the total cost price of $5$ shirts and $10$ pants is $Rs. 1600$,we have:
$5p + 10q = 1600$ --- $(i)$
Profit on $5$ shirts at $15\%$ is $\frac{15}{100} \times 5p = 0.75p$.
Loss on $10$ pants at $10\%$ is $\frac{10}{100} \times 10q = q$.
Given the overall profit is $Rs. 90$:
$0.75p - q = 90$ --- $(ii)$
From $(ii)$,$q = 0.75p - 90$.
Substitute this into $(i)$:
$5p + 10(0.75p - 90) = 1600$
$5p + 7.5p - 900 = 1600$
$12.5p = 2500$
$p = \frac{2500}{12.5} = 200$.
Now,find $q$:
$q = 0.75(200) - 90 = 150 - 90 = 60$.
Thus,the cost price of a shirt is $Rs. 200$ and a pant is $Rs. 60$.
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View Solution84
DifficultMCQ
At a cost of $60$ paise per article,Sarika produces $750$ articles. She sets the selling price such that if only $600$ articles are sold,she would have made a profit of $40 \%$ on the total outlay. However,$120$ articles got spoilt and she was able to sell $630$ articles at this price. Find her actual profit or loss percent as a percentage of the total outlay,assuming that the unsold articles are useless.
A
$47 \% \text{ profit}$
B
$51 \% \text{ profit}$
C
$36 \% \text{ loss}$
D
$28 \% \text{ loss}$
Solution
(A) Total cost price $(CP)$ of $750$ articles $= 750 \times 0.60 = Rs. 450$.
To make a $40 \%$ profit on the total outlay $(Rs. 450)$ by selling only $600$ articles,the required total selling price $(SP)$ is:
$SP = 450 + (0.40 \times 450) = 450 \times 1.4 = Rs. 630$.
Therefore,the selling price per article is:
$SP \text{ per article} = \frac{630}{600} = Rs. 1.05$.
Sarika sells $630$ articles at this price. Her actual total revenue is:
$Total \text{ } SP = 630 \times 1.05 = Rs. 661.5$.
Actual profit $= Total \text{ } SP - Total \text{ } CP = 661.5 - 450 = Rs. 211.5$.
Actual profit percentage $= \left( \frac{211.5}{450} \right) \times 100 = 47 \%$.
Thus,Sarika earns a $47 \%$ profit on her total investment.
To make a $40 \%$ profit on the total outlay $(Rs. 450)$ by selling only $600$ articles,the required total selling price $(SP)$ is:
$SP = 450 + (0.40 \times 450) = 450 \times 1.4 = Rs. 630$.
Therefore,the selling price per article is:
$SP \text{ per article} = \frac{630}{600} = Rs. 1.05$.
Sarika sells $630$ articles at this price. Her actual total revenue is:
$Total \text{ } SP = 630 \times 1.05 = Rs. 661.5$.
Actual profit $= Total \text{ } SP - Total \text{ } CP = 661.5 - 450 = Rs. 211.5$.
Actual profit percentage $= \left( \frac{211.5}{450} \right) \times 100 = 47 \%$.
Thus,Sarika earns a $47 \%$ profit on her total investment.
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MediumMCQ
Kritika bought $25$ $i-pads$ and $i-phones$ for $Rs. 205000$. She sold $80\%$ of the $i-pads$ and $12$ $i-phones$ for a profit of $Rs. 40000$. Each $i-pad$ was marked up by $20\%$ over cost and each $i-phone$ was sold at a profit of $Rs. 2000$. The remaining $i-pads$ and $3$ $i-phones$ could not be sold. What is Kritika's overall profit/loss?
A
$Rs. 500$ profit
B
$Rs. 1000$ loss
C
$Rs. 1500$ profit
D
no profit,no loss
Solution
(B) Let the number of $i-pads$ be $x$ and $i-phones$ be $y$. We have $x + y = 25$.
Kritika sold $80\%$ of $i-pads$ $(0.8x)$ and $12$ $i-phones$ for a profit of $Rs. 40000$.
The cost price of the items sold is $80\%$ of the total cost price because she sold $80\%$ of the $i-pads$ and the problem implies the $12$ $i-phones$ also represent $80\%$ of the $i-phones$ (since $12/15 = 0.8$).
Total cost price $(CP)$ = $Rs. 205000$.
Cost price of items sold = $80\% \text{ of } 205000 = 0.8 \times 205000 = Rs. 164000$.
Selling price $(SP)$ of items sold = $CP + \text{Profit} = 164000 + 40000 = Rs. 204000$.
The remaining $20\%$ of the items ($5$ items total) were not sold,meaning their value is lost.
Total $SP$ of all items = $SP \text{ of sold items} + SP \text{ of unsold items} = 204000 + 0 = Rs. 204000$.
