A English
Profit and Loss Questions in English
Competitive Exam Quantitative Aptitude · Profit and Loss · Profit and Loss
452+
Questions
English
Language
100%
With Solutions
Showing 50 of 452 questions in English
101
DifficultMCQ
Abhishek makes a profit of $Rs. 110$ if he sells a certain number of pens at the price of $Rs. 2.5$ per pen and incurs a loss of $Rs. 55$ if he sells the same number of pens for $Rs. 1.75$ per pen. How many pens does Abhishek have?
A
$220$
B
$240$
C
$200$
D
Cannot be determined
Solution
$ (A) $ Let the number of pens be $x$.
The cost price $(CP)$ of the pens remains the same in both cases.
We know that $CP = SP - \text{Profit}$ and $CP = SP + \text{Loss}$.
Equating the two expressions for $CP$:
$SP_1 - \text{Profit} = SP_2 + \text{Loss}$
Given:
$SP_1 = 2.5x$
$\text{Profit} = 110$
$SP_2 = 1.75x$
$\text{Loss} = 55$
Substituting these values into the equation:
$2.5x - 110 = 1.75x + 55$
Rearranging the terms:
$2.5x - 1.75x = 55 + 110$
$0.75x = 165$
$x = 165 / 0.75$
$x = 220$
Therefore, Abhishek has $220$ pens.
The cost price $(CP)$ of the pens remains the same in both cases.
We know that $CP = SP - \text{Profit}$ and $CP = SP + \text{Loss}$.
Equating the two expressions for $CP$:
$SP_1 - \text{Profit} = SP_2 + \text{Loss}$
Given:
$SP_1 = 2.5x$
$\text{Profit} = 110$
$SP_2 = 1.75x$
$\text{Loss} = 55$
Substituting these values into the equation:
$2.5x - 110 = 1.75x + 55$
Rearranging the terms:
$2.5x - 1.75x = 55 + 110$
$0.75x = 165$
$x = 165 / 0.75$
$x = 220$
Therefore, Abhishek has $220$ pens.
0 likes
View Solution102
MediumMCQ
Ram purchased a computer set for $Rs. 12500$ and spent $Rs. 300$ on transportation and $Rs. 800$ on installation. At what price should he sell it to earn an overall profit of $15\%$? (in $Rs.$)
A
$14560$
B
$14375$
C
$15460$
D
$15640$
Solution
(D) The total Cost Price $(CP)$ of the computer set includes the purchase price,transportation,and installation charges.
Total $CP = 12500 + 300 + 800 = Rs. 13600$.
To earn a profit of $15\%$,the Selling Price $(SP)$ is calculated as:
$SP = CP \times (1 + \frac{\text{Profit}\%}{100})$
$SP = 13600 \times (1 + \frac{15}{100})$
$SP = 13600 \times 1.15 = Rs. 15640$.
Total $CP = 12500 + 300 + 800 = Rs. 13600$.
To earn a profit of $15\%$,the Selling Price $(SP)$ is calculated as:
$SP = CP \times (1 + \frac{\text{Profit}\%}{100})$
$SP = 13600 \times (1 + \frac{15}{100})$
$SP = 13600 \times 1.15 = Rs. 15640$.
0 likes
View Solution103
MediumMCQ
Mahesh purchased $25\, kg$ of rice at $Rs. 32$ per $kg$ and $15\, kg$ of rice at $Rs. 36$ per $kg.$ He mixed the two varieties of rice and sold it at $Rs. 40.20$ per $kg.$ What is the percent profit earned (in $\%$)?
A
$25$
B
$40$
C
$30$
D
$20$
Solution
(D) Total $CP$ of the mixture $= (25 \times 32) + (15 \times 36) = 800 + 540 = Rs. 1340$.
Total quantity of rice $= 25 + 15 = 40\, kg$.
$CP$ of $1\, kg$ of the mixture $= \frac{1340}{40} = Rs. 33.50$.
$SP$ of $1\, kg$ of the mixture $= Rs. 40.20$.
Profit $= SP - CP = 40.20 - 33.50 = Rs. 6.70$.
Profit $\% = \left( \frac{\text{Profit}}{CP} \right) \times 100 = \left( \frac{6.70}{33.50} \right) \times 100 = 0.2 \times 100 = 20\%$.
Total quantity of rice $= 25 + 15 = 40\, kg$.
$CP$ of $1\, kg$ of the mixture $= \frac{1340}{40} = Rs. 33.50$.
$SP$ of $1\, kg$ of the mixture $= Rs. 40.20$.
Profit $= SP - CP = 40.20 - 33.50 = Rs. 6.70$.
Profit $\% = \left( \frac{\text{Profit}}{CP} \right) \times 100 = \left( \frac{6.70}{33.50} \right) \times 100 = 0.2 \times 100 = 20\%$.
0 likes
View Solution104
DifficultMCQ
While selling a watch,a shopkeeper gives a discount of $15 \%$. If he gives a discount of $20 \%$,he earns $Rs. 51$ less as profit. What is the original price of the watch? (in $Rs$)
A
$920$
B
$985$
C
$1125$
D
$1020$
Solution
(D) Let the original price (marked price) of the watch be $Rs. x$.
In the first case,the discount is $15 \%$,so the selling price is $x \times (1 - 0.15) = 0.85x$.
In the second case,the discount is $20 \%$,so the selling price is $x \times (1 - 0.20) = 0.80x$.
The difference in the selling price is given as $Rs. 51$,which represents the reduction in profit.
Therefore,$0.85x - 0.80x = 51$.
$0.05x = 51$.
$x = \frac{51}{0.05} = \frac{5100}{5} = 1020$.
Thus,the original price of the watch is $Rs. 1020$.
In the first case,the discount is $15 \%$,so the selling price is $x \times (1 - 0.15) = 0.85x$.
In the second case,the discount is $20 \%$,so the selling price is $x \times (1 - 0.20) = 0.80x$.
The difference in the selling price is given as $Rs. 51$,which represents the reduction in profit.
Therefore,$0.85x - 0.80x = 51$.
$0.05x = 51$.
$x = \frac{51}{0.05} = \frac{5100}{5} = 1020$.
Thus,the original price of the watch is $Rs. 1020$.
0 likes
View Solution105
MediumMCQ
$A$ shopkeeper purchased $245$ pieces of an article at $Rs. 30$ per piece. He spent $Rs. 980$ on transport and $Rs. 1470$ on packing the articles. He sold the articles at the rate of $Rs. 50$ per piece. What is the percent profit earned?
A
$25$
B
$20$
C
$28$
D
$22.5$
Solution
(A) Cost Price $(CP)$ of $245$ pieces of article $= 245 \times 30 = Rs. 7350$.
Total $CP$ (including transport and packing) $= 7350 + 980 + 1470 = Rs. 9800$.
$CP$ of $1$ piece $= \frac{9800}{245} = Rs. 40$.
Selling Price $(SP)$ of $1$ piece $= Rs. 50$.
Profit $= SP - CP = 50 - 40 = Rs. 10$.
Profit $\% = \left( \frac{\text{Profit}}{CP} \right) \times 100 = \left( \frac{10}{40} \right) \times 100 = 25 \%$.
Total $CP$ (including transport and packing) $= 7350 + 980 + 1470 = Rs. 9800$.
$CP$ of $1$ piece $= \frac{9800}{245} = Rs. 40$.
Selling Price $(SP)$ of $1$ piece $= Rs. 50$.
Profit $= SP - CP = 50 - 40 = Rs. 10$.
Profit $\% = \left( \frac{\text{Profit}}{CP} \right) \times 100 = \left( \frac{10}{40} \right) \times 100 = 25 \%$.
0 likes
View Solution106
MediumMCQ
An article is marked for sale at $Rs. 504$. The shopkeeper gives a discount of $5\%$ on the marked price and still earns a profit of $20\%$. What is the cost price of the article? (in $Rs.$)
A
$399$
B
$405$
C
$403$
D
$400$
Solution
(A) Given: Marked Price $(MP)$ = $Rs. 504$,Discount = $5\%$,Profit = $20\%$.
First,calculate the Selling Price $(SP)$:
$SP = MP - (Discount\% \text{ of } MP)$
$SP = 504 - (0.05 \times 504) = 504 - 25.2 = Rs. 478.80$.
Now,calculate the Cost Price $(CP)$:
We know that $SP = CP \times (1 + \text{Profit}\%)$.
$478.80 = CP \times (1 + 0.20)$
$478.80 = CP \times 1.20$
$CP = \frac{478.80}{1.20} = Rs. 399$.
Therefore,the cost price of the article is $Rs. 399$.
First,calculate the Selling Price $(SP)$:
$SP = MP - (Discount\% \text{ of } MP)$
$SP = 504 - (0.05 \times 504) = 504 - 25.2 = Rs. 478.80$.
Now,calculate the Cost Price $(CP)$:
We know that $SP = CP \times (1 + \text{Profit}\%)$.
$478.80 = CP \times (1 + 0.20)$
$478.80 = CP \times 1.20$
$CP = \frac{478.80}{1.20} = Rs. 399$.
Therefore,the cost price of the article is $Rs. 399$.
0 likes
View Solution107
MediumMCQ
$A$ shopkeeper sold an article for $Rs. 400$ after giving a $20\%$ discount on the labelled price and made a $30\%$ profit on the cost price. What would have been the percentage profit,had he not given the discount (in $\%$)?
A
$25$
B
$35$
C
$50$
D
$62.5$
Solution
(D) Let the cost price be $CP$ and the marked price be $MP$.
Given that the shopkeeper makes a $30\%$ profit on $CP$,the selling price $SP = 1.30 \times CP$.
Also,the shopkeeper gives a $20\%$ discount on $MP$,so $SP = 0.80 \times MP$.
Equating the two expressions for $SP$: $0.80 \times MP = 1.30 \times CP$,which gives $MP = \frac{1.30}{0.80} \times CP = 1.625 \times CP$.
If no discount is given,the selling price would be equal to the marked price,i.e.,$SP_{new} = MP = 1.625 \times CP$.
The profit percentage would then be $\frac{SP_{new} - CP}{CP} \times 100 = \frac{1.625 \times CP - CP}{CP} \times 100 = 0.625 \times 100 = 62.5\%$.
Given that the shopkeeper makes a $30\%$ profit on $CP$,the selling price $SP = 1.30 \times CP$.
Also,the shopkeeper gives a $20\%$ discount on $MP$,so $SP = 0.80 \times MP$.
Equating the two expressions for $SP$: $0.80 \times MP = 1.30 \times CP$,which gives $MP = \frac{1.30}{0.80} \times CP = 1.625 \times CP$.
If no discount is given,the selling price would be equal to the marked price,i.e.,$SP_{new} = MP = 1.625 \times CP$.
The profit percentage would then be $\frac{SP_{new} - CP}{CP} \times 100 = \frac{1.625 \times CP - CP}{CP} \times 100 = 0.625 \times 100 = 62.5\%$.
0 likes
View Solution108
EasyMCQ
Suresh purchased a $TV$ set for $Rs. 11250$. He spent $Rs. 800$ on installation and $Rs. 150$ on transportation. At what price should it be sold so that the profit earned would be $15\%$,if no discount was offered? (in $Rs.$)
A
$12938$
B
$14030$
C
$13450$
D
$15467$
Solution
(B) The total Cost Price $(CP)$ for Suresh includes the purchase price,installation charges,and transportation costs.
