Discount (True and Banker’s) Questions in English

(B) Let the printed price of the book be $100$.
The bookseller gets a $30 \%$ commission from the publisher,so the cost price for the bookseller is $100 - 30 = 70$.
The bookseller allows a $10 \%$ discount on the printed price,so the selling price is $100 - 10 = 90$.
Profit = Selling Price - Cost Price = $90 - 70 = 20$.
Profit percentage = $(\frac{\text{Profit}}{\text{Cost Price}}) \times 100 = (\frac{20}{70}) \times 100 = \frac{200}{7} = 28 \frac{4}{7} \%$.

(C) Let the printed price $(M.P)$ be $Rs. 100$.
Since the retailer gets a discount of $40 \%$,the cost price $(C.P)$ for the retailer is $100 - 40 = Rs. 60$.
The retailer sells the article at the printed price,so the selling price $(S.P)$ is $Rs. 100$.
The gain is $S.P - C.P = 100 - 60 = Rs. 40$.
The gain percentage is calculated as $\frac{\text{Gain}}{C.P} \times 100$.
Gain $\% = \frac{40}{60} \times 100 = \frac{2}{3} \times 100 = 66\frac{2}{3} \%$.

(C) Given: Cost Price $(C.P.)$ = $Rs. 900$.
Desired profit percentage = $20\%$.
Selling Price $(S.P.)$ = $C.P. + \text{Profit} = 900 + (20\% \text{ of } 900) = 900 + 180 = Rs. 1080$.
Let the list price (Marked Price,$M.P.$) be $x$.
Discount allowed = $10\%$.
Therefore,$S.P. = M.P. - (10\% \text{ of } M.P.) = 90\% \text{ of } M.P. = 0.9x$.
Equating the $S.P.$ values: $0.9x = 1080$.
$x = \frac{1080}{0.9} = 1200$.
Thus,the list price is $Rs. 1200$.

(C) Let the marked price be $M.P$.
Given that the discount allowed is $20 \%$.
The selling price $(S.P)$ is calculated as $S.P = M.P \times (100 \% - \text{Discount} \%)$.
$S.P = M.P \times (100 \% - 20 \%) = M.P \times 80 \%$.
Given $S.P = Rs. 740$.
So,$740 = M.P \times 0.80$.
$M.P = \frac{740}{0.80} = \frac{74000}{80} = Rs. 925$.
Therefore,the marked price of the article is $Rs. 925$.

(B) Let the marked price be $x$.
Given that the discount is $15\%$,the selling price is $100\% - 15\% = 85\%$ of the marked price.
According to the problem,$85\% \text{ of } x = 119$.
$0.85 \times x = 119$.
$x = \frac{119}{0.85}$.
$x = \frac{11900}{85} = 140$.
Therefore,the marked price of the shirt before the discount was $Rs.\,140$.

(B) Let the marked price be $MP$.
Given that a discount of $Rs. 42$ is allowed,the selling price $(SP)$ is $SP = MP - 42$.
It is also given that the new reduced price is $86 \%$ of the marked price,so $SP = 0.86 \times MP$.
Equating the two expressions for $SP$:
$MP - 42 = 0.86 \times MP$
$MP - 0.86 \times MP = 42$
$0.14 \times MP = 42$
$MP = \frac{42}{0.14} = \frac{4200}{14} = 300$.
Thus,the marked price is $Rs. 300$.

(C) Let the marked price of the watch be $M.P.$
When the discount is $5 \%$,the selling price is $95 \% \text{ of } M.P. = 0.95 \times M.P.$
When the discount is $7 \%$,the selling price is $93 \% \text{ of } M.P. = 0.93 \times M.P.$
The difference in profit is given as $Rs. 15$,which corresponds to the difference in selling prices:
$(0.95 \times M.P.) - (0.93 \times M.P.) = 15$
$0.02 \times M.P. = 15$
$M.P. = \frac{15}{0.02} = \frac{1500}{2} = 750$
Therefore,the marked price of the watch is $Rs. 750$.