Overall Profit/Loss = $\text{Total } SP - \text{Total } CP = 204000 - 205000 = -1000$.
Therefore,Kritika incurred an overall loss of $Rs. 1000$.
Kritika sold $80\%$ of $i-pads$ $(0.8x)$ and $12$ $i-phones$ for a profit of $Rs. 40000$.
The cost price of the items sold is $80\%$ of the total cost price because she sold $80\%$ of the $i-pads$ and the problem implies the $12$ $i-phones$ also represent $80\%$ of the $i-phones$ (since $12/15 = 0.8$).
Total cost price $(CP)$ = $Rs. 205000$.
Cost price of items sold = $80\% \text{ of } 205000 = 0.8 \times 205000 = Rs. 164000$.
Selling price $(SP)$ of items sold = $CP + \text{Profit} = 164000 + 40000 = Rs. 204000$.
The remaining $20\%$ of the items ($5$ items total) were not sold,meaning their value is lost.
Total $SP$ of all items = $SP \text{ of sold items} + SP \text{ of unsold items} = 204000 + 0 = Rs. 204000$.
Overall Profit/Loss = $\text{Total } SP - \text{Total } CP = 204000 - 205000 = -1000$.
Therefore,Kritika incurred an overall loss of $Rs. 1000$.
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View Solution86
DifficultMCQ
Sasha goes to a shop to buy a sofa set and a center table. She bargains for a $10 \%$ discount on the center table and a $25 \%$ discount on the sofa set. However,the manager,by mistake,interchanged the discount percentage figures while making the bill and Sasha paid accordingly. When compared to what she should have paid for her purchases,what percentage did Sasha pay extra,given that the center table costs $40 \%$ as much as the sofa set (in $\%$)?
A
$7.1$
B
$7.5$
C
$7.9$
D
$8.1$
Solution
(D) Let the cost of the sofa set be $Rs. 100$. Then,the cost of the center table is $Rs. 40$ (since it is $40 \%$ of the sofa set cost).
According to the original agreement,the cost of the center table should be:
$= \frac{90}{100} \times 40 = Rs. 36$ ($10 \%$ discount on the center table).
The cost of the sofa set should be:
$= \frac{75}{100} \times 100 = Rs. 75$ ($25 \%$ discount on the sofa set).
Total expected payment $= 36 + 75 = Rs. 111$.
According to the manager,the discount percentages were interchanged:
Cost of the center table $= \frac{75}{100} \times 40 = Rs. 30$.
Cost of the sofa set $= \frac{90}{100} \times 100 = Rs. 90$.
Total actual payment made $= 30 + 90 = Rs. 120$.
Extra money paid $= 120 - 111 = Rs. 9$.
Percentage extra paid $= \frac{9}{111} \times 100 \approx 8.1 \%$.
According to the original agreement,the cost of the center table should be:
$= \frac{90}{100} \times 40 = Rs. 36$ ($10 \%$ discount on the center table).
The cost of the sofa set should be:
$= \frac{75}{100} \times 100 = Rs. 75$ ($25 \%$ discount on the sofa set).
Total expected payment $= 36 + 75 = Rs. 111$.
According to the manager,the discount percentages were interchanged:
Cost of the center table $= \frac{75}{100} \times 40 = Rs. 30$.
Cost of the sofa set $= \frac{90}{100} \times 100 = Rs. 90$.
Total actual payment made $= 30 + 90 = Rs. 120$.
Extra money paid $= 120 - 111 = Rs. 9$.
Percentage extra paid $= \frac{9}{111} \times 100 \approx 8.1 \%$.
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View Solution87
DifficultMCQ
Paras Health Care made $3000$ strips of vitamin tablets at a cost of $Rs. 4800$. The company gave away $1000$ strips of tablets to doctors as free samples. $A$ discount of $25\%$ is given on the printed price. Find the ratio of profit in $Rs.$ if the price is raised from $Rs. 3.25$ to $Rs. 4.25$ per strip and if at the latter price,samples to doctors were done away with.
A
$36.7$
B
$49.3$
C
$63.5$
D
$71.7$
Solution
(C) Case $1$: If the printed rate is $Rs. 3.25$ per strip.
Total strips sold $= 3000 - 1000 = 2000$ strips.
Selling price per strip after $25\%$ discount $= 3.25 \times (1 - 0.25) = 3.25 \times 0.75 = Rs. 2.4375$.
Total sales revenue $= 2000 \times 2.4375 = Rs. 4875$.
Profit $= 4875 - 4800 = Rs. 75$.
Case $2$: If the printed rate is $Rs. 4.25$ per strip and no free samples are given.
Total strips sold $= 3000$ strips.
Selling price per strip after $25\%$ discount $= 4.25 \times 0.75 = Rs. 3.1875$.
Total sales revenue $= 3000 \times 3.1875 = Rs. 9562.5$.