$CP = 11250 + 800 + 150 = 12200 \text{ Rs.}$
To earn a profit of $15\%$,the Selling Price $(SP)$ is calculated as:
$SP = CP \times (1 + \frac{\text{Profit}\%}{100})$
$SP = 12200 \times (1 + \frac{15}{100})$
$SP = 12200 \times 1.15 = 14030 \text{ Rs.}$
Therefore,the $TV$ should be sold for $14030 \text{ Rs.}$
$CP = 11250 + 800 + 150 = 12200 \text{ Rs.}$
To earn a profit of $15\%$,the Selling Price $(SP)$ is calculated as:
$SP = CP \times (1 + \frac{\text{Profit}\%}{100})$
$SP = 12200 \times (1 + \frac{15}{100})$
$SP = 12200 \times 1.15 = 14030 \text{ Rs.}$
Therefore,the $TV$ should be sold for $14030 \text{ Rs.}$
0 likes
View Solution109
MediumMCQ
$Mr.$ $A$ sold goods to $Mr.$ $B$ at a $10\%$ discount on the printed rate. The discounted value is $Rs. 1242$. If a $15\%$ profit is earned on the purchase rate by selling the goods at the printed rate,what is the purchase rate? (in $Rs.$)
A
$1242$
B
$1380$
C
$1280$
D
$1200$
Solution
(D) Step $1$: Find the printed rate (marked price).
Given that the discounted value is $Rs. 1242$ at a $10\%$ discount.
Let the printed rate be $P$.
$P \times (1 - 0.10) = 1242$
$P \times 0.90 = 1242$
$P = 1242 / 0.90 = 1380$.
Step $2$: Find the purchase rate (cost price).
It is given that selling the goods at the printed rate $(Rs. 1380)$ yields a $15\%$ profit on the purchase rate $(CP)$.
$SP = CP \times (1 + \text{Profit}\%)$
$1380 = CP \times (1 + 0.15)$
$1380 = CP \times 1.15$
$CP = 1380 / 1.15 = 1200$.
Therefore,the purchase rate is $Rs. 1200$.
Given that the discounted value is $Rs. 1242$ at a $10\%$ discount.
Let the printed rate be $P$.
$P \times (1 - 0.10) = 1242$
$P \times 0.90 = 1242$
$P = 1242 / 0.90 = 1380$.
Step $2$: Find the purchase rate (cost price).
It is given that selling the goods at the printed rate $(Rs. 1380)$ yields a $15\%$ profit on the purchase rate $(CP)$.
$SP = CP \times (1 + \text{Profit}\%)$
$1380 = CP \times (1 + 0.15)$
$1380 = CP \times 1.15$
$CP = 1380 / 1.15 = 1200$.
Therefore,the purchase rate is $Rs. 1200$.
0 likes
View Solution110
MediumMCQ
Rajesh purchased a mobile phone and a refrigerator for $Rs. 12000$ and $Rs. 10000$ respectively. She sold the refrigerator at a loss of $12\%$ and the mobile phone at a profit of $8\%$. What is her overall loss or profit?
A
Loss of $Rs. 280$
B
Profit of $Rs. 2160$
C
Loss of $Rs. 240$
D
Profit of $Rs. 2060$
Solution
(C) Cost Price $(CP)$ of the refrigerator $= Rs. 10000$. Loss $= 12\%$.
Loss amount $= 12\% \text{ of } 10000 = \frac{12}{100} \times 10000 = Rs. 1200$.
Selling Price $(SP)$ of the refrigerator $= 10000 - 1200 = Rs. 8800$.
Cost Price $(CP)$ of the mobile phone $= Rs. 12000$. Profit $= 8\%$.
Profit amount $= 8\% \text{ of } 12000 = \frac{8}{100} \times 12000 = Rs. 960$.
Selling Price $(SP)$ of the mobile phone $= 12000 + 960 = Rs. 12960$.
Total $CP = 10000 + 12000 = Rs. 22000$.
Total $SP = 8800 + 12960 = Rs. 21760$.
Since Total $SP < $ Total $CP$,there is an overall loss.
Loss $= 22000 - 21760 = Rs. 240$.
Loss amount $= 12\% \text{ of } 10000 = \frac{12}{100} \times 10000 = Rs. 1200$.
Selling Price $(SP)$ of the refrigerator $= 10000 - 1200 = Rs. 8800$.
Cost Price $(CP)$ of the mobile phone $= Rs. 12000$. Profit $= 8\%$.
Profit amount $= 8\% \text{ of } 12000 = \frac{8}{100} \times 12000 = Rs. 960$.
Selling Price $(SP)$ of the mobile phone $= 12000 + 960 = Rs. 12960$.
Total $CP = 10000 + 12000 = Rs. 22000$.
Total $SP = 8800 + 12960 = Rs. 21760$.
Since Total $SP < $ Total $CP$,there is an overall loss.
Loss $= 22000 - 21760 = Rs. 240$.
0 likes
View Solution111
MediumMCQ
Abhishek purchased $140$ shirts and $250$ trousers at $Rs. 450$ and $Rs. 550$ respectively. What should be the overall average selling price of shirts and trousers so that $40 \%$ profit is earned? (in $Rs.$) (rounded off to the next integer)
A
$725$
B
$710$
C
$720$
D
$700$
Solution
(C) Total Cost Price $(CP)$ of $140$ shirts and $250$ trousers is calculated as:
$Total CP = (140 \times 450) + (250 \times 550) = 63000 + 137500 = Rs. 200500$
To earn a $40 \%$ profit,the total Selling Price $(SP)$ must be:
$Total SP = CP \times (1 + \frac{40}{100}) = 200500 \times 1.4 = Rs. 280700$
The total number of items is $140 + 250 = 390$.
The average selling price per item is:
$Average SP = \frac{Total SP}{Total Items} = \frac{280700}{390} \approx 719.74$
Rounding off to the next integer,we get $Rs. 720$.
$Total CP = (140 \times 450) + (250 \times 550) = 63000 + 137500 = Rs. 200500$
To earn a $40 \%$ profit,the total Selling Price $(SP)$ must be:
$Total SP = CP \times (1 + \frac{40}{100}) = 200500 \times 1.4 = Rs. 280700$
The total number of items is $140 + 250 = 390$.
The average selling price per item is:
$Average SP = \frac{Total SP}{Total Items} = \frac{280700}{390} \approx 719.74$
Rounding off to the next integer,we get $Rs. 720$.
0 likes
View Solution112
MediumMCQ
$A$ trader marks his goods $40 \%$ above the cost price and allows a discount of $25 \%$. The profit he makes,is in $\%$:
A
$15$
B
$10$
C
$5$
D
$2$
Solution
(C) Let the cost price $(CP)$ be $Rs. 100$.
The marked price $(MP)$ is $40 \%$ above the $CP$,so $MP = 100 + 40 = Rs. 140$.
$A$ discount of $25 \%$ is allowed on the $MP$,so the selling price $(SP)$ is $140 - (25 \% \text{ of } 140) = 140 - 35 = Rs. 105$.
The profit is $SP - CP = 105 - 100 = Rs. 5$.
The profit percentage is $\left( \frac{\text{Profit}}{CP} \right) \times 100 = \left( \frac{5}{100} \right) \times 100 = 5 \%$.
The marked price $(MP)$ is $40 \%$ above the $CP$,so $MP = 100 + 40 = Rs. 140$.
$A$ discount of $25 \%$ is allowed on the $MP$,so the selling price $(SP)$ is $140 - (25 \% \text{ of } 140) = 140 - 35 = Rs. 105$.
The profit is $SP - CP = 105 - 100 = Rs. 5$.
The profit percentage is $\left( \frac{\text{Profit}}{CP} \right) \times 100 = \left( \frac{5}{100} \right) \times 100 = 5 \%$.
0 likes
View Solution113
DifficultMCQ
$A$ man sold his two cars for $Rs. 4.5$ lakh each. In the sale of the first car, he incurred $20\%$ profit, and in the sale of the second, he incurred $20\%$ loss. What is the total amount of profit or loss?
A
profit of $Rs. 20250$
B
loss of $Rs. 20250$
C
profit of $Rs. 37500$
D
loss of $Rs. 37500$
Solution
(D) Selling price of each car $(SP)$ = $Rs. 4,50,000$.
Total $SP$ = $4,50,000 + 4,50,000 = Rs. 9,00,000$.
For the first car: $SP = 4,50,000$, Profit = $20\%$.
Cost Price $(CP_1)$ = $SP / (1 + Profit\%) = 4,50,000 / 1.2 = Rs. 3,75,000$.
For the second car: $SP = 4,50,000$, Loss = $20\%$.
Cost Price $(CP_2)$ = $SP / (1 - Loss\%) = 4,50,000 / 0.8 = Rs. 5,62,500$.
Total $CP = CP_1 + CP_2 = 3,75,000 + 5,62,500 = Rs. 9,37,500$.
Since Total $CP$ > Total $SP$, there is a loss.
Loss = Total $CP - $ Total $SP = 9,37,500 - 9,00,000 = Rs. 37,500$.
Total $SP$ = $4,50,000 + 4,50,000 = Rs. 9,00,000$.
For the first car: $SP = 4,50,000$, Profit = $20\%$.
Cost Price $(CP_1)$ = $SP / (1 + Profit\%) = 4,50,000 / 1.2 = Rs. 3,75,000$.
For the second car: $SP = 4,50,000$, Loss = $20\%$.
Cost Price $(CP_2)$ = $SP / (1 - Loss\%) = 4,50,000 / 0.8 = Rs. 5,62,500$.
Total $CP = CP_1 + CP_2 = 3,75,000 + 5,62,500 = Rs. 9,37,500$.
Since Total $CP$ > Total $SP$, there is a loss.
Loss = Total $CP - $ Total $SP = 9,37,500 - 9,00,000 = Rs. 37,500$.
0 likes
View Solution114
DifficultMCQ
By selling an article at $80 \%$ of its marked price,a shopkeeper makes a loss of $10 \%$. What will be the profit percentage if he sells it at $95 \%$ of its marked price (in $\%$)?
A
$6.9$
B
$5$
C
$5.9$
D
$12.5$
Solution
(A) Let the marked price $(MP)$ be $Rs. 100$.
Selling price $(SP_1)$ at $80 \%$ of $MP = 0.80 \times 100 = Rs. 80$.
Given a loss of $10 \%$,the cost price $(CP)$ is calculated as:
$CP = \frac{SP_1}{1 - \text{Loss}\%} = \frac{80}{0.90} = Rs. \frac{800}{9}$.
Now,if the article is sold at $95 \%$ of its $MP$,the new selling price $(SP_2)$ is $Rs. 95$.
Profit = $SP_2 - CP = 95 - \frac{800}{9} = \frac{855 - 800}{9} = Rs. \frac{55}{9}$.
Profit percentage = $\left( \frac{\text{Profit}}{CP} \right) \times 100 = \left( \frac{55/9}{800/9} \right) \times 100 = \frac{55}{800} \times 100 = \frac{55}{8} = 6.875 \% \approx 6.9 \%$.
Selling price $(SP_1)$ at $80 \%$ of $MP = 0.80 \times 100 = Rs. 80$.
