Question

By selling a watch for Rs.$480$a man gains $25\%$ How much percent would he gain by selling it for Rs.$432$?
A. $15\%$
B. $6\dfrac{1}{4}\%$
C. $12\dfrac{1}{2}\%$
D. $25\%$

Answer 1

Hint: We will solve this problem in two parts.
In the first part we will find the Cost Price of Watch by using the selling Price and the percentage of Profit.
In the second part we will find the profit percentage by using the cost price obtained in the part one, the selling price of the watch.
We will use the below formulas in this problem when they are required.
Profit $=$Selling Price $-$Cost price.
Profit Percentage $=\dfrac{\text{Profit}}{\text{Cost Price}}\times 100$

Complete step by step answer:
Given that, the selling price of the watch is $\text{S}\text{.P}=480$
Let the Cost Price is $\text{C}\text{.P}=x$, then the profit is
$\begin{align}
  & \text{P}=\text{S}\text{.P}-\text{C}\text{.P} \\
 & =\text{480}-x
\end{align}$
Now the profit percentage is
$\begin{align}
  & \text{Profit Percentage}=\dfrac{\text{Profit}}{\text{Cost Price}}\times 100 \\
 & =\dfrac{480-x}{x}\times 100
\end{align}$
But in the problem, they mentioned profit percentage as $25\%$, then
$\begin{align}
  & \Rightarrow \dfrac{480-x}{x}\times 100=25 \\
 & \Rightarrow 480\times 100-100x=25x \\
 & \Rightarrow 100x+25x=480\times 100 \\
 & \Rightarrow x=\dfrac{480\times 100}{125} \\
 & \Rightarrow x =384
\end{align}$
So, the cost price of the watch is Rs.$384$. This is the end of the first part. Now we are going to the second part where we have to calculate the profit percentage.
Given that, the selling price is Rs.$432$
The profit is
$\begin{align}
  & \text{P}=\text{S}\text{.P}-\text{C}\text{.P} \\
 & \Rightarrow \text{P} =432-384 \\
 &\Rightarrow \text{P} =48
\end{align}$
Now the percentage of profit is
$\begin{align}
  & \text{P }\!\!\%\!\!\text{ }=\dfrac{\text{P}}{\text{C}\text{.P}}\times 100 \\
 &\Rightarrow \text{P }\!\!\%\!\!\text{ }=\dfrac{48}{384}\times 100 \\
 &\Rightarrow \text{P }\!\!\%\!\!\text{ }=12.5
\end{align}$

Hence the profit percentage is $12.5\%=12\dfrac{1}{2}\%$

Note: Here we have used the terms Cost Price, Selling Price, Profit. They are defined as below
Cost Price (CP): The cost price is the amount of money spent on making the product. For example, if Leela is making cotton skirts, the amount of money spent on getting the cotton fabric, buttons, and other materials are referred to as the cost price.
Selling Price (SP): After investing in making a product, a businessman always aims to earn more than what he spent. So, in this case, Leela is selling her skirts at a price above her cost price. The cost at which the product is sold is called Selling Price. It is the price the customer (buyer) pays for the product.
Profit (P): In math, profit is the difference between the selling price and the cost price. But only if the SP > CP, then there is a profit.
Profit percentage: We can write profit percentage as
Profit Percentage $=\dfrac{\text{Profit}}{\text{Cost Price}}\times 100$