Profit $= 9562.5 - 4800 = Rs. 4762.5$.
Ratio of profit $= \frac{4762.5}{75} = 63.5$.
Total strips sold $= 3000 - 1000 = 2000$ strips.
Selling price per strip after $25\%$ discount $= 3.25 \times (1 - 0.25) = 3.25 \times 0.75 = Rs. 2.4375$.
Total sales revenue $= 2000 \times 2.4375 = Rs. 4875$.
Profit $= 4875 - 4800 = Rs. 75$.
Case $2$: If the printed rate is $Rs. 4.25$ per strip and no free samples are given.
Total strips sold $= 3000$ strips.
Selling price per strip after $25\%$ discount $= 4.25 \times 0.75 = Rs. 3.1875$.
Total sales revenue $= 3000 \times 3.1875 = Rs. 9562.5$.
Profit $= 9562.5 - 4800 = Rs. 4762.5$.
Ratio of profit $= \frac{4762.5}{75} = 63.5$.
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View Solution88
DifficultMCQ
$APD$ printed $3000$ copies of 'Career Power' at a cost of $Rs. 240000$. It gave $500$ copies free to different philanthropic institutions. It allowed a discount of $25\%$ on the published price and gave one copy free for every $25$ copies bought at a time. It was able to sell all the copies in this manner. If the published price is $Rs. 325$,then what is its overall gain or loss percentage in the whole transaction?
A
$89\%$ gain
B
$120\%$ loss
C
$140\%$ loss
D
$143.75\%$ gain
Solution
(D) Cost Price $(CP)$ = $Rs. 240000$ for $3000$ copies.
Published Price = $Rs. 325$.
Selling Price $(SP)$ per copy after $25\%$ discount = $325 \times (1 - 0.25) = 325 \times 0.75 = Rs. 243.75$.
Total copies available for sale = $3000 - 500 = 2500$ copies.
For every $25$ copies bought,$1$ is free. This means in a set of $26$ copies,only $25$ are paid for.
Number of sets of $25$ copies in $2500$ copies = $2500 / 25 = 100$ sets.
Total free copies given during sale = $100$ copies.
Total copies sold (paid) = $2500 - 100 = 2400$ copies.
Total Revenue $(SP)$ = $2400 \times 243.75 = Rs. 585000$.
Profit = $SP - CP = 585000 - 240000 = Rs. 345000$.
Profit Percentage = $(Profit / CP) \times 100 = (345000 / 240000) \times 100 = 143.75\%$.
Published Price = $Rs. 325$.
Selling Price $(SP)$ per copy after $25\%$ discount = $325 \times (1 - 0.25) = 325 \times 0.75 = Rs. 243.75$.
Total copies available for sale = $3000 - 500 = 2500$ copies.
For every $25$ copies bought,$1$ is free. This means in a set of $26$ copies,only $25$ are paid for.
Number of sets of $25$ copies in $2500$ copies = $2500 / 25 = 100$ sets.
Total free copies given during sale = $100$ copies.
Total copies sold (paid) = $2500 - 100 = 2400$ copies.
Total Revenue $(SP)$ = $2400 \times 243.75 = Rs. 585000$.
Profit = $SP - CP = 585000 - 240000 = Rs. 345000$.
Profit Percentage = $(Profit / CP) \times 100 = (345000 / 240000) \times 100 = 143.75\%$.
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View Solution89
DifficultMCQ
Surbhi bought a combined total of $25$ i-pads and i-phones. She marked up the i-pad by $20 \%$ on the cost price,while each i-phone was marked up by $Rs. 2000$. She was able to sell $75 \%$ of the i-pads and $2$ i-phones and make a profit of $Rs. 49000$. The remaining i-pads and $3$ i-phones could not be sold by her. Find her overall profit or loss if she gets no return on unsold items and it is known that an i-phone costs $50 \%$ of an i-pad.
A
Gain of $Rs. 48500$
B
Loss of $Rs. 48500$
C
Gain of $Rs. 51400$
D
No profit,no loss
Solution
(B) Let the number of i-pads be $x$ and i-phones be $y$. Given $x + y = 25$. Let $CP$ of an i-pad be $C_p$. Then $CP$ of an i-phone is $0.5 C_p$.
Selling Price $(SP)$ of an i-pad $= 1.2 C_p$. Profit per i-pad $= 0.2 C_p$.
Selling Price $(SP)$ of an i-phone $= 0.5 C_p + 2000$. Profit per i-phone $= 2000$.
Total profit from $0.75x$ i-pads and $2$ i-phones is $49000$.
$(0.75x)(0.2 C_p) + 2(2000) = 49000 \implies 0.15 x C_p = 45000 \implies x C_p = 300000$.
Since $3$ i-phones were unsold,$y = 2 + 3 = 5$. Thus $x = 25 - 5 = 20$.