Given a loss of $10 \%$,the cost price $(CP)$ is calculated as:
$CP = \frac{SP_1}{1 - \text{Loss}\%} = \frac{80}{0.90} = Rs. \frac{800}{9}$.
Now,if the article is sold at $95 \%$ of its $MP$,the new selling price $(SP_2)$ is $Rs. 95$.
Profit = $SP_2 - CP = 95 - \frac{800}{9} = \frac{855 - 800}{9} = Rs. \frac{55}{9}$.
Profit percentage = $\left( \frac{\text{Profit}}{CP} \right) \times 100 = \left( \frac{55/9}{800/9} \right) \times 100 = \frac{55}{800} \times 100 = \frac{55}{8} = 6.875 \% \approx 6.9 \%$.
0 likes
View Solution115
DifficultMCQ
$A$ trader purchases a wrist watch and a pendulum for $Rs. 390$. He sells them making a profit of $10 \%$ on the watch and $15 \%$ on the pendulum. He earns a total profit of $Rs. 51.50$. The difference between the original prices of the pendulum and the watch is equal to? (in $Rs.$)
A
$80$
B
$120$
C
$110$
D
$100$
Solution
(C) Let the cost price $(CP)$ of the wrist watch be $Rs. x$.
Then,the $CP$ of the pendulum is $Rs. (390 - x)$.
Profit on the watch $= 10 \% \text{ of } x = 0.10x$.
Profit on the pendulum $= 15 \% \text{ of } (390 - x) = 0.15(390 - x) = 58.5 - 0.15x$.
Total profit $= 0.10x + 58.5 - 0.15x = 58.5 - 0.05x$.
Given that the total profit is $Rs. 51.50$,we have:
$58.5 - 0.05x = 51.50$
$0.05x = 58.5 - 51.50 = 7.00$
$x = \frac{7}{0.05} = 140$.
So,the $CP$ of the wrist watch is $Rs. 140$.
The $CP$ of the pendulum is $390 - 140 = Rs. 250$.
The difference between the original prices is $250 - 140 = Rs. 110$.
Then,the $CP$ of the pendulum is $Rs. (390 - x)$.
Profit on the watch $= 10 \% \text{ of } x = 0.10x$.
Profit on the pendulum $= 15 \% \text{ of } (390 - x) = 0.15(390 - x) = 58.5 - 0.15x$.
Total profit $= 0.10x + 58.5 - 0.15x = 58.5 - 0.05x$.
Given that the total profit is $Rs. 51.50$,we have:
$58.5 - 0.05x = 51.50$
$0.05x = 58.5 - 51.50 = 7.00$
$x = \frac{7}{0.05} = 140$.
So,the $CP$ of the wrist watch is $Rs. 140$.
The $CP$ of the pendulum is $390 - 140 = Rs. 250$.
The difference between the original prices is $250 - 140 = Rs. 110$.
0 likes
View Solution116
DifficultMCQ
$A$ tradesman gives $4 \%$ discount on the marked price and gives $1$ book free for buying every $15$ books and thus gains $35 \%$. The marked price is increased above the cost price by (approx.) (in $\%$).
A
$40$
B
$3$
C
$50$
D
$20$
Solution
(A) Let the $CP$ of each book be $Rs. 100$.
For every $15$ books purchased,the customer gets $1$ book free,meaning the customer receives $16$ books for the price of $15$.
The total $CP$ for $16$ books is $16 \times 100 = Rs. 1600$.
The tradesman gains $35 \%$,so the total $SP$ for $16$ books is $1600 \times 1.35 = Rs. 2160$.
The $SP$ of $1$ book is $2160 / 16 = Rs. 135$.
Since the tradesman gives a $4 \%$ discount on the marked price $(MP)$,we have $0.96 \times MP = 135$.
$MP = 135 / 0.96 = Rs. 140.625$.
The percentage increase of $MP$ over $CP$ is $((140.625 - 100) / 100) \times 100 = 40.625 \%$.
Rounding to the nearest integer,the increase is approximately $40 \%$.
For every $15$ books purchased,the customer gets $1$ book free,meaning the customer receives $16$ books for the price of $15$.
The total $CP$ for $16$ books is $16 \times 100 = Rs. 1600$.
The tradesman gains $35 \%$,so the total $SP$ for $16$ books is $1600 \times 1.35 = Rs. 2160$.
The $SP$ of $1$ book is $2160 / 16 = Rs. 135$.
Since the tradesman gives a $4 \%$ discount on the marked price $(MP)$,we have $0.96 \times MP = 135$.
$MP = 135 / 0.96 = Rs. 140.625$.
The percentage increase of $MP$ over $CP$ is $((140.625 - 100) / 100) \times 100 = 40.625 \%$.
Rounding to the nearest integer,the increase is approximately $40 \%$.
0 likes
View Solution117
DifficultMCQ
$A$ shopkeeper purchased $150$ identical pieces of furniture at the rate of $Rs. 250$ each. He spent an amount of $Rs. 2500$ on packing. He fixed the price of each furniture at $Rs. 320$. However,he decided to give a discount of $5 \%$ on the labeled price. What is the percent profit earned by him (in $\%$)?
A
$16$
B
$15$
C
$14$
D
$20$
Solution
(C) Total cost price of $150$ pieces of furniture $= 150 \times 250 = Rs. 37500$.
Total packing charges $= Rs. 2500$.
Total investment (Total Cost Price) $= 37500 + 2500 = Rs. 40000$.
Cost price per piece $= \frac{40000}{150} = Rs. \frac{800}{3}$.
Marked price per piece $= Rs. 320$.
Discount $= 5 \%$ of $320 = \frac{5}{100} \times 320 = Rs. 16$.
Selling price per piece $= 320 - 16 = Rs. 304$.
Profit per piece $= 304 - \frac{800}{3} = \frac{912 - 800}{3} = Rs. \frac{112}{3}$.
Profit percentage $= \left( \frac{\text{Profit}}{\text{Cost Price}} \right) \times 100 = \left( \frac{112/3}{800/3} \right) \times 100 = \frac{112}{800} \times 100 = \frac{112}{8} = 14 \%$.
Total packing charges $= Rs. 2500$.
Total investment (Total Cost Price) $= 37500 + 2500 = Rs. 40000$.
Cost price per piece $= \frac{40000}{150} = Rs. \frac{800}{3}$.
Marked price per piece $= Rs. 320$.
Discount $= 5 \%$ of $320 = \frac{5}{100} \times 320 = Rs. 16$.
Selling price per piece $= 320 - 16 = Rs. 304$.
Profit per piece $= 304 - \frac{800}{3} = \frac{912 - 800}{3} = Rs. \frac{112}{3}$.
Profit percentage $= \left( \frac{\text{Profit}}{\text{Cost Price}} \right) \times 100 = \left( \frac{112/3}{800/3} \right) \times 100 = \frac{112}{800} \times 100 = \frac{112}{8} = 14 \%$.
0 likes
View Solution118
DifficultMCQ
An $Ox$ and a carriage together cost $Rs. 8000$. The ox is sold at a profit of $10\%$ and the carriage is sold at a loss of $10\%$. If the total profit made is $2.5\%$,then what is the cost price of the ox? (in $Rs.$)
A
$3000$
B
$3500$
C
$4000$
D
$5000$
Solution
(D) Let the cost price $(CP)$ of the ox be $Rs. x$.
Then,the $CP$ of the carriage is $Rs. (8000 - x)$.
The selling price $(SP)$ of the ox after a $10\%$ profit is $x + 0.10x = 1.1x$.
The $SP$ of the carriage after a $10\%$ loss is $(8000 - x) - 0.10(8000 - x) = 0.9(8000 - x)$.
The total cost price is $Rs. 8000$. The total profit is $2.5\%$,so the total selling price is $8000 \times (1 + 0.025) = 8000 \times 1.025 = Rs. 8200$.
Equating the sum of individual selling prices to the total selling price:
$1.1x + 0.9(8000 - x) = 8200$
$1.1x + 7200 - 0.9x = 8200$
$0.2x = 8200 - 7200$
$0.2x = 1000$
$x = 1000 / 0.2 = 5000$.
Therefore,the cost price of the ox is $Rs. 5000$.
Then,the $CP$ of the carriage is $Rs. (8000 - x)$.
The selling price $(SP)$ of the ox after a $10\%$ profit is $x + 0.10x = 1.1x$.
The $SP$ of the carriage after a $10\%$ loss is $(8000 - x) - 0.10(8000 - x) = 0.9(8000 - x)$.
The total cost price is $Rs. 8000$. The total profit is $2.5\%$,so the total selling price is $8000 \times (1 + 0.025) = 8000 \times 1.025 = Rs. 8200$.
Equating the sum of individual selling prices to the total selling price:
$1.1x + 0.9(8000 - x) = 8200$
$1.1x + 7200 - 0.9x = 8200$
$0.2x = 8200 - 7200$
$0.2x = 1000$
$x = 1000 / 0.2 = 5000$.
Therefore,the cost price of the ox is $Rs. 5000$.
0 likes
View Solution119
DifficultMCQ
With a $5 \%$ discount on the cost of sugar,a buyer could purchase $2 \text{ kg}$ more sugar for $Rs. 608$. What is the initial selling price of sugar per kg?
A
$15.50$
B
$15$
C
$16.50$
D
$16$
Solution
(D) Let the initial price of sugar be $P$ per kg.
Initial quantity purchased for $Rs. 608$ is $Q = \frac{608}{P}$ kg.
After a $5 \%$ discount,the new price is $P' = 0.95P$.
The new quantity purchased for $Rs. 608$ is $Q' = \frac{608}{0.95P}$.
Given that the buyer can purchase $2 \text{ kg}$ more,we have $Q' - Q = 2$.
$\frac{608}{0.95P} - \frac{608}{P} = 2$.
$\frac{608}{P} \left( \frac{1}{0.95} - 1 \right) = 2$.
$\frac{608}{P} \left( \frac{1 - 0.95}{0.95} \right) = 2$.
$\frac{608}{P} \left( \frac{0.05}{0.95} \right) = 2$.
$\frac{608}{P} \left( \frac{1}{19} \right) = 2$.
$608 = 38P$.
$P = \frac{608}{38} = 16$.
Therefore,the initial selling price of sugar is $Rs. 16$ per kg.
Initial quantity purchased for $Rs. 608$ is $Q = \frac{608}{P}$ kg.
After a $5 \%$ discount,the new price is $P' = 0.95P$.
The new quantity purchased for $Rs. 608$ is $Q' = \frac{608}{0.95P}$.
Given that the buyer can purchase $2 \text{ kg}$ more,we have $Q' - Q = 2$.
$\frac{608}{0.95P} - \frac{608}{P} = 2$.
$\frac{608}{P} \left( \frac{1}{0.95} - 1 \right) = 2$.
$\frac{608}{P} \left( \frac{1 - 0.95}{0.95} \right) = 2$.
$\frac{608}{P} \left( \frac{0.05}{0.95} \right) = 2$.
$\frac{608}{P} \left( \frac{1}{19} \right) = 2$.
$608 = 38P$.
$P = \frac{608}{38} = 16$.
Therefore,the initial selling price of sugar is $Rs. 16$ per kg.
0 likes
View Solution120
DifficultMCQ
$A$ trader marked his goods at $20 \%$ above the cost price. He sold half the stock at the marked price,one quarter at a discount of $20 \%$ on the marked price,and the rest at a discount of $40 \%$ on the marked price. What is his total gain percentage?
