Question

A shopkeeper earns a profit of \[15\%\] after selling a book at $20\%$ discount on the printed price. Find the ratio of the cost price and the printed price of the book?
(a) $16:23$,
(b) $20:23$,
(c) $23:16$,
(d) $23:20$.

Answer 1

Hint: We start solving the problem by assigning the variables for the cost, printed and selling prices of the book. We then find the selling price of the book using the information that the shopkeeper sold $20\%$ less than the printed price of the book. We then use the information that shopkeeper got $15\%$ profit after selling and use the fact that $profit\%=\dfrac{selling\ price-\text{cost } price}{\operatorname{cost } price}\times 100$ to get the required ratio after making necessary calculations.

Complete step-by-step answer:
According to the problem, we have given that the shopkeeper earns a profit of \[15\%\] after selling a book at $20\%$ discount on the printed price. We need to find the ratio of the cost price and the printed price of the book.
Let us assume the cost price, printed price and the selling price be c, p and s.
According to the problem, we have given that the selling price is $20\%$ less than the printed price.
So, we get the selling price = $\left( 100-20 \right)\%$ of printed price.
$\Rightarrow $Selling price = $80\%$ of printed price.
We know that $x\%$ of y = $\dfrac{x}{100}\times y$.
$\Rightarrow s=\dfrac{80}{100}\times p$.
$\Rightarrow s=0.8p$---(1).
According to the problem, we are given that the shop keeper earned a profit of $15\%$ on selling the book at a price of $0.8p$.
We know that $profit\%=\dfrac{selling\ price-\text{cost } price}{\operatorname{cost} price}\times 100$.
So, we get $15\%=\dfrac{0.8p-c}{c}\times 100$.
$\Rightarrow 0.15=\dfrac{0.8p}{c}-1$.
$\Rightarrow 1.15=\dfrac{0.8p}{c}$.
$\Rightarrow \dfrac{c}{p}=\dfrac{0.8}{1.15}$.
$\Rightarrow \dfrac{c}{p}=\dfrac{80}{115}$.
$\Rightarrow \dfrac{c}{p}=\dfrac{16}{23}$.
So, we have found the ratio of cost price and printed price of the book as $16:23$.

So, the correct answer is “Option (a)”.

Note: We can see that there are high chances of making mistakes while solving this problem. So, we need to solve each step properly in order to avoid the mistakes. We can also find the total amount profit gained by the shopkeeper after getting the ratio between cost price and the printed price, as we are taking all the values in terms of printed price. Similarly, we can also expect problems to find the selling price and price of the book.