$20 C_p = 300000 \implies C_p = 15000$. $CP$ of i-phone $= 7500$.
Total Cost Price $= 20(15000) + 5(7500) = 300000 + 37500 = 337500$.
Total Revenue $= (0.75 \times 20)(1.2 \times 15000) + 2(7500 + 2000) = 15(18000) + 2(9500) = 270000 + 19000 = 289000$.
Overall Loss $= 337500 - 289000 = 48500$.
Selling Price $(SP)$ of an i-pad $= 1.2 C_p$. Profit per i-pad $= 0.2 C_p$.
Selling Price $(SP)$ of an i-phone $= 0.5 C_p + 2000$. Profit per i-phone $= 2000$.
Total profit from $0.75x$ i-pads and $2$ i-phones is $49000$.
$(0.75x)(0.2 C_p) + 2(2000) = 49000 \implies 0.15 x C_p = 45000 \implies x C_p = 300000$.
Since $3$ i-phones were unsold,$y = 2 + 3 = 5$. Thus $x = 25 - 5 = 20$.
$20 C_p = 300000 \implies C_p = 15000$. $CP$ of i-phone $= 7500$.
Total Cost Price $= 20(15000) + 5(7500) = 300000 + 37500 = 337500$.
Total Revenue $= (0.75 \times 20)(1.2 \times 15000) + 2(7500 + 2000) = 15(18000) + 2(9500) = 270000 + 19000 = 289000$.
Overall Loss $= 337500 - 289000 = 48500$.
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View Solution90
DifficultMCQ
$A$ merchant buys $4000 \, kg$ of wheat,one-fifth of which he sells at a gain of $5 \%$,one-fourth at a gain of $10 \%$,one-half at a gain of $12 \%$,and the remainder at a gain of $16 \%$. If he had sold the whole at a gain of $11 \%$,he would have made $Rs. 72.80$ more. What was the cost price of the crop per $kg$? (in $Rs.$)
A
$2$
B
$2.60$
C
$2.50$
D
$2.80$
Solution
(B) Let the total cost price of $4000 \, kg$ of wheat be $C$.
First,we calculate the weighted average profit percentage.
The fractions of the total quantity are $\frac{1}{5}, \frac{1}{4}, \frac{1}{2}$,and the remainder is $1 - (\frac{1}{5} + \frac{1}{4} + \frac{1}{2}) = 1 - \frac{4+5+10}{20} = 1 - \frac{19}{20} = \frac{1}{20}$.
Total profit percentage $P = (\frac{1}{5} \times 5) + (\frac{1}{4} \times 10) + (\frac{1}{2} \times 12) + (\frac{1}{20} \times 16) \%$.
$P = 1 + 2.5 + 6 + 0.8 = 10.3 \%$.
If he sold the whole at $11 \%$,the profit would be $11 \%$.
The difference in profit is $11 \% - 10.3 \% = 0.7 \%$.
Given that $0.7 \% \text{ of } C = Rs. 72.80$.
$C = \frac{72.80}{0.007} = Rs. 10400$.
The cost price per $kg = \frac{10400}{4000} = Rs. 2.60$.
First,we calculate the weighted average profit percentage.
The fractions of the total quantity are $\frac{1}{5}, \frac{1}{4}, \frac{1}{2}$,and the remainder is $1 - (\frac{1}{5} + \frac{1}{4} + \frac{1}{2}) = 1 - \frac{4+5+10}{20} = 1 - \frac{19}{20} = \frac{1}{20}$.
Total profit percentage $P = (\frac{1}{5} \times 5) + (\frac{1}{4} \times 10) + (\frac{1}{2} \times 12) + (\frac{1}{20} \times 16) \%$.
$P = 1 + 2.5 + 6 + 0.8 = 10.3 \%$.
If he sold the whole at $11 \%$,the profit would be $11 \%$.
The difference in profit is $11 \% - 10.3 \% = 0.7 \%$.
Given that $0.7 \% \text{ of } C = Rs. 72.80$.
$C = \frac{72.80}{0.007} = Rs. 10400$.
The cost price per $kg = \frac{10400}{4000} = Rs. 2.60$.
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MediumMCQ
Ajit calculates his profit percentage on the selling price,whereas Rohit calculates his on the cost price. They find that the difference between their profits is $Rs. 100$. If the selling price for both of them is the same and both of them get a $25\%$ profit,find their selling price (in $Rs.$).
A
$1200$
B
$1500$
C
$1800$
D
$2000$
Solution
(D) Let the selling price $(SP)$ for both be $Rs. P$.
For Ajit,profit is calculated on $SP$:
Profit $= 25\% \text{ of } SP = 0.25P = \frac{P}{4}$.
For Rohit,profit is calculated on cost price $(CP)$:
Profit $= 25\% \text{ of } CP = 0.25 \times CP$.