A
$2$
B
$4.5$
C
$13.5$
D
$15$
Solution
(A) Let the total quantity of goods be $4$ units and the cost price $(CP)$ of each unit be $Rs. 100$.
Total $CP = 4 \times 100 = Rs. 400$.
Marked Price $(MP)$ per unit $= 100 + 20\% \text{ of } 100 = Rs. 120$.
Total $MP$ for $4$ units $= 4 \times 120 = Rs. 480$.
Now,the trader sells the stock as follows:
$1$. Half the stock ($2$ units) at $MP$: $2 \times 120 = Rs. 240$.
$2$. One quarter ($1$ unit) at $20\%$ discount on $MP$: $120 - 20\% \text{ of } 120 = 120 - 24 = Rs. 96$.
$3$. The rest ($1$ unit) at $40\%$ discount on $MP$: $120 - 40\% \text{ of } 120 = 120 - 48 = Rs. 72$.
Total Selling Price $(SP)$ $= 240 + 96 + 72 = Rs. 408$.
Total Gain $= SP - CP = 408 - 400 = Rs. 8$.
Gain percentage $= (\text{Gain} / CP) \times 100 = (8 / 400) \times 100 = 2\%$.
Total $CP = 4 \times 100 = Rs. 400$.
Marked Price $(MP)$ per unit $= 100 + 20\% \text{ of } 100 = Rs. 120$.
Total $MP$ for $4$ units $= 4 \times 120 = Rs. 480$.
Now,the trader sells the stock as follows:
$1$. Half the stock ($2$ units) at $MP$: $2 \times 120 = Rs. 240$.
$2$. One quarter ($1$ unit) at $20\%$ discount on $MP$: $120 - 20\% \text{ of } 120 = 120 - 24 = Rs. 96$.
$3$. The rest ($1$ unit) at $40\%$ discount on $MP$: $120 - 40\% \text{ of } 120 = 120 - 48 = Rs. 72$.
Total Selling Price $(SP)$ $= 240 + 96 + 72 = Rs. 408$.
Total Gain $= SP - CP = 408 - 400 = Rs. 8$.
Gain percentage $= (\text{Gain} / CP) \times 100 = (8 / 400) \times 100 = 2\%$.
0 likes
View Solution121
MediumMCQ
$A$ shopkeeper marks his goods at $25\%$ above his cost price and allows customers a discount of $12 \frac{1}{2}\%$ for cash. Find his $\%$ profit?
A
$12 \frac{4}{5}\%$
B
$9 \frac{3}{7}\%$
C
$7 \frac{5}{8}\%$
D
$9 \frac{3}{8}\%$
Solution
(D) Let the cost price $(CP)$ be $Rs. 100$.
The marked price $(MP)$ is $25\%$ above the $CP$, so $MP = 100 + 25 = Rs. 125$.
The discount offered is $12 \frac{1}{2}\%$ of the $MP$, which is $\frac{25}{2} \% = 0.125$.
Discount amount $= 125 \times \frac{25}{2 \times 100} = 125 \times \frac{1}{8} = Rs. 15.625$ or $Rs. 15 \frac{5}{8}$.
The selling price $(SP)$ is $MP - \text{Discount} = 125 - 15.625 = Rs. 109.375$ or $Rs. 109 \frac{3}{8}$.
Profit $= SP - CP = 109.375 - 100 = Rs. 9.375$.
Profit percentage $= \frac{\text{Profit}}{CP} \times 100 = \frac{9.375}{100} \times 100 = 9.375\%$, which is $9 \frac{3}{8}\%$.
The marked price $(MP)$ is $25\%$ above the $CP$, so $MP = 100 + 25 = Rs. 125$.
The discount offered is $12 \frac{1}{2}\%$ of the $MP$, which is $\frac{25}{2} \% = 0.125$.
Discount amount $= 125 \times \frac{25}{2 \times 100} = 125 \times \frac{1}{8} = Rs. 15.625$ or $Rs. 15 \frac{5}{8}$.
The selling price $(SP)$ is $MP - \text{Discount} = 125 - 15.625 = Rs. 109.375$ or $Rs. 109 \frac{3}{8}$.
Profit $= SP - CP = 109.375 - 100 = Rs. 9.375$.
Profit percentage $= \frac{\text{Profit}}{CP} \times 100 = \frac{9.375}{100} \times 100 = 9.375\%$, which is $9 \frac{3}{8}\%$.
0 likes
View Solution122
MediumMCQ
$A$ trader marks the price of his goods $25 \%$ above the cost price but allows a $12.5 \%$ discount for cash payment. If he sells the goods for $Rs. 875$,find the cost price of the goods (in $Rs.$).
A
$800$
B
$875$
C
$925$
D
$975$
Solution
(A) Let the cost price $(CP)$ be $x$.
The marked price $(MP)$ is $25 \%$ above the cost price,so $MP = x \times (1 + 0.25) = 1.25x$.
$A$ discount of $12.5 \%$ is allowed on the marked price,so the selling price $(SP)$ is $MP \times (1 - 0.125) = 1.25x \times 0.875$.
Given that $SP = Rs. 875$,we have:
$1.25x \times 0.875 = 875$
$x = \frac{875}{1.25 \times 0.875}$
$x = \frac{875}{1.09375} = 800$
Alternatively,calculating $MP$ first:
$MP = 875 \times \left(\frac{100}{100 - 12.5}\right) = 875 \times \left(\frac{100}{87.5}\right) = 1000$.
Now,$CP = MP \times \left(\frac{100}{100 + 25}\right) = 1000 \times \left(\frac{100}{125}\right) = 800$.
The marked price $(MP)$ is $25 \%$ above the cost price,so $MP = x \times (1 + 0.25) = 1.25x$.
$A$ discount of $12.5 \%$ is allowed on the marked price,so the selling price $(SP)$ is $MP \times (1 - 0.125) = 1.25x \times 0.875$.
Given that $SP = Rs. 875$,we have:
$1.25x \times 0.875 = 875$
$x = \frac{875}{1.25 \times 0.875}$
$x = \frac{875}{1.09375} = 800$
Alternatively,calculating $MP$ first:
$MP = 875 \times \left(\frac{100}{100 - 12.5}\right) = 875 \times \left(\frac{100}{87.5}\right) = 1000$.
Now,$CP = MP \times \left(\frac{100}{100 + 25}\right) = 1000 \times \left(\frac{100}{125}\right) = 800$.
0 likes
View Solution123
DifficultMCQ
Harkesh bought a certain quantity of tomato at the rate of $Rs. 1500$ per quintal. $10 \%$ of the tomato was spoiled. At what price in $Rs.$ per quintal should he sell the remaining to gain $20 \%$ of his outlay?
A
$1800$
B
$2000$
C
$2200$
D
$2400$
Solution
(B) Let the total quantity of tomato be $100 \text{ quintals}$.
Total cost price $(CP)$ $= 100 \times 1500 = Rs. 1,50,000$.
Since $10 \%$ of the tomato is spoiled,the remaining quantity is $100 - 10 = 90 \text{ quintals}$.
To gain $20 \%$ on the total outlay,the total selling price $(SP)$ must be $120 \%$ of the total $CP$.
Total $SP = 1,50,000 \times 1.20 = Rs. 1,80,000$.
Selling price per quintal for the remaining $90 \text{ quintals} = \frac{1,80,000}{90} = Rs. 2000$ per quintal.
Total cost price $(CP)$ $= 100 \times 1500 = Rs. 1,50,000$.
Since $10 \%$ of the tomato is spoiled,the remaining quantity is $100 - 10 = 90 \text{ quintals}$.
To gain $20 \%$ on the total outlay,the total selling price $(SP)$ must be $120 \%$ of the total $CP$.
Total $SP = 1,50,000 \times 1.20 = Rs. 1,80,000$.
Selling price per quintal for the remaining $90 \text{ quintals} = \frac{1,80,000}{90} = Rs. 2000$ per quintal.
0 likes
View Solution124
DifficultMCQ
Aman buys $5$ laptops and $7$ computers for $Rs. 58500$. He sells the laptops at a profit of $10\%$ and computers at a profit of $16\%$ and his total gain is $Rs. 7110$. What price does he pay for a laptop? (in $Rs.$)
A
$7500$
B
$8200$
C
$9100$
D
$10500$
Solution
(A) Let the cost price of one laptop be $Rs. y$.
The total cost price of $5$ laptops is $Rs. 5y$.
The total cost price of $7$ computers is $Rs. (58500 - 5y)$.
The total profit is given by the sum of profits from laptops and computers:
$10\% \text{ of } 5y + 16\% \text{ of } (58500 - 5y) = 7110$
$\frac{10}{100} \times 5y + \frac{16}{100} \times (58500 - 5y) = 7110$
$0.5y + 0.16(58500 - 5y) = 7110$
$0.5y + 9360 - 0.8y = 7110$
$-0.3y = 7110 - 9360$
$-0.3y = -2250$
$y = \frac{2250}{0.3} = 7500$
Therefore,the cost price of one laptop is $Rs. 7500$.
The total cost price of $5$ laptops is $Rs. 5y$.
The total cost price of $7$ computers is $Rs. (58500 - 5y)$.
The total profit is given by the sum of profits from laptops and computers:
$10\% \text{ of } 5y + 16\% \text{ of } (58500 - 5y) = 7110$
$\frac{10}{100} \times 5y + \frac{16}{100} \times (58500 - 5y) = 7110$
$0.5y + 0.16(58500 - 5y) = 7110$
$0.5y + 9360 - 0.8y = 7110$
$-0.3y = 7110 - 9360$
$-0.3y = -2250$
$y = \frac{2250}{0.3} = 7500$
Therefore,the cost price of one laptop is $Rs. 7500$.
0 likes
View Solution125
MediumMCQ
$A$ reduction of $10 \%$ in the price of rice enables a person to obtain $25 \text{ kg}$ more for $Rs. 2250$. Find the reduced price per $\text{kg}$ of the rice (in $Rs.$).
A
$8.50$
B
$9$
C
$10.50$
D
$11$
Solution
(B) Let the original price of rice be $x$ per $\text{kg}$.
Total amount spent = $Rs. 2250$.
Original quantity of rice = $\frac{2250}{x} \text{ kg}$.
Reduced price = $x - 0.10x = 0.90x$.
New quantity of rice = $\frac{2250}{0.90x} = \frac{2500}{x} \text{ kg}$.
According to the problem,the difference in quantity is $25 \text{ kg}$:
$\frac{2500}{x} - \frac{2250}{x} = 25$.
$\frac{250}{x} = 25$.
$x = 10$.
The original price was $Rs. 10$ per $\text{kg}$.
The reduced price is $10 \times 0.90 = Rs. 9$ per $\text{kg}$.
Alternatively: $A$ reduction of $10 \%$ on $Rs. 2250$ is $Rs. 225$. This saving allows the purchase of $25 \text{ kg}$ of rice at the new price. Therefore,the reduced price per $\text{kg}$ is $\frac{225}{25} = Rs. 9$.
Total amount spent = $Rs. 2250$.
Original quantity of rice = $\frac{2250}{x} \text{ kg}$.
Reduced price = $x - 0.10x = 0.90x$.
New quantity of rice = $\frac{2250}{0.90x} = \frac{2500}{x} \text{ kg}$.