(B) Given that the profit is $Rs. 6000$,which corresponds to $25 \%$ of the cost price $(C.P.)$.
$25 \% \text{ of } C.P. = 6000$
$C.P. = \frac{6000 \times 100}{25} = Rs. 24000$
Now,the selling price $(S.P.)$ is $C.P. + \text{Profit} = 24000 + 6000 = Rs. 30000$.
The shopkeeper allows a $20 \%$ discount on the advertised price (marked price),meaning the selling price is $80 \%$ of the advertised price.
$0.80 \times \text{Advertised Price} = 30000$
$\text{Advertised Price} = \frac{30000}{0.80} = Rs. 37500$.

(B) Let the cost price $(C.P.)$ be $x$.
The marked price $(M.P.)$ is $30 \%$ above the cost price,so $M.P. = x + 0.30x = 1.30x$.
$A$ discount of $15 \%$ is allowed on the marked price,so the selling price $(S.P.)$ is $85 \%$ of $M.P.$
$S.P. = 0.85 \times 1.30x = 1.105x$.
Given that $S.P. = Rs. 910$,we have $1.105x = 910$.
$x = \frac{910}{1.105} \approx 823.53$.
Rounding to the nearest provided option,the cost price is approximately $Rs. 823.5$.

(D) For $A$: The discount on the first $Rs. 20,000$ is $8\%$. So,the price charged is $92\%$ of $20,000 = 0.92 \times 20,000 = Rs. 18,400$.
The discount on the remaining $Rs. 16,000$ is $5\%$. So,the price charged is $95\%$ of $16,000 = 0.95 \times 16,000 = Rs. 15,200$.
Total price charged by $A = 18,400 + 15,200 = Rs. 33,600$.
For $B$: The discount on the total price of $Rs. 36,000$ is $7\%$. So,the price charged is $93\%$ of $36,000 = 0.93 \times 36,000 = Rs. 33,480$.
Thus,the actual prices charged are $A = Rs. 33,600$ and $B = Rs. 33,480$.

(B) The discount offered is $25 \%$ of the price per metre.
Discount per metre $= 25 \% \text{ of } 32 = 32 \times \frac{25}{100} = Rs. 8$.
To get a total rebate of $Rs. 40$,the number of metres to be purchased is calculated by dividing the total required rebate by the discount per metre.
Number of metres $= \frac{40}{8} = 5 \text{ metres}$.

(C) The marked price of the watch is $Rs. 230$.
The discount percentage is $12 \%$.
The discount amount is calculated as: $12 \% \text{ of } 230 = \frac{12}{100} \times 230 = 27.6$.
The sale price (Selling Price) is calculated as: $\text{Marked Price} - \text{Discount} = 230 - 27.6 = 202.4$.
Alternatively,the sale price is $88 \% \text{ of } 230 = 0.88 \times 230 = 202.4$.
Therefore,the sale price of the watch is $Rs. 202.4$.

(B) Let the listed price of the article be $x$.
Given that the discount allowed is $15 \%$.
The selling price is the listed price minus the discount.
Selling Price $= x - (15 \% \text{ of } x) = x - 0.15x = 0.85x$.
We are given that the customer pays $Rs. 318.75$,so $0.85x = 318.75$.
$x = \frac{318.75}{0.85}$.
$x = 375$.
Therefore,the listed price of the article is $Rs. 375.00$.

(B) Given:
Marked Price $(MP)$ = $Rs.\, 7500$
Discount percentage = $6 \%$
The formula for Selling Price $(SP)$ is:
$SP = MP \times (1 - \frac{\text{Discount } \%}{100})$
Substituting the values:
$SP = 7500 \times (1 - \frac{6}{100})$
$SP = 7500 \times (1 - 0.06)$
$SP = 7500 \times 0.94$
$SP = 7050$
Thus,the selling price of the washing machine is $Rs.\, 7050$.

(D) The marked price $(M.P.)$ of the article is $Rs.\, 20,000$.
Two successive discounts of $7 \%$ each are applied.
The selling price $(S.P.)$ can be calculated as:
$S.P. = M.P. \times (1 - \frac{7}{100}) \times (1 - \frac{7}{100})$
$S.P. = 20,000 \times 0.93 \times 0.93$
$S.P. = 20,000 \times 0.8649$
$S.P. = 17,298$
Therefore,the selling price of the article is $Rs.\, 17,298$.