Since $SP = CP + \text{Profit}$,we have $P = CP + 0.25CP = 1.25CP$.
Thus,$CP = \frac{P}{1.25} = 0.8P = \frac{4P}{5}$.
Rohit's profit $= SP - CP = P - 0.8P = 0.2P = \frac{P}{5}$.
The difference between their profits is given as $Rs. 100$:
$\frac{P}{4} - \frac{P}{5} = 100$.
$\frac{5P - 4P}{20} = 100$.
$\frac{P}{20} = 100$.
$P = 2000$.
Therefore,the selling price is $Rs. 2000$.
For Ajit,profit is calculated on $SP$:
Profit $= 25\% \text{ of } SP = 0.25P = \frac{P}{4}$.
For Rohit,profit is calculated on cost price $(CP)$:
Profit $= 25\% \text{ of } CP = 0.25 \times CP$.
Since $SP = CP + \text{Profit}$,we have $P = CP + 0.25CP = 1.25CP$.
Thus,$CP = \frac{P}{1.25} = 0.8P = \frac{4P}{5}$.
Rohit's profit $= SP - CP = P - 0.8P = 0.2P = \frac{P}{5}$.
The difference between their profits is given as $Rs. 100$:
$\frac{P}{4} - \frac{P}{5} = 100$.
$\frac{5P - 4P}{20} = 100$.
$\frac{P}{20} = 100$.
$P = 2000$.
Therefore,the selling price is $Rs. 2000$.
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DifficultMCQ
$A$ pen was sold for a certain sum and there was a loss of $20 \%$. Had it been sold for $Rs. 12$ more,there would have been a gain of $30 \%$. What would be the profit percentage if the pen was sold for $Rs. 4.80$ more than the original selling price?
A
$15 \%$
B
$23 \%$
C
$29 \%$
D
No profit,no loss
Solution
(D) Let the cost price $(CP)$ of the pen be $Rs. x$.
Initially,the pen is sold at a loss of $20 \%$. Therefore,the selling price $(SP_1)$ is $x - 0.20x = 0.80x$.
If the pen were sold for $Rs. 12$ more,the new selling price $(SP_2)$ would be $0.80x + 12$. At this price,there is a gain of $30 \%$,so $SP_2 = x + 0.30x = 1.30x$.
Equating the two expressions for $SP_2$: $0.80x + 12 = 1.30x$.
$12 = 1.30x - 0.80x = 0.50x$.
$x = \frac{12}{0.50} = 24$.
So,the $CP$ is $Rs. 24$.
The original selling price $(SP_1)$ is $0.80 \times 24 = Rs. 19.20$.
If the pen is sold for $Rs. 4.80$ more than the original selling price,the new selling price $(SP_3)$ is $19.20 + 4.80 = Rs. 24$.
Since $SP_3 = CP = Rs. 24$,the profit percentage is $0 \%$,meaning there is no profit and no loss.
Initially,the pen is sold at a loss of $20 \%$. Therefore,the selling price $(SP_1)$ is $x - 0.20x = 0.80x$.
If the pen were sold for $Rs. 12$ more,the new selling price $(SP_2)$ would be $0.80x + 12$. At this price,there is a gain of $30 \%$,so $SP_2 = x + 0.30x = 1.30x$.
Equating the two expressions for $SP_2$: $0.80x + 12 = 1.30x$.
$12 = 1.30x - 0.80x = 0.50x$.
$x = \frac{12}{0.50} = 24$.
So,the $CP$ is $Rs. 24$.
The original selling price $(SP_1)$ is $0.80 \times 24 = Rs. 19.20$.
If the pen is sold for $Rs. 4.80$ more than the original selling price,the new selling price $(SP_3)$ is $19.20 + 4.80 = Rs. 24$.
Since $SP_3 = CP = Rs. 24$,the profit percentage is $0 \%$,meaning there is no profit and no loss.
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MediumMCQ
$A$ white goods dealer pays $10 \%$ custom duty on an iPhone that costs $Rs. 25000$ in $UK$. For how much should he mark it,if he desires to make a profit of $20 \%$ after giving a discount of $25 \%$ to the buyer? (in $Rs$)
A
$32000$
B
$38000$
C
$44000$
D
Cannot be determined
Solution
(C) The cost price $(CP)$ of the iPhone to the dealer,including the $10 \%$ custom duty,is:
$CP = 25000 + (10 \% \text{ of } 25000) = 25000 + 2500 = Rs. 27500$.
To earn a profit of $20 \%$,the required selling price $(SP)$ is:
$SP = CP \times (1 + \text{Profit } \%) = 27500 \times 1.20 = Rs. 33000$.
Let the marked price be $MP$. The dealer offers a discount of $25 \%$,so the selling price is $75 \%$ of the marked price:
$SP = MP \times (1 - 0.25) = 0.75 \times MP$.