According to the problem,the difference in quantity is $25 \text{ kg}$:
$\frac{2500}{x} - \frac{2250}{x} = 25$.
$\frac{250}{x} = 25$.
$x = 10$.
The original price was $Rs. 10$ per $\text{kg}$.
The reduced price is $10 \times 0.90 = Rs. 9$ per $\text{kg}$.
Alternatively: $A$ reduction of $10 \%$ on $Rs. 2250$ is $Rs. 225$. This saving allows the purchase of $25 \text{ kg}$ of rice at the new price. Therefore,the reduced price per $\text{kg}$ is $\frac{225}{25} = Rs. 9$.
0 likes
View Solution126
MediumMCQ
$A$ shopkeeper mixes $26 \, kg$ of wheat which costs $Rs. 20$ per $kg$ with $30 \, kg$ of wheat which costs $Rs. 36$ per $kg$ and sells the mixture at $Rs. 30$ per $kg$. Find the profit percent. (in $\%$)
A
$5$
B
$9$
C
$12$
D
$15$
Solution
(A) Total Cost Price $(CP)$ of $26 \, kg$ wheat $= 26 \times 20 = Rs. 520$.
Total Cost Price $(CP)$ of $30 \, kg$ wheat $= 30 \times 36 = Rs. 1080$.
Total Cost Price of the mixture $= 520 + 1080 = Rs. 1600$.
Total quantity of the mixture $= 26 + 30 = 56 \, kg$.
Total Selling Price $(SP)$ of $56 \, kg$ mixture $= 56 \times 30 = Rs. 1680$.
Profit $= SP - CP = 1680 - 1600 = Rs. 80$.
Profit percent $= (\text{Profit} / CP) \times 100 = (80 / 1600) \times 100 = 5 \%$.
Total Cost Price $(CP)$ of $30 \, kg$ wheat $= 30 \times 36 = Rs. 1080$.
Total Cost Price of the mixture $= 520 + 1080 = Rs. 1600$.
Total quantity of the mixture $= 26 + 30 = 56 \, kg$.
Total Selling Price $(SP)$ of $56 \, kg$ mixture $= 56 \times 30 = Rs. 1680$.
Profit $= SP - CP = 1680 - 1600 = Rs. 80$.
Profit percent $= (\text{Profit} / CP) \times 100 = (80 / 1600) \times 100 = 5 \%$.
0 likes
View Solution127
DifficultMCQ
$A$ sold a pen to $B$ at a profit of $20\%,$ $B$ sold the same pen to $C$ for $Rs.\,75$ thereby making a profit of $25 \% .$ Find the price at which $A$ bought the pen? (in $Rs.$)
A
$20$
B
$42$
C
$50$
D
$64$
Solution
(C) Let the cost price for $A$ be $x$.
$A$ sold the pen to $B$ at a profit of $20\%$,so the cost price for $B$ is $x \times (1 + 0.20) = 1.2x$.
$B$ sold the pen to $C$ for $Rs.\,75$ at a profit of $25\%$.
Therefore,the cost price for $B$ is $\frac{75}{1 + 0.25} = \frac{75}{1.25} = Rs.\,60$.
Equating the two values for the cost price of $B$: $1.2x = 60$.
Solving for $x$: $x = \frac{60}{1.2} = 50$.
Thus,$A$ bought the pen for $Rs.\,50$.
$A$ sold the pen to $B$ at a profit of $20\%$,so the cost price for $B$ is $x \times (1 + 0.20) = 1.2x$.
$B$ sold the pen to $C$ for $Rs.\,75$ at a profit of $25\%$.
Therefore,the cost price for $B$ is $\frac{75}{1 + 0.25} = \frac{75}{1.25} = Rs.\,60$.
Equating the two values for the cost price of $B$: $1.2x = 60$.
Solving for $x$: $x = \frac{60}{1.2} = 50$.
Thus,$A$ bought the pen for $Rs.\,50$.
0 likes
View Solution128
DifficultMCQ
Seema sells a pen to Sapna at a profit of $25 \%$. Sapna sells it to Asha at a profit of $10 \%$ and Asha sells it to Kavita at a profit of $5 \%$. If Asha sells it for $Rs.\,231$,find the cost price at which Seema bought the pen? (in $Rs.$)
A
$195$
B
$160$
C
$145$
D
$135$
Solution
(B) Let the cost price $(CP)$ of the pen for Seema be $Rs.\,x$.
Seema sells it to Sapna at a profit of $25 \%$,so the $CP$ for Sapna is $x \times (1 + 0.25) = 1.25x$.
Sapna sells it to Asha at a profit of $10 \%$,so the $CP$ for Asha is $1.25x \times (1 + 0.10) = 1.25x \times 1.1 = 1.375x$.
Asha sells it to Kavita at a profit of $5 \%$,so the selling price $(SP)$ for Asha is $1.375x \times (1 + 0.05) = 1.375x \times 1.05 = 1.44375x$.
Given that Asha sells it for $Rs.\,231$,we have:
$1.44375x = 231$
$x = \frac{231}{1.44375}$
$x = 160$
Therefore,the cost price at which Seema bought the pen is $Rs.\,160$.
Seema sells it to Sapna at a profit of $25 \%$,so the $CP$ for Sapna is $x \times (1 + 0.25) = 1.25x$.
Sapna sells it to Asha at a profit of $10 \%$,so the $CP$ for Asha is $1.25x \times (1 + 0.10) = 1.25x \times 1.1 = 1.375x$.
Asha sells it to Kavita at a profit of $5 \%$,so the selling price $(SP)$ for Asha is $1.375x \times (1 + 0.05) = 1.375x \times 1.05 = 1.44375x$.
Given that Asha sells it for $Rs.\,231$,we have:
$1.44375x = 231$
$x = \frac{231}{1.44375}$
$x = 160$
Therefore,the cost price at which Seema bought the pen is $Rs.\,160$.
0 likes
View Solution129
MediumMCQ
Mohit purchased $40 \, kg$ of wheat at $Rs. 12.50$ per $kg$ and $25 \, kg$ of wheat at $Rs. 15.10$ per $kg$. He mixed the two qualities of wheat for selling. At what rate should it be sold to gain $10 \%$? (in $Rs.$)
A
$13.25$
B
$13.50$
C
$14.75$
D
$14.85$
Solution
(D) Step $1$: Calculate the total cost price $(CP)$ of the mixture.
Total $CP = (40 \times 12.50) + (25 \times 15.10) = 500 + 377.50 = Rs. 877.50$.
Step $2$: Calculate the total weight of the mixture.
Total weight $= 40 + 25 = 65 \, kg$.
Step $3$: Calculate the $CP$ per $kg$ of the mixture.
$CP$ per $kg = \frac{877.50}{65} = Rs. 13.50$.
Step $4$: Calculate the selling price $(SP)$ to gain $10 \%$.
$SP = CP \times (1 + \frac{\text{Gain} \%}{100}) = 13.50 \times (1 + 0.10) = 13.50 \times 1.10 = Rs. 14.85$.
Therefore,the mixture should be sold at $Rs. 14.85$ per $kg$.
Total $CP = (40 \times 12.50) + (25 \times 15.10) = 500 + 377.50 = Rs. 877.50$.
Step $2$: Calculate the total weight of the mixture.
Total weight $= 40 + 25 = 65 \, kg$.
Step $3$: Calculate the $CP$ per $kg$ of the mixture.
$CP$ per $kg = \frac{877.50}{65} = Rs. 13.50$.
Step $4$: Calculate the selling price $(SP)$ to gain $10 \%$.
$SP = CP \times (1 + \frac{\text{Gain} \%}{100}) = 13.50 \times (1 + 0.10) = 13.50 \times 1.10 = Rs. 14.85$.
Therefore,the mixture should be sold at $Rs. 14.85$ per $kg$.
0 likes
View Solution130
DifficultMCQ
If the cost price of $20$ articles is equal to the selling price of $15$ articles,find the profit percent?
A
$33 \frac{1}{2} \%$
B
$33 \frac{1}{3} \%$
C
$33 \frac{1}{5} \%$
D
$33 \frac{1}{7} \%$
Solution
(B) Let the cost price $(CP)$ of $1$ article be $x$.
Then,$CP$ of $20$ articles $= 20x$.
Given that $CP$ of $20$ articles $= SP$ of $15$ articles.
So,$SP$ of $15$ articles $= 20x$.
$SP$ of $1$ article $= \frac{20x}{15} = \frac{4x}{3}$.
Profit $= SP - CP = \frac{4x}{3} - x = \frac{x}{3}$.
Profit $\% = \left( \frac{\text{Profit}}{CP} \right) \times 100 = \left( \frac{x/3}{x} \right) \times 100 = \frac{100}{3} \% = 33 \frac{1}{3} \%$.
Then,$CP$ of $20$ articles $= 20x$.
Given that $CP$ of $20$ articles $= SP$ of $15$ articles.
So,$SP$ of $15$ articles $= 20x$.
$SP$ of $1$ article $= \frac{20x}{15} = \frac{4x}{3}$.
Profit $= SP - CP = \frac{4x}{3} - x = \frac{x}{3}$.
Profit $\% = \left( \frac{\text{Profit}}{CP} \right) \times 100 = \left( \frac{x/3}{x} \right) \times 100 = \frac{100}{3} \% = 33 \frac{1}{3} \%$.
0 likes
View Solution131
MediumMCQ
$A$ trader sells rice at a profit of $5 \%$ and uses a weight which is $25 \%$ less. Find the total percentage gain.
A
$20$
B
$30$
C
$40$
D
$50$
Solution
(C) Let the cost price of $1 \ kg$ of rice be $₹ 100$.
The trader sells the rice at a $5 \%$ profit,so the selling price for the quantity he actually gives is $₹ 105$.
Since he uses a weight that is $25 \%$ less,he is actually giving $1000 \ g - 250 \ g = 750 \ g$ of rice instead of $1000 \ g$.
The cost price of $750 \ g$ of rice is $₹ 75$.
Now,the trader sells $750 \ g$ for $₹ 105$.
Profit $= \text{Selling Price} - \text{Cost Price} = 105 - 75 = 30$.
Percentage Profit $= \left( \frac{\text{Profit}}{\text{Cost Price}} \right) \times 100 = \left( \frac{30}{75} \right) \times 100 = \frac{2}{5} \times 100 = 40 \%$.
The trader sells the rice at a $5 \%$ profit,so the selling price for the quantity he actually gives is $₹ 105$.
Since he uses a weight that is $25 \%$ less,he is actually giving $1000 \ g - 250 \ g = 750 \ g$ of rice instead of $1000 \ g$.
The cost price of $750 \ g$ of rice is $₹ 75$.
Now,the trader sells $750 \ g$ for $₹ 105$.
Profit $= \text{Selling Price} - \text{Cost Price} = 105 - 75 = 30$.
Percentage Profit $= \left( \frac{\text{Profit}}{\text{Cost Price}} \right) \times 100 = \left( \frac{30}{75} \right) \times 100 = \frac{2}{5} \times 100 = 40 \%$.
0 likes
View Solution132
DifficultMCQ
$A$ person purchases $8$ pens for ₹ $10$ and sells $10$ pens for ₹ $8$. How much profit or loss percentage does he make?