(B) Let the marked price of the article be $100$.
After the first discount of $a \%$,the price becomes $100 - a$.
After the second discount of $b \%$ on the remaining price,the discount amount is $\frac{b}{100} \times (100 - a) = b - \frac{ab}{100}$.
The total discount is the sum of the two discounts: $a + (b - \frac{ab}{100}) = a + b - \frac{ab}{100}$.
Therefore,the equivalent single discount is $\left(a + b - \frac{ab}{100}\right) \%$.

(C) Let the $C.P.$ (Cost Price) of the article be $Rs. 100$.
Since the article is marked $40 \%$ above the cost price, the Marked Price $(M.P.)$ $= 100 + 40 = Rs. 140$.
A discount of $30 \%$ is allowed on the marked price.
$S.P.$ (Selling Price) $= M.P. - (30 \% \text{ of } M.P.) = 140 - (0.30 \times 140) = 140 - 42 = Rs. 98$.
Since the $S.P.$ $(Rs. 98)$ is less than the $C.P.$ $(Rs. 100)$, there is a loss.
Loss $= C.P. - S.P. = 100 - 98 = Rs. 2$.
Loss percentage $= (\text{Loss} / C.P.) \times 100 = (2 / 100) \times 100 = 2 \%$.

(D) First,calculate the single equivalent discount for two successive discounts of $36 \%$ and $4 \%$.
Using the formula for successive discounts: $D_{eq} = (a + b - \frac{a \times b}{100}) \%$.
$D_{eq} = (36 + 4 - \frac{36 \times 4}{100}) \% = (40 - 1.44) \% = 38.56 \%$.
The difference between the single discount of $40 \%$ and the successive discounts of $38.56 \%$ is $40 \% - 38.56 \% = 1.44 \%$.
Now,calculate $1.44 \%$ of $Rs. 500$:
Difference $= \frac{1.44}{100} \times 500 = 1.44 \times 5 = Rs. 7.20$.

(D) Cost of one apple $= Rs. 25$.
Cost of $12$ apples (at the individual rate) $= 25 \times 12 = Rs. 300$.
Actual amount paid for a dozen $= Rs. 250$.
Discount amount $= 300 - 250 = Rs. 50$.
Percentage discount $= \frac{\text{Discount}}{\text{Original Price}} \times 100$.
Percentage discount $= \frac{50}{300} \times 100 = \frac{1}{6} \times 100 \approx 16.67 \%$.
Rounding to the nearest whole number,the approximate discount is $17 \%$.

(A) Let the marked price be $Rs.\, x$.
In the first case,with a single discount of $30 \%$,the selling price $(S.P._1)$ is:
$S.P._1 = x \times (1 - 0.30) = 0.70x$.
In the second case,with successive discounts of $20 \%$ and $10 \%$,the effective discount is calculated as:
Effective Discount $= 20 + 10 - \frac{20 \times 10}{100} = 30 - 2 = 28 \%$.
Therefore,the selling price $(S.P._2)$ is:
$S.P._2 = x \times (1 - 0.28) = 0.72x$.
The difference between the two selling prices is given as $Rs.\, 72$:
$0.72x - 0.70x = 72$
$0.02x = 72$
$x = \frac{72}{0.02} = \frac{7200}{2} = 3600$.
Thus,the marked price is $Rs.\, 3600$.

(B) Let the marked price be $100$.
After a $10 \%$ discount,the price becomes $100 - 10 = 90$.
After a $20 \%$ discount on $90$,the price becomes $90 - (0.20 \times 90) = 90 - 18 = 72$.
After a $30 \%$ discount on $72$,the price becomes $72 - (0.30 \times 72) = 72 - 21.6 = 50.4$.
The total discount is $100 - 50.4 = 49.6 \%$.
Alternatively,using the formula for two successive discounts $a$ and $b$: $D = a + b - (ab/100)$.
For $10 \%$ and $20 \%$: $10 + 20 - (10 \times 20 / 100) = 30 - 2 = 28 \%$.
For $28 \%$ and $30 \%$: $28 + 30 - (28 \times 30 / 100) = 58 - 8.4 = 49.6 \%$.