Equating the selling price:
$0.75 \times MP = 33000$.
$MP = \frac{33000}{0.75} = Rs. 44000$.
$CP = 25000 + (10 \% \text{ of } 25000) = 25000 + 2500 = Rs. 27500$.
To earn a profit of $20 \%$,the required selling price $(SP)$ is:
$SP = CP \times (1 + \text{Profit } \%) = 27500 \times 1.20 = Rs. 33000$.
Let the marked price be $MP$. The dealer offers a discount of $25 \%$,so the selling price is $75 \%$ of the marked price:
$SP = MP \times (1 - 0.25) = 0.75 \times MP$.
Equating the selling price:
$0.75 \times MP = 33000$.
$MP = \frac{33000}{0.75} = Rs. 44000$.
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DifficultMCQ
$A$ cab driver makes a profit of $20 \%$ on every trip when he carries $3$ passengers and the price of petrol is $Rs. 30$ a litre. Find the percentage profit for the same journey if he goes with four passengers per trip and the price of petrol reduces to $Rs. 24$ a litre? (in $\%$)
(Assume that revenue per passenger is the same in both the cases.)
(Assume that revenue per passenger is the same in both the cases.)
A
$100$
B
$76$
C
$54$
D
$43$
Solution
(A) Let the cost price $(CP)$ of the trip be the price of petrol,which is $Rs. 30$.
The selling price $(SP)$ for carrying $3$ passengers is $3x$,where $x$ is the revenue per passenger.
Given that the profit is $20 \%$,we have:
$\text{Profit } \% = \frac{SP - CP}{CP} \times 100$
$20 = \frac{3x - 30}{30} \times 100$
$0.2 = \frac{3x - 30}{30}$
$6 = 3x - 30$
$3x = 36 \Rightarrow x = 12$.
Now,for the second case:
New $CP = Rs. 24$.
New $SP = 4 \times x = 4 \times 12 = Rs. 48$.
New Profit $\% = \frac{SP - CP}{CP} \times 100$
$= \frac{48 - 24}{24} \times 100$
$= \frac{24}{24} \times 100 = 100 \%$.
The selling price $(SP)$ for carrying $3$ passengers is $3x$,where $x$ is the revenue per passenger.
Given that the profit is $20 \%$,we have:
$\text{Profit } \% = \frac{SP - CP}{CP} \times 100$
$20 = \frac{3x - 30}{30} \times 100$
$0.2 = \frac{3x - 30}{30}$
$6 = 3x - 30$
$3x = 36 \Rightarrow x = 12$.
Now,for the second case:
New $CP = Rs. 24$.
New $SP = 4 \times x = 4 \times 12 = Rs. 48$.
New Profit $\% = \frac{SP - CP}{CP} \times 100$
$= \frac{48 - 24}{24} \times 100$
$= \frac{24}{24} \times 100 = 100 \%$.
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View Solution95
MediumMCQ
Anil bought an item with $12 \frac{1}{2} \%$ discount on the labelled price. He sold the item with $17 \frac{1}{2} \%$ profit on the labelled price. What was his percent profit on the price he bought?
A
$35 \%$
B
$34 \frac{1}{7} \%$
C
$34 \frac{2}{7} \%$
D
$35 \frac{2}{7} \%$
Solution
(C) Let the labelled price of the article be $Rs. \, y$.
The cost price $(CP)$ of the article is the price after a $12 \frac{1}{2} \%$ discount:
$CP = y \times \left(1 - \frac{12.5}{100}\right) = y \times \frac{87.5}{100} = y \times \frac{7}{8} = Rs. \, \frac{7}{8} y$.
The selling price $(SP)$ of the article is the price after a $17 \frac{1}{2} \%$ profit on the labelled price:
$SP = y \times \left(1 + \frac{17.5}{100}\right) = y \times \frac{117.5}{100} = y \times \frac{47}{40} = Rs. \, \frac{47}{40} y$.
Profit = $SP - CP = \frac{47}{40} y - \frac{7}{8} y = \frac{47 - 35}{40} y = \frac{12}{40} y = Rs. \, \frac{3}{10} y$.
Percentage profit on the cost price = $\left(\frac{\text{Profit}}{CP}\right) \times 100 = \left(\frac{\frac{12}{40} y}{\frac{7}{8} y}\right) \times 100 = \left(\frac{12}{40} \times \frac{8}{7}\right) \times 100 = \frac{12}{35} \times 100 = \frac{240}{7} = 34 \frac{2}{7} \%$.
The cost price $(CP)$ of the article is the price after a $12 \frac{1}{2} \%$ discount:
$CP = y \times \left(1 - \frac{12.5}{100}\right) = y \times \frac{87.5}{100} = y \times \frac{7}{8} = Rs. \, \frac{7}{8} y$.