A
$30 \%$ gain
B
$30 \%$ loss
C
$36 \%$ gain
D
$36 \%$ loss
Solution
(D) Cost price of $8$ pens $= ₹ 10$.
Cost price of $1$ pen $= ₹ \frac{10}{8} = ₹ 1.25$.
Selling price of $10$ pens $= ₹ 8$.
Selling price of $1$ pen $= ₹ \frac{8}{10} = ₹ 0.80$.
Since the selling price is less than the cost price,there is a loss.
Loss $= \text{Cost Price} - \text{Selling Price} = 1.25 - 0.80 = ₹ 0.45$.
Loss percentage $= \left( \frac{\text{Loss}}{\text{Cost Price}} \right) \times 100 = \left( \frac{0.45}{1.25} \right) \times 100 = 36 \%$.
Alternatively,using the cross-multiplication method:
$\text{Loss percentage} = \left( \frac{x^2 - y^2}{x^2} \right) \times 100$ where $x$ is the number of pens bought for $y$ rupees.
Here,$8$ pens for $10$ rupees and $10$ pens for $8$ rupees.
Loss percentage $= \frac{10^2 - 8^2}{10^2} \times 100 = \frac{100 - 64}{100} \times 100 = 36 \%$.
Therefore,the loss is $36 \%$.
Cost price of $1$ pen $= ₹ \frac{10}{8} = ₹ 1.25$.
Selling price of $10$ pens $= ₹ 8$.
Selling price of $1$ pen $= ₹ \frac{8}{10} = ₹ 0.80$.
Since the selling price is less than the cost price,there is a loss.
Loss $= \text{Cost Price} - \text{Selling Price} = 1.25 - 0.80 = ₹ 0.45$.
Loss percentage $= \left( \frac{\text{Loss}}{\text{Cost Price}} \right) \times 100 = \left( \frac{0.45}{1.25} \right) \times 100 = 36 \%$.
Alternatively,using the cross-multiplication method:
$\text{Loss percentage} = \left( \frac{x^2 - y^2}{x^2} \right) \times 100$ where $x$ is the number of pens bought for $y$ rupees.
Here,$8$ pens for $10$ rupees and $10$ pens for $8$ rupees.
Loss percentage $= \frac{10^2 - 8^2}{10^2} \times 100 = \frac{100 - 64}{100} \times 100 = 36 \%$.
Therefore,the loss is $36 \%$.
0 likes
View Solution133
MediumMCQ
$A$ shopkeeper buys articles at $8$ for $Rs\,16$ and sells them at $9$ for $Rs\,20$. What is his gain or loss percent?
A
$10 \%$ loss
B
$10 \%$ gain
C
$11 \frac{1}{9} \%$ gain
D
$11 \frac{1}{9} \%$ loss
Solution
(C) Cost Price $(CP)$ of $8$ articles $= Rs\,16$. Therefore,$CP$ of $1$ article $= Rs\,16/8 = Rs\,2$.
Selling Price $(SP)$ of $9$ articles $= Rs\,20$. Therefore,$SP$ of $1$ article $= Rs\,20/9$.
Since $SP > CP$,there is a gain.
Gain $= SP - CP = \frac{20}{9} - 2 = \frac{20-18}{9} = Rs\,\frac{2}{9}$.
Gain percent $= \left( \frac{\text{Gain}}{CP} \times 100 \right) \% = \left( \frac{2/9}{2} \times 100 \right) \% = \frac{100}{9} \% = 11 \frac{1}{9} \% \text{ gain}$.
Selling Price $(SP)$ of $9$ articles $= Rs\,20$. Therefore,$SP$ of $1$ article $= Rs\,20/9$.
Since $SP > CP$,there is a gain.
Gain $= SP - CP = \frac{20}{9} - 2 = \frac{20-18}{9} = Rs\,\frac{2}{9}$.
Gain percent $= \left( \frac{\text{Gain}}{CP} \times 100 \right) \% = \left( \frac{2/9}{2} \times 100 \right) \% = \frac{100}{9} \% = 11 \frac{1}{9} \% \text{ gain}$.
0 likes
View Solution134
EasyMCQ
$A$ person bought an article for $Rs. 240$. For how much should he sell it so as to lose $20\%$?
A
$120$
B
$180$
C
$240$
D
$192$
Solution
(D) Given,Cost Price $(C.P.)$ = $Rs. 240$.
Loss percentage = $20\%$.
To find the Selling Price $(S.P.)$ at a loss of $20\%$,we use the formula:
$S.P. = C.P. \times \left(1 - \frac{\text{Loss}\%}{100}\right)$
$S.P. = 240 \times \left(1 - \frac{20}{100}\right)$
$S.P. = 240 \times \left(1 - 0.20\right)$
$S.P. = 240 \times 0.80$
$S.P. = 192$
Therefore,the person should sell the article for $Rs. 192$ to incur a loss of $20\%$.
Loss percentage = $20\%$.
To find the Selling Price $(S.P.)$ at a loss of $20\%$,we use the formula:
$S.P. = C.P. \times \left(1 - \frac{\text{Loss}\%}{100}\right)$
$S.P. = 240 \times \left(1 - \frac{20}{100}\right)$
$S.P. = 240 \times \left(1 - 0.20\right)$
$S.P. = 240 \times 0.80$
$S.P. = 192$
Therefore,the person should sell the article for $Rs. 192$ to incur a loss of $20\%$.
0 likes
View Solution135
MediumMCQ
By selling an article for $Rs. 384$,a trader gains $20 \%$. Find the cost price of the article.
A
$160$
B
$240$
C
$320$
D
$480$
Solution
(C) Let the cost price $(C.P.)$ be $x$.
Given that the selling price $(S.P.)$ is $Rs. 384$ and the gain percentage is $20 \%$.
The formula for selling price is $S.P. = C.P. \times (1 + \frac{\text{Gain} \%}{100})$.
Substituting the values: $384 = x \times (1 + \frac{20}{100})$.
$384 = x \times (1 + 0.2) = 1.2x$.
$x = \frac{384}{1.2} = \frac{3840}{12} = 320$.
Therefore,the cost price of the article is $Rs. 320$.
Given that the selling price $(S.P.)$ is $Rs. 384$ and the gain percentage is $20 \%$.
The formula for selling price is $S.P. = C.P. \times (1 + \frac{\text{Gain} \%}{100})$.
Substituting the values: $384 = x \times (1 + \frac{20}{100})$.
$384 = x \times (1 + 0.2) = 1.2x$.
$x = \frac{384}{1.2} = \frac{3840}{12} = 320$.
Therefore,the cost price of the article is $Rs. 320$.
0 likes
View Solution136
MediumMCQ
$A$ sells an article to $B$ at a profit of $20 \%$ and $B$ sells it to $C$ at a loss of $10 \%$. If $C$ pays $Rs. 540$ for it,at what price did $A$ buy?
A
$400$
B
$500$
C
$600$
D
$700$
Solution
(B) Let the cost price for $A$ be $x$.
$A$ sells the article to $B$ at a profit of $20 \%$,so the selling price for $A$ (which is the cost price for $B$) is $x \times (1 + 0.20) = 1.2x$.
$B$ sells the article to $C$ at a loss of $10 \%$,so the selling price for $B$ (which is the cost price for $C$) is $1.2x \times (1 - 0.10) = 1.2x \times 0.9 = 1.08x$.
Given that $C$ pays $Rs. 540$,we have $1.08x = 540$.
Solving for $x$: $x = \frac{540}{1.08} = 500$.
Thus,$A$ bought the article for $Rs. 500$.
$A$ sells the article to $B$ at a profit of $20 \%$,so the selling price for $A$ (which is the cost price for $B$) is $x \times (1 + 0.20) = 1.2x$.
$B$ sells the article to $C$ at a loss of $10 \%$,so the selling price for $B$ (which is the cost price for $C$) is $1.2x \times (1 - 0.10) = 1.2x \times 0.9 = 1.08x$.
Given that $C$ pays $Rs. 540$,we have $1.08x = 540$.
Solving for $x$: $x = \frac{540}{1.08} = 500$.
Thus,$A$ bought the article for $Rs. 500$.
0 likes
View Solution137
MediumMCQ
$A$ man sold a cow at a loss of $12 \%$. If he had sold it at a gain of $6 \%$,he would have received $₹ 72$ more. What was the cost price of the cow?
A
$300$
B
$500$
C
$400$
D
$600$
Solution
(C) Let the cost price of the cow be $CP$.
Selling price at $12 \%$ loss $= CP - 0.12 CP = 0.88 CP$.
Selling price at $6 \%$ gain $= CP + 0.06 CP = 1.06 CP$.
According to the problem,the difference between these two selling prices is $₹ 72$.
$1.06 CP - 0.88 CP = 72$.
$0.18 CP = 72$.
$CP = \frac{72}{0.18} = \frac{7200}{18} = ₹ 400$.
Therefore,the cost price of the cow is $₹ 400$.
Selling price at $12 \%$ loss $= CP - 0.12 CP = 0.88 CP$.
Selling price at $6 \%$ gain $= CP + 0.06 CP = 1.06 CP$.
According to the problem,the difference between these two selling prices is $₹ 72$.
$1.06 CP - 0.88 CP = 72$.
$0.18 CP = 72$.
$CP = \frac{72}{0.18} = \frac{7200}{18} = ₹ 400$.
Therefore,the cost price of the cow is $₹ 400$.
0 likes
View Solution138
EasyMCQ
An article is sold for $Rs. 4950$ at a gain of $10 \%$. What would have been the gain or loss per cent if it had been sold for $Rs. 4275$?
A
$10 \%$ gain
B
$10 \%$ loss
C
$5 \%$ gain
D
$5 \%$ loss
Solution
(D) First,calculate the Cost Price $(C.P.)$ of the article.
Given $S.P. = Rs. 4950$ and $\text{Gain} = 10 \%$.
$C.P. = S.P. \times \frac{100}{100 + \text{Gain} \%}$
$C.P. = 4950 \times \frac{100}{110} = 45 \times 100 = Rs. 4500$.
Now,if the article is sold for $S.P._{new} = Rs. 4275$.
Since $S.P._{new} < C.P.$,there is a loss.
$\text{Loss} = C.P. - S.P._{new} = 4500 - 4275 = Rs. 225$.
$\text{Loss} \% = \left( \frac{\text{Loss}}{C.P.} \right) \times 100 = \left( \frac{225}{4500} \right) \times 100 = \frac{225}{45} = 5 \%$.
Therefore,there is a $5 \%$ loss.
Given $S.P. = Rs. 4950$ and $\text{Gain} = 10 \%$.
$C.P. = S.P. \times \frac{100}{100 + \text{Gain} \%}$
$C.P. = 4950 \times \frac{100}{110} = 45 \times 100 = Rs. 4500$.
Now,if the article is sold for $S.P._{new} = Rs. 4275$.
Since $S.P._{new} < C.P.$,there is a loss.
$\text{Loss} = C.P. - S.P._{new} = 4500 - 4275 = Rs. 225$.
$\text{Loss} \% = \left( \frac{\text{Loss}}{C.P.} \right) \times 100 = \left( \frac{225}{4500} \right) \times 100 = \frac{225}{45} = 5 \%$.
Therefore,there is a $5 \%$ loss.
0 likes
View Solution139
MediumMCQ
$A$ machine is sold at a profit of $15 \%$. Had it been sold for $Rs\, 540$ more,$24 \%$ would have been gained. Find the cost price.
