Question

A shopkeeper sells a badminton racket whose marked price is $Rs.30$ at a discount of $15\%$ and gives a shuttlecock costing $Rs.1.50$ free with each racket. Even then he makes a profit of $20\%$. His cost price per racket is
(a) $Rs.21$
(b) $Rs.21.25$
(c) $Rs.20$
(d) $Rs.19.75$

Answer 1

Hint: We know that profit is given by the formula, $\%\text{Profit=}\dfrac{S.P.-C.P.}{C.P.}$and discount is given on the marked prize. So, we will find the selling price of the racket and then we will deduct the price of the shuttlecock and whatever is remaining from that we will find the cost price based on that.

Complete step by step answer:
Now, in question we are given that the marked price of racket is $Rs.30$ so, it can be shown mathematically as,
$M.P=30$
Now, it is given that shopkeeper gives $15\%$ discount so the selling price can be given as,
$S.P.=\dfrac{\left( 100-15 \right)}{100}\times 30$
$S.P.=\dfrac{85}{100}\times 30=Rs.25.50$
Now, the selling price of racket alone is $Rs.25.50$, but shopkeeper also gives a shuttle cock of $Rs.1.50$ free, so the final selling price can be given as,
$S.P.=25.50-1.50=Rs.24$
Now, even on selling it with discount the shopkeeper earns a profit of $20\%$, so from that we will find the cost price by using the formula of profit which can be given as,
$\%\text{Profit=}\dfrac{S.P.-C.P.}{C.P.}$
Substituting the values, we will get,
$20\%\text{=}\dfrac{24-C.P.}{C.P.}\Rightarrow \dfrac{20}{100}\text{=}\dfrac{24-C.P.}{C.P.}$
$\Rightarrow 20C.P.=\left( 24 \right)\left( 100 \right)-100C.P.$
$\Rightarrow 20C.P.+100C.P.=2400$
$\Rightarrow C.P.=\dfrac{2400}{120}=Rs.20$
Thus, the cost price of badminton is $Rs.20$.
Hence, option (c) is the correct answer.


Note: Students should always remember Marked price is the price of the product which is labelled by the shopkeeper it is also known as maximum retail price M.R.P. A shopkeeper always gives a discount on marked up price and he would never give on the cost price in order to earn some profit. So, students must take care about this while solving the problem because they might calculate a discount on the cost price and due to that the problem will go wrong.