Question

A publisher gives his distributor a discount of $30\%$ on the printed price of the books. The distributor sells those books to a bookseller at $20\%$ discount on the printed price and the bookseller sells these books at the printed price. Calculate the profit percent made by the distributor?
(a) $11\dfrac{1}{7}\%$
(b) $14\dfrac{2}{7}\%$
(c) $17\dfrac{1}{7}\%$
(d) $20\dfrac{2}{7}\%$

Answer 1

Hint: Let us assume that the printed price of the book is Rs 100. Now, as the publisher gives the distributor at the discount of $30\%$ so find the amount that distributor has to give to the publisher by subtracting $30\%$of 100 from 100. This will be the cost price. Now, the distributor sells those books to the bookseller with a discount of $20\%$ so the selling price of the books for the distributor is to subtract $20\%$ of 100 from 100. After solving the selling price and cost price of the distributor see whether the selling price is greater or smaller than cost price accordingly use the formula for profit or loss percentage.

Complete step by step answer:
Let us assume that the printed price on the book is Rs 100.
A publisher gives his distributor a discount of $30\%$ on the printed price so the cost price for the distributor is calculated by subtracting $30\%$ of 100 from 100.
Cost price of the books for the distributor is equal to:
$\begin{aligned} & 100-\left( \dfrac{30}{100} \right)100 \\\ & =100\left( 1-\dfrac{30}{100} \right) \\\ \end{aligned}$
$\begin{aligned} & =100\left( \dfrac{100-30}{100} \right) \\\ & =100\left( \dfrac{70}{100} \right) \\\ & =70 \\\ \end{aligned}$
Hence, the cost price of the books for distributors is Rs 70.
Now, the distributor sells those books to the bookseller with a discount of $20\%$ so the selling price of the books for the distributor is calculated by subtracting $20\%$ of 100 from 100.
Selling price of the books for the distributor is equal to:
$\begin{aligned} & 100-\left( \dfrac{20}{100} \right)100 \\\ & =100-20 \\\ & =80 \\\ \end{aligned}$
Hence, the selling price of the books for the distributor is Rs 80.
As you can see, the selling price is greater than the cost price so profit has been incurred for the distributor.
We know that the formula for profit percentage is equal to:
$\text{Profit}=\dfrac{S.P.-C.P.}{C.P.}\times 100$
In the above formula, S.P. is the selling price and C.P. is the cost price. Substituting S.P. as Rs 80 and cost price as Rs 70 in the above formula we will get the profit percentage.
$\begin{aligned} & \text{Profit}=\dfrac{80-70}{70}\times 100 \\\ & \Rightarrow \text{Profit}=\dfrac{10}{70}\times 100 \\\ & \Rightarrow \text{Profit}=\dfrac{100}{7}\% \\\ \end{aligned}$
We are getting the answer in proper fraction but the options are given in improper fraction so converting this proper fraction into improper fraction we get the profit percentage as:
$14\dfrac{2}{7}\%$
Hence, the correct option is (b).

Note: Instead of assuming the printed price as Rs 100, you can also assume the printed price as Rs x. But assuming the printed price as 100 will reduce the calculations because when we apply the discount of $20\%\And 30\%$ then it will be easy to calculate $20\%$ of 100 and $30\%$ of 100 as compared to $20\%$ of x and $30\%$ of x. And as 100 is the whole number and this is something we deal in our everyday life so the calculations will become quicker.