A
$4800$
B
$5400$
C
$6000$
D
$6400$
Solution
(C) Let the cost price of the machine be $CP$.
Initially,the machine is sold at a profit of $15 \%$,so the selling price $SP_1 = CP + 0.15 CP = 1.15 CP$.
If it is sold for $Rs\, 540$ more,the new selling price $SP_2 = SP_1 + 540 = 1.15 CP + 540$.
In this case,the profit is $24 \%$,so $SP_2 = CP + 0.24 CP = 1.24 CP$.
Equating the two expressions for $SP_2$:
$1.24 CP = 1.15 CP + 540$
$1.24 CP - 1.15 CP = 540$
$0.09 CP = 540$
$CP = \frac{540}{0.09} = \frac{54000}{9} = 6000$.
Therefore,the cost price is $Rs\, 6000$.
Initially,the machine is sold at a profit of $15 \%$,so the selling price $SP_1 = CP + 0.15 CP = 1.15 CP$.
If it is sold for $Rs\, 540$ more,the new selling price $SP_2 = SP_1 + 540 = 1.15 CP + 540$.
In this case,the profit is $24 \%$,so $SP_2 = CP + 0.24 CP = 1.24 CP$.
Equating the two expressions for $SP_2$:
$1.24 CP = 1.15 CP + 540$
$1.24 CP - 1.15 CP = 540$
$0.09 CP = 540$
$CP = \frac{540}{0.09} = \frac{54000}{9} = 6000$.
Therefore,the cost price is $Rs\, 6000$.
0 likes
View Solution140
EasyMCQ
$A$ person sold a radio at a loss of $5 \%$. Had he sold it for $Rs. 210$ more,he would have gained $25 \%$. For what value should he sell it in order to gain $35 \%?$
A
$645$
B
$954$
C
$654$
D
$945$
Solution
(D) Let the cost price of the radio be $CP$.
Initially,the radio is sold at a loss of $5 \%$,so the selling price $SP_1 = CP \times (1 - 0.05) = 0.95 \times CP$.
If sold for $Rs. 210$ more,the new selling price $SP_2 = SP_1 + 210 = 0.95 \times CP + 210$.
In this case,the gain is $25 \%$,so $SP_2 = CP \times (1 + 0.25) = 1.25 \times CP$.
Equating the two expressions for $SP_2$: $1.25 \times CP = 0.95 \times CP + 210$.
$0.30 \times CP = 210$,which gives $CP = \frac{210}{0.30} = 700$.
The cost price of the radio is $Rs. 700$.
To gain $35 \%$,the required selling price $SP_3 = CP \times (1 + 0.35) = 700 \times 1.35 = 945$.
Thus,the radio should be sold for $Rs. 945$ to gain $35 \%$.
Initially,the radio is sold at a loss of $5 \%$,so the selling price $SP_1 = CP \times (1 - 0.05) = 0.95 \times CP$.
If sold for $Rs. 210$ more,the new selling price $SP_2 = SP_1 + 210 = 0.95 \times CP + 210$.
In this case,the gain is $25 \%$,so $SP_2 = CP \times (1 + 0.25) = 1.25 \times CP$.
Equating the two expressions for $SP_2$: $1.25 \times CP = 0.95 \times CP + 210$.
$0.30 \times CP = 210$,which gives $CP = \frac{210}{0.30} = 700$.
The cost price of the radio is $Rs. 700$.
To gain $35 \%$,the required selling price $SP_3 = CP \times (1 + 0.35) = 700 \times 1.35 = 945$.
Thus,the radio should be sold for $Rs. 945$ to gain $35 \%$.
0 likes
View Solution141
DifficultMCQ
An article is sold at a profit of $20 \%$. If both the cost price and selling price are $Rs. 150$ less,the profit would be $5 \%$ more. Find the cost price.
A
$750$
B
$650$
C
$950$
D
$850$
Solution
(A) Let the cost price of the article be $Rs. x$.
Then,the initial selling price $= \frac{120}{100} \times x = 1.2x$.
New cost price $= Rs. (x - 150)$.
New selling price $= Rs. (1.2x - 150)$.
The new profit percentage is $20 \% + 5 \% = 25 \%$.
Using the profit formula: $\text{Profit } \% = \frac{\text{Selling Price} - \text{Cost Price}}{\text{Cost Price}} \times 100$.
$25 = \frac{(1.2x - 150) - (x - 150)}{x - 150} \times 100$.
$25 = \frac{0.2x}{x - 150} \times 100$.
$25(x - 150) = 20x$.
$25x - 3750 = 20x$.
$5x = 3750$.
$x = 750$.
Therefore,the cost price is $Rs. 750$.
Then,the initial selling price $= \frac{120}{100} \times x = 1.2x$.
New cost price $= Rs. (x - 150)$.
New selling price $= Rs. (1.2x - 150)$.
The new profit percentage is $20 \% + 5 \% = 25 \%$.
Using the profit formula: $\text{Profit } \% = \frac{\text{Selling Price} - \text{Cost Price}}{\text{Cost Price}} \times 100$.
$25 = \frac{(1.2x - 150) - (x - 150)}{x - 150} \times 100$.
$25 = \frac{0.2x}{x - 150} \times 100$.
$25(x - 150) = 20x$.
$25x - 3750 = 20x$.
$5x = 3750$.
$x = 750$.
Therefore,the cost price is $Rs. 750$.
0 likes
View Solution142
MediumMCQ
$A$ trader sells his table at a profit of $15 \%$ and the chair at a loss of $7 \frac{1}{2} \%,$ but on the whole he gains $Rs. 50.$ If he sells the table at a loss of $7 \frac{1}{2} \%,$ and the chair at a profit of $15 \%,$ then he neither gains nor loses. Find the cost price of the table.
A
$\frac{5000}{9}$
B
$\frac{4000}{9}$
C
$\frac{4400}{9}$
D
$\frac{5300}{9}$
Solution
(B) Let the cost price of the table be $Rs. t$ and that of the chair be $Rs. c.$
According to the first condition:
$0.15t - 0.075c = 50$
Multiplying by $100$ to simplify:
$15t - 7.5c = 5000$
$15t - \frac{15}{2}c = 5000$
$30t - 15c = 10000$ $...(1)$
According to the second condition:
$-7.5t + 15c = 0$
$15c = 7.5t$
$c = \frac{7.5}{15}t = 0.5t = \frac{t}{2}$ $...(2)$
Substituting $(2)$ into $(1)$:
$30t - 15(\frac{t}{2}) = 10000$
$60t - 15t = 20000$
$45t = 20000$
$t = \frac{20000}{45} = \frac{4000}{9}$
Thus,the cost price of the table is $Rs. \frac{4000}{9}$.
According to the first condition:
$0.15t - 0.075c = 50$
Multiplying by $100$ to simplify:
$15t - 7.5c = 5000$
$15t - \frac{15}{2}c = 5000$
$30t - 15c = 10000$ $...(1)$
According to the second condition:
$-7.5t + 15c = 0$
$15c = 7.5t$
$c = \frac{7.5}{15}t = 0.5t = \frac{t}{2}$ $...(2)$
Substituting $(2)$ into $(1)$:
$30t - 15(\frac{t}{2}) = 10000$
$60t - 15t = 20000$
$45t = 20000$
$t = \frac{20000}{45} = \frac{4000}{9}$
Thus,the cost price of the table is $Rs. \frac{4000}{9}$.
0 likes
View Solution143
MediumMCQ
$A$ vendor started selling vegetables at $Rs. 10$ per $kg$,but could not find buyers at this rate. So,he reduced the price to $Rs. 8.10$ per $kg$,but uses a faulty weight of $900\, g$ for $1\, kg$. Find the percent change in the actual price or loss. (in $\%$)
A
$5$
B
$10$
C
$15$
D
$20$
Solution
(B) The initial selling price was $Rs. 10$ per $kg$.
After the reduction,the vendor sells $900\, g$ for $Rs. 8.10$.
To find the actual price per $kg$ $(1000\, g)$,we calculate:
Actual price = $\frac{8.10}{900} \times 1000 = Rs. 9$ per $kg$.
The change in price is $10 - 9 = Rs. 1$.
The percentage change is $\frac{1}{10} \times 100\% = 10\%$.
After the reduction,the vendor sells $900\, g$ for $Rs. 8.10$.
To find the actual price per $kg$ $(1000\, g)$,we calculate:
Actual price = $\frac{8.10}{900} \times 1000 = Rs. 9$ per $kg$.
The change in price is $10 - 9 = Rs. 1$.
The percentage change is $\frac{1}{10} \times 100\% = 10\%$.
0 likes
View Solution144
DifficultMCQ
The cost price of $6$ pens is equal to the selling price of $4$ pens. Find the profit percent. (in $\%$)
A
$25$
B
$60$
C
$50$
D
$80$
Solution
(C) Let the cost price $(C.P.)$ of $1$ pen be $x$.
Then,the $C.P.$ of $6$ pens $= 6x$.
The selling price $(S.P.)$ of $4$ pens is given as equal to the $C.P.$ of $6$ pens,so $S.P.$ of $4$ pens $= 6x$.
Therefore,the $S.P.$ of $1$ pen $= \frac{6x}{4} = 1.5x$.
Profit on $1$ pen $= S.P. - C.P. = 1.5x - x = 0.5x$.
Profit percentage $= \frac{\text{Profit}}{C.P.} \times 100 = \frac{0.5x}{x} \times 100 = 50\%$.
Then,the $C.P.$ of $6$ pens $= 6x$.
The selling price $(S.P.)$ of $4$ pens is given as equal to the $C.P.$ of $6$ pens,so $S.P.$ of $4$ pens $= 6x$.
Therefore,the $S.P.$ of $1$ pen $= \frac{6x}{4} = 1.5x$.
Profit on $1$ pen $= S.P. - C.P. = 1.5x - x = 0.5x$.
Profit percentage $= \frac{\text{Profit}}{C.P.} \times 100 = \frac{0.5x}{x} \times 100 = 50\%$.
0 likes
View Solution145
MediumMCQ
If the cost price of $20$ tables is equal to the selling price of $25$ tables,find the loss percentage. (in $\%$)
A
$10$
B
$20$
C
$30$
D
$40$
Solution
(B) Let the cost price $(C.P.)$ of $1$ table be $x$.
Then,the $C.P.$ of $20$ tables $= 20x$.
According to the problem,the $C.P.$ of $20$ tables is equal to the selling price $(S.P.)$ of $25$ tables.
So,$S.P.$ of $25$ tables $= 20x$.
Therefore,the $S.P.$ of $1$ table $= \frac{20x}{25} = 0.8x$.
Since $S.P. < C.P.$,there is a loss.
Loss $= C.P. - S.P. = x - 0.8x = 0.2x$.
Loss percentage $= (\frac{\text{Loss}}{C.P.}) \times 100 = (\frac{0.2x}{x}) \times 100 = 20\%$.
Then,the $C.P.$ of $20$ tables $= 20x$.
According to the problem,the $C.P.$ of $20$ tables is equal to the selling price $(S.P.)$ of $25$ tables.
So,$S.P.$ of $25$ tables $= 20x$.
Therefore,the $S.P.$ of $1$ table $= \frac{20x}{25} = 0.8x$.
Since $S.P. < C.P.$,there is a loss.
