Question

A shopkeeper sells a badminton racket whose marked price is Rs 30 at a discount of $15\%$. A shuttle cock costing Rs 1.50 is given free with each racket. The shopkeeper makes a profit of $20\%$ so his cost price per racket is:
(a) Rs 19.75
(b) Rs 20
(c) Rs 21
(d) Rs 21.25

Answer 1

Hint: The marked price is given as Rs 30 at a discount of $15\%$ which means the selling price is equal to the multiplication of 30 with $\left( 100-15 \right)\%$. Now, it is also given that he hives shuttlecock free with a racket which costs Rs 1.50. So subtracting 1.50 from the selling price that we have calculated above will give the final selling price. It is also given that the shopkeeper makes a profit of $20\%$. So we are going to use the formula of profit, $\text{Profit}=\dfrac{\text{S}\text{.P}\text{.}-\text{C}\text{.P}\text{.}}{\text{C}\text{.P}\text{.}}\times 100$ where S.P. is the selling price and C.P. is the cost price. Solving this equation of profit will give you the value of C.P.

Complete step-by-step answer:
It is given that the marked price of the racket is Rs 30 at a discount of $15\%$. The shopkeeper sells it at a discount of $15\%$ so the selling price of the racket is calculated by multiplying 30 with $85\%$.
Selling price of the racket $=30\left( \dfrac{85}{100} \right)$
One zero will be cancelled out from the numerator and denominator of the above equation.
Selling price of the racket $=3\left( \dfrac{85}{10} \right)=\text{Rs }25.5$
Now, it is also given that the shopkeeper gives shuttle cock of Rs 1.5 as free with each racket so Rs 1.5 is the cost which bears by the shopkeeper so we have to subtract Rs 1.5 from the selling price of the racket that we have calculated above.
Selling price when the shuttle cost is given free $=\text{Rs}\left( 25.5-1.5 \right)=\text{Rs}24$
The shopkeeper has also earned a profit of $20\%$ so to calculate the cost price of 1 racket we are going to use the formula of a profit which is given below:
$\text{Profit}=\dfrac{\text{S}\text{.P}\text{.}-\text{C}\text{.P}\text{.}}{\text{C}\text{.P}\text{.}}\times 100$
In the above formula, S.P. is the selling price and C.P. is the cost price substituting S.P. as Rs 24 and profit as $20\%$ in the above formula we get,
$20=\dfrac{24-\text{C}\text{.P}\text{.}}{\text{C}\text{.P}\text{.}}\times 100$
On cross – multiplying the above equation we get,
$\begin{align}
  & 20\left( C.P. \right)=\left( 24-C.P. \right)\times 100 \\
 & \Rightarrow 20\left( C.P. \right)=2400-100\left( C.P. \right) \\
\end{align}$
Rearranging the above equation we get,
$\begin{align}
  & 100\left( C.P. \right)+20\left( C.P. \right)=2400 \\
 & \Rightarrow 120\left( C.P. \right)=2400 \\
\end{align}$
Dividing 120 on both the sides we get,
$\begin{align}
  & C.P.=\dfrac{2400}{120} \\
 & \Rightarrow C.P.=\text{Rs}20 \\
\end{align}$
The above calculation is giving the cost price of 1 racket is Rs 20.
Hence, the correct option is (b).

Note: The mistake that could happen in the above solution is that don’t consider the marked price as the selling price or the cost price because it is neither selling price nor cost price. Marked price is the price written on the racket which is not implying the shopkeeper is selling at this price because the shopkeeper is giving shuttlecock also free with racket which costs some money to the shopkeeper.
It has also observed that in the formula for profit usually students are forgetful to write 100 which is given below:
$\text{Profit}=\dfrac{\text{S}\text{.P}\text{.}-\text{C}\text{.P}\text{.}}{\text{C}\text{.P}\text{.}}\times 100$
So, make sure you don’t make such mistakes.