The selling price $(SP)$ of the article is the price after a $17 \frac{1}{2} \%$ profit on the labelled price:
$SP = y \times \left(1 + \frac{17.5}{100}\right) = y \times \frac{117.5}{100} = y \times \frac{47}{40} = Rs. \, \frac{47}{40} y$.
Profit = $SP - CP = \frac{47}{40} y - \frac{7}{8} y = \frac{47 - 35}{40} y = \frac{12}{40} y = Rs. \, \frac{3}{10} y$.
Percentage profit on the cost price = $\left(\frac{\text{Profit}}{CP}\right) \times 100 = \left(\frac{\frac{12}{40} y}{\frac{7}{8} y}\right) \times 100 = \left(\frac{12}{40} \times \frac{8}{7}\right) \times 100 = \frac{12}{35} \times 100 = \frac{240}{7} = 34 \frac{2}{7} \%$.
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View Solution96
DifficultMCQ
Divyam bought an article with $15 \%$ discount on the labelled price. He sold the article with $10 \%$ profit on the labelled price. What was his percent profit on the price he bought?
A
$28 \frac{7}{17} \%$
B
$29 \frac{7}{17} \%$
C
$29 \frac{5}{17} \%$
D
Data inadequate
Solution
(B) Let the labelled price of the article be $Rs. \, a$.
The cost price $(CP)$ of the article is $a \times (1 - 0.15) = 0.85a = \frac{17}{20}a$.
The selling price $(SP)$ of the article is $a \times (1 + 0.10) = 1.10a = \frac{11}{10}a$.
The profit earned is $SP - CP = \frac{11}{10}a - \frac{17}{20}a = \frac{22a - 17a}{20} = \frac{5a}{20}$.
The profit percentage on the cost price is $\left( \frac{\text{Profit}}{CP} \right) \times 100$.
Profit percentage $= \left( \frac{5a/20}{17a/20} \right) \times 100 = \frac{5}{17} \times 100 = \frac{500}{17} \%$.
Dividing $500$ by $17$,we get $29$ as the quotient and $7$ as the remainder.
Thus,the profit percentage is $29 \frac{7}{17} \%$.
The cost price $(CP)$ of the article is $a \times (1 - 0.15) = 0.85a = \frac{17}{20}a$.
The selling price $(SP)$ of the article is $a \times (1 + 0.10) = 1.10a = \frac{11}{10}a$.
The profit earned is $SP - CP = \frac{11}{10}a - \frac{17}{20}a = \frac{22a - 17a}{20} = \frac{5a}{20}$.
The profit percentage on the cost price is $\left( \frac{\text{Profit}}{CP} \right) \times 100$.
Profit percentage $= \left( \frac{5a/20}{17a/20} \right) \times 100 = \frac{5}{17} \times 100 = \frac{500}{17} \%$.
Dividing $500$ by $17$,we get $29$ as the quotient and $7$ as the remainder.
Thus,the profit percentage is $29 \frac{7}{17} \%$.
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View Solution97
MediumMCQ
$A$ shopkeeper sold chairs at $Rs. 2139$ each after giving a $7 \%$ discount on the labelled price. Had he not given the discount, he would have earned a profit of $15 \%$ on the cost price. What was the cost price of each chair? (in $Rs.$)
A
$2500$
B
$2100$
C
$2000$
D
$1900$
Solution
(C) Step $1$: Calculate the labelled price (marked price) of the chair.
Given selling price $(SP)$ = $Rs. 2139$ and discount = $7 \%$.
Labelled Price $(LP)$ = $\frac{SP \times 100}{100 - \text{Discount } \%} = \frac{2139 \times 100}{93} = Rs. 2300$.
Step $2$: Calculate the cost price $(CP)$.
Let the cost price be $x$.
If no discount is given, the selling price would be equal to the labelled price, i.e., $Rs. 2300$.
Profit percentage = $15 \%$.
We know that $SP = CP \times (1 + \frac{\text{Profit } \%}{100})$.
$2300 = x \times (1 + \frac{15}{100}) = x \times 1.15$.
$x = \frac{2300}{1.15} = 2000$.
Therefore, the cost price of each chair is $Rs. 2000$.
Given selling price $(SP)$ = $Rs. 2139$ and discount = $7 \%$.
Labelled Price $(LP)$ = $\frac{SP \times 100}{100 - \text{Discount } \%} = \frac{2139 \times 100}{93} = Rs. 2300$.
Step $2$: Calculate the cost price $(CP)$.
Let the cost price be $x$.
If no discount is given, the selling price would be equal to the labelled price, i.e., $Rs. 2300$.
Profit percentage = $15 \%$.
We know that $SP = CP \times (1 + \frac{\text{Profit } \%}{100})$.
$2300 = x \times (1 + \frac{15}{100}) = x \times 1.15$.
$x = \frac{2300}{1.15} = 2000$.
