Question

Subhash purchased a tape recorder at ${{\left( \dfrac{9}{10} \right)}^{th}}$ of its selling price and sold it at 8% more than its S.P. His gain percent is
(A) 8%
(B) 10%
(C) 18%
(D) 20%

Answer 1

Hint: We solve this problem by first assuming the selling price of the tape recorder as S. Then we find the cost price of the tape recorder as it is equal to ${{\left( \dfrac{9}{10} \right)}^{th}}$ of its selling price.

Complete step by step answer:
Then we find the new selling price of the tape from the given information. Then we find the profit for selling it using the formula $\text{Profit}=S.P-C.P$ and then use the formula $\text{Gain Percent}=\dfrac{\text{Profit}}{C.P}\times 100$ to find the gain percent.
We are given that Subhash purchased a tape recorder at ${{\left( \dfrac{9}{10} \right)}^{th}}$ of its selling price.
Let us assume that the S.P, that is Selling price of the tape recorder is S.
As he bought the tape recorder at ${{\left( \dfrac{9}{10} \right)}^{th}}$ of its selling price, we get
$C.P=\dfrac{9}{10}\times S.P$
So, substituting the value of S we get,
$\Rightarrow C.P=\dfrac{9}{10}\times S=\dfrac{9S}{10}$
We are also given that then he sold the tape recorder at the cost 8% more than the selling price.
We know that the selling price is S. Then as he sold it at the cost 8% more than the selling price, the new selling price becomes,
$\begin{align}
  & \Rightarrow S.P=S+\left( \dfrac{8}{100}\times S \right) \\
 & \Rightarrow S.P=S+\dfrac{8S}{100} \\
 & \Rightarrow S.P=\dfrac{108S}{100} \\
\end{align}$
As he sold the tape recorder after buying it, the Cost Price of the tape recorder is
$\Rightarrow C.P=\dfrac{9S}{10}$
Now we need to find the percentage gain.
Let us consider the formula for gain percent,
$\text{Gain Percent}=\dfrac{\text{Profit}}{C.P}\times 100$
First, we need to find the profit for selling so let us consider the formula for profit,
$\text{Profit}=S.P-C.P$
Using this formula, we get the value of profit as,
$\begin{align}
  & \Rightarrow \text{Profit}=\dfrac{108S}{100}-\dfrac{9S}{10} \\
 & \Rightarrow \text{Profit}=\dfrac{108S}{100}-\dfrac{90S}{100}=\dfrac{18S}{100} \\
 & \Rightarrow \text{Profit}=\dfrac{9S}{50} \\
\end{align}$
Substituting the obtained value of profit in the above formula for gain percent, we can find the gain percent as,
$\begin{align}
  & \Rightarrow \text{Gain Percent}=\dfrac{\dfrac{9S}{50}}{\dfrac{9S}{10}}\times 100 \\
 & \Rightarrow \text{Gain Percent}=\dfrac{10}{50}\times 100 \\
 & \Rightarrow \text{Gain Percent}=20\% \\
\end{align}$
Hence, we get gain percent equal to 20%.
Hence, the answer is Option D.

Note:
 The common mistake that happens while solving this question is many people take the formula for gain percent wrong. Most people take the formula for gain percent as $\text{Gain Percent}=\dfrac{\text{Profit}}{S.P}\times 100$. But it is wrong as the denominator for the gain percent is C.P not S.P. The correct formula is $\text{Gain Percent}=\dfrac{\text{Profit}}{C.P}\times 100$.