Loss $= C.P. - S.P. = x - 0.8x = 0.2x$.
Loss percentage $= (\frac{\text{Loss}}{C.P.}) \times 100 = (\frac{0.2x}{x}) \times 100 = 20\%$.
0 likes
View Solution146
DifficultMCQ
$A$ man sells an article at a loss of $5 \%$. If he had bought it at $20 \%$ more and sold it for $Rs. 115$ less,he would have made a loss of $40 \%$. Find the cost price of the article.
A
$400$
B
$450$
C
$500$
D
$600$
Solution
(C) Let the cost price of the article be $P$.
Initial selling price $(S.P._1)$ $= P \times (1 - 0.05) = 0.95P$.
If the cost price increases by $20 \%$,the new cost price $(C.P._2)$ $= P \times 1.20 = 1.2P$.
The new loss is $40 \%$,so the new selling price $(S.P._2)$ $= 1.2P \times (1 - 0.40) = 1.2P \times 0.60 = 0.72P$.
According to the problem,the difference between the two selling prices is $115$.
$S.P._1 - S.P._2 = 115$
$0.95P - 0.72P = 115$
$0.23P = 115$
$P = \frac{115}{0.23} = 500$.
Therefore,the cost price of the article is $₹ 500$.
Initial selling price $(S.P._1)$ $= P \times (1 - 0.05) = 0.95P$.
If the cost price increases by $20 \%$,the new cost price $(C.P._2)$ $= P \times 1.20 = 1.2P$.
The new loss is $40 \%$,so the new selling price $(S.P._2)$ $= 1.2P \times (1 - 0.40) = 1.2P \times 0.60 = 0.72P$.
According to the problem,the difference between the two selling prices is $115$.
$S.P._1 - S.P._2 = 115$
$0.95P - 0.72P = 115$
$0.23P = 115$
$P = \frac{115}{0.23} = 500$.
Therefore,the cost price of the article is $₹ 500$.
0 likes
View Solution147
MediumMCQ
When Ram sold his book for $Rs. 255$,he made a loss of $15\%$. For how much should he have sold it if he wanted to make a profit of $5\%$?
A
$275$
B
$315$
C
$295$
D
$335$
Solution
(B) Step $1$: Calculate the Cost Price $(C.P.)$ of the book.
Given that the Selling Price $(S.P.)$ is $Rs. 255$ and the loss is $15\%$.
$C.P. = S.P. \times \frac{100}{100 - \text{Loss}\%} = 255 \times \frac{100}{85} = 3 \times 100 = Rs. 300$.
Step $2$: Calculate the required Selling Price $(S.P.)$ for a profit of $5\%$.
$S.P. = C.P. \times \frac{100 + \text{Profit}\%}{100} = 300 \times \frac{105}{100} = 3 \times 105 = Rs. 315$.
Given that the Selling Price $(S.P.)$ is $Rs. 255$ and the loss is $15\%$.
$C.P. = S.P. \times \frac{100}{100 - \text{Loss}\%} = 255 \times \frac{100}{85} = 3 \times 100 = Rs. 300$.
Step $2$: Calculate the required Selling Price $(S.P.)$ for a profit of $5\%$.
$S.P. = C.P. \times \frac{100 + \text{Profit}\%}{100} = 300 \times \frac{105}{100} = 3 \times 105 = Rs. 315$.
0 likes
View Solution148
DifficultMCQ
$A$ man invests $Rs. 21,000$ in shares of a company. He sells one-third of the total shares at a profit of $10\%$. However,he has to sell the remaining shares at a $5\%$ loss. Find his overall profit or loss percentage.
A
$10\%$ profit
B
$10\%$ loss
C
No profit,no loss
D
$5\%$ loss
Solution
(C) Total investment $(C.P.)$ $= ₹ 21,000$.
$C.P.$ of one-third of the shares $= \frac{1}{3} \times 21,000 = ₹ 7,000$.
$S.P.$ of one-third of the shares at $10\%$ profit $= 7,000 \times (1 + \frac{10}{100}) = 7,000 \times 1.1 = ₹ 7,700$.
$C.P.$ of the remaining two-thirds of the shares $= 21,000 - 7,000 = ₹ 14,000$.
$S.P.$ of the remaining two-thirds of the shares at $5\%$ loss $= 14,000 \times (1 - \frac{5}{100}) = 14,000 \times 0.95 = ₹ 13,300$.
Total $S.P. = 7,700 + 13,300 = ₹ 21,000$.
Since Total $S.P. = Total C.P. = ₹ 21,000$,there is no profit and no loss.
$C.P.$ of one-third of the shares $= \frac{1}{3} \times 21,000 = ₹ 7,000$.
$S.P.$ of one-third of the shares at $10\%$ profit $= 7,000 \times (1 + \frac{10}{100}) = 7,000 \times 1.1 = ₹ 7,700$.
$C.P.$ of the remaining two-thirds of the shares $= 21,000 - 7,000 = ₹ 14,000$.
$S.P.$ of the remaining two-thirds of the shares at $5\%$ loss $= 14,000 \times (1 - \frac{5}{100}) = 14,000 \times 0.95 = ₹ 13,300$.
Total $S.P. = 7,700 + 13,300 = ₹ 21,000$.
Since Total $S.P. = Total C.P. = ₹ 21,000$,there is no profit and no loss.
0 likes
View Solution149
MediumMCQ
$A$ man buys $100 \, kg$ of sugar for $Rs. \, 2400$. He sold $1/4$th of the stock at a loss of $5 \%$. At what per cent profit should he sell the remaining stock so as to make an overall profit of $20 \%$ on the whole transaction? (in $\%$)
A
$25$
B
$27 \frac{1}{3}$
C
$28$
D
$28 \frac{1}{3}$
Solution
(D) Total cost price = $Rs. \, 2400$.
Total desired profit = $20 \% \text{ of } 2400 = 0.20 \times 2400 = Rs. \, 480$.
Quantity sold at $5 \% \text{ loss} = 1/4 \times 100 \, kg = 25 \, kg$.
Cost price of $25 \, kg = 1/4 \times 2400 = Rs. \, 600$.
Loss on $25 \, kg = 5 \% \text{ of } 600 = 0.05 \times 600 = Rs. \, 30$.
Remaining quantity = $100 - 25 = 75 \, kg$.
Remaining cost price = $2400 - 600 = Rs. \, 1800$.
Let the required profit percentage on the remaining stock be $P$.
Profit needed on remaining stock = $Rs. \, 480 + Rs. \, 30 = Rs. \, 510$.
$P = (510 / 1800) \times 100 = 510 / 18 = 28.33 \% = 28 \frac{1}{3} \%$.
Total desired profit = $20 \% \text{ of } 2400 = 0.20 \times 2400 = Rs. \, 480$.
Quantity sold at $5 \% \text{ loss} = 1/4 \times 100 \, kg = 25 \, kg$.
Cost price of $25 \, kg = 1/4 \times 2400 = Rs. \, 600$.
Loss on $25 \, kg = 5 \% \text{ of } 600 = 0.05 \times 600 = Rs. \, 30$.
Remaining quantity = $100 - 25 = 75 \, kg$.
Remaining cost price = $2400 - 600 = Rs. \, 1800$.
Let the required profit percentage on the remaining stock be $P$.
Profit needed on remaining stock = $Rs. \, 480 + Rs. \, 30 = Rs. \, 510$.
$P = (510 / 1800) \times 100 = 510 / 18 = 28.33 \% = 28 \frac{1}{3} \%$.
0 likes
View Solution150
DifficultMCQ
$A$ man buys $300$ dozen of bananas for $Rs. 3,600$. He sold $1/3$ of the stock at a loss of $10\%$ and the remaining $2/3$ of the stock at a gain of $10\%$. Find his overall percent profit or loss.
A
$\frac{10}{3}\%$ gain
B
$\frac{10}{3}\%$ loss
C
$\frac{14}{3}\%$ loss
D
$\frac{14}{3}\%$ gain
Solution
(A) Total cost price $(CP)$ = $Rs. 3,600$.
Cost price of $1/3$ of the stock = $\frac{1}{3} \times 3,600 = Rs. 1,200$.
Cost price of $2/3$ of the stock = $\frac{2}{3} \times 3,600 = Rs. 2,400$.
Selling price $(SP)$ of $1/3$ stock at $10\%$ loss = $1,200 \times (1 - 0.10) = 1,200 \times 0.9 = Rs. 1,080$.
Selling price $(SP)$ of $2/3$ stock at $10\%$ gain = $2,400 \times (1 + 0.10) = 2,400 \times 1.1 = Rs. 2,640$.
Total $SP = 1,080 + 2,640 = Rs. 3,720$.
Total profit = $Total SP - Total CP = 3,720 - 3,600 = Rs. 120$.
Overall profit percentage = $(\frac{Profit}{Total CP}) \times 100 = (\frac{120}{3,600}) \times 100 = \frac{1}{30} \times 100 = \frac{10}{3}\%$.
Since the result is positive,it is a gain of $\frac{10}{3}\%$.
Cost price of $1/3$ of the stock = $\frac{1}{3} \times 3,600 = Rs. 1,200$.
Cost price of $2/3$ of the stock = $\frac{2}{3} \times 3,600 = Rs. 2,400$.
Selling price $(SP)$ of $1/3$ stock at $10\%$ loss = $1,200 \times (1 - 0.10) = 1,200 \times 0.9 = Rs. 1,080$.
Selling price $(SP)$ of $2/3$ stock at $10\%$ gain = $2,400 \times (1 + 0.10) = 2,400 \times 1.1 = Rs. 2,640$.
Total $SP = 1,080 + 2,640 = Rs. 3,720$.
Total profit = $Total SP - Total CP = 3,720 - 3,600 = Rs. 120$.
Overall profit percentage = $(\frac{Profit}{Total CP}) \times 100 = (\frac{120}{3,600}) \times 100 = \frac{1}{30} \times 100 = \frac{10}{3}\%$.
Since the result is positive,it is a gain of $\frac{10}{3}\%$.
0 likes
View SolutionProfit and Loss — Profit and Loss · Frequently Asked Questions
1Are these Profit and Loss questions useful for JEE and NEET?
Yes. All questions in this section are mapped to JEE Main and NEET exam patterns. Previous year questions from JEE Main, NEET, GUJCET and state-level exams are included with full solutions.
2Can I switch to Hindi or Gujarati for these questions?
Yes. Use the language tabs in the hero section or the sidebar to view the same questions and solutions in English, Hindi or Gujarati.
3How do I generate a question paper from this subtopic?
Use the Vedclass Exam Paper Generator — select the chapter and subtopic, set difficulty, and generate Sets A, B, C, D automatically. First 3 chapters of every subject are free.
Vedclass Products
For Students
Vedclass Test Series
Mock tests in real JEE/NEET style with performance analysis. 5-day free trial.
Start Free TrialFor Teachers
Exam Paper Generator
Generate Set A/B/C/D papers from this chapter in 2 minutes. 3 chapters free.
Try FreeFor Institutes
Online Exam Module
Live online exams with unlimited students, 360° analytics & white-label branding.
See DemoFor Teachers & Institutes
Generate a Profit and Loss Exam Paper in 2 Minutes
Select subtopic & difficulty — Sets A, B, C, D auto-generated with No Repeat logic.
First 3 chapters of every subject are free — no payment required.