Therefore, the cost price of each chair is $Rs. 2000$.
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View Solution98
MediumMCQ
$A$ shopkeeper sold decks at $Rs. 166$ each after giving $17\%$ discount on the labelled price. Had he not given the discount,he would have earned a profit of $25\%$ on the cost price. What was the cost price of each deck? (in $Rs.$)
A
$165$
B
$155$
C
$160$
D
$164$
Solution
(C) Let the labelled price be $L$ and the cost price be $CP$.
Given that the selling price $SP = Rs. 166$ after a $17\%$ discount.
$SP = L \times (1 - 0.17) = 0.83L = 166$.
$L = 166 / 0.83 = Rs. 200$.
If no discount was given,the selling price would be equal to the labelled price,i.e.,$Rs. 200$.
In this case,the profit is $25\%$,so $SP = CP \times (1 + 0.25) = 1.25 \times CP$.
$200 = 1.25 \times CP$.
$CP = 200 / 1.25 = Rs. 160$.
Therefore,the cost price of each deck is $Rs. 160$.
Given that the selling price $SP = Rs. 166$ after a $17\%$ discount.
$SP = L \times (1 - 0.17) = 0.83L = 166$.
$L = 166 / 0.83 = Rs. 200$.
If no discount was given,the selling price would be equal to the labelled price,i.e.,$Rs. 200$.
In this case,the profit is $25\%$,so $SP = CP \times (1 + 0.25) = 1.25 \times CP$.
$200 = 1.25 \times CP$.
$CP = 200 / 1.25 = Rs. 160$.
Therefore,the cost price of each deck is $Rs. 160$.
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View Solution99
DifficultMCQ
$A$ garment company declared $15\%$ discount for wholesale buyers. Mr. Ashish bought garments from the company for $Rs. 25000$ after getting the discount. He fixed the selling price of the garments in such a way that he earned a profit of $8\%$ on the original company price. What is the approximate total selling price? (in $Rs.$)
A
$28000$
B
$29000$
C
$31700$
D
$28500$
Solution
(C) Let the original company price be $X$.
Given that Mr. Ashish received a $15\%$ discount,the price he paid is $85\%$ of $X$.
$0.85X = 25000$
$X = \frac{25000}{0.85} = Rs. 29411.76$
Mr. Ashish wants to earn a profit of $8\%$ on the original company price $(X)$.
Profit $= 8\% \text{ of } 29411.76 = 0.08 \times 29411.76 = Rs. 2352.94$
Total Selling Price $= \text{Original Price} + \text{Profit}$
Total Selling Price $= 29411.76 + 2352.94 = Rs. 31764.70$
The approximate total selling price is $Rs. 31700$.
Given that Mr. Ashish received a $15\%$ discount,the price he paid is $85\%$ of $X$.
$0.85X = 25000$
$X = \frac{25000}{0.85} = Rs. 29411.76$
Mr. Ashish wants to earn a profit of $8\%$ on the original company price $(X)$.
Profit $= 8\% \text{ of } 29411.76 = 0.08 \times 29411.76 = Rs. 2352.94$
Total Selling Price $= \text{Original Price} + \text{Profit}$
Total Selling Price $= 29411.76 + 2352.94 = Rs. 31764.70$
The approximate total selling price is $Rs. 31700$.
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View Solution100
MediumMCQ
$A$ garment company declared $14 \%$ discount for wholesale buyers. Mr. Swami bought garments from the company for $Rs. 860$ after getting the discount. He fixed the selling price of the garments in such a way that he earned a profit of $6 \%$ on the original company price. What is the approximate total selling price (in $Rs.$)?
A
$1060$
B
$1160$
C
$960$
D
Cannot be determined
Solution
(A) Step $1$: Calculate the original price of the garments before the discount.
Original Price $= \frac{\text{Discounted Price} \times 100}{100 - \text{Discount } \%}$
Original Price $= \frac{860 \times 100}{100 - 14} = \frac{86000}{86} = Rs. 1000$.
Step $2$: Calculate the selling price to earn a $6 \%$ profit on the original price.
Profit $= 6 \% \text{ of } 1000 = \frac{6}{100} \times 1000 = Rs. 60$.
Selling Price $= \text{Original Price} + \text{Profit} = 1000 + 60 = Rs. 1060$.
Original Price $= \frac{\text{Discounted Price} \times 100}{100 - \text{Discount } \%}$
Original Price $= \frac{860 \times 100}{100 - 14} = \frac{86000}{86} = Rs. 1000$.
Step $2$: Calculate the selling price to earn a $6 \%$ profit on the original price.
Profit $= 6 \% \text{ of } 1000 = \frac{6}{100} \times 1000 = Rs. 60$.
Selling Price $= \text{Original Price} + \text{Profit} = 1000 + 60 = Rs. 1060$.
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