Question

A man sells two scooters for Rs. $12000$ each. He makes a profit of $20\%$ on one and a loss of $20\%$ on the other. The profit/ loss on the sell is
A. Loss $1000$rs
B. Profit $1000$rs
C. Loss $1200$rs
D. Profit $1200$rs

Answer 1

Hint: In the problem we have the selling prices of two scooters but we don’t have the cost price of the two scooters, so we will calculate the cost price of two scooters from the given profit percentage and loss percentage by using the known formulas. After getting the cost prices of two scooters we will calculate the profit and loss by checking the selling and cost price.

Complete step by step answer:
Given that,
Selling price of each scooter is Rs. $12000$.
Profit percentage on selling one scooter is $20\%$.
Let the cost price of the one scooter is Rs. $x$.
Now the profit on the scooter is given by $P=\text{Selling Price}-\text{Cost Price}=12000-x$.
Now the profit percentage is given by
$\begin{align}
  & P\%=\dfrac{P}{\text{Cost Price}}\times 100 \\
 & \Rightarrow P\%=\dfrac{12000-x}{x}\times 100 \\
\end{align}$
But the profit percentage is $20\%$, then
$\begin{align}
  & \dfrac{12000-x}{x}\times 100=20 \\
 & \Rightarrow \left( 12000-x \right)100=20x \\
 & \Rightarrow 1200000-100x=20x \\
 & \Rightarrow 120x=1200000 \\
 & \Rightarrow x=10000 \\
\end{align}$
Hence the cost price of the scooter on which seller got a $20\%$ profit is Rs. $10000$.
Given that, the seller got a $20\%$ loss on selling the second scooter. Let the cost price of the second scooter is Rs. $y$, then the loss is given by $L=\text{Cost Price}-\text{Selling Price}=y-12000$.
Now the loss percentage is
$\begin{align}
  & L\%=\dfrac{L}{\text{Cost Price}}\times 100 \\
 & \Rightarrow L\%=\dfrac{y-12000}{y}\times 100 \\
\end{align}$
But we have the loss percentage as $20\%$, then
$\begin{align}
  & \dfrac{y-12000}{y}\times 100=20 \\
 & \Rightarrow 100y-1200000=20y \\
 & \Rightarrow 100y-20y=1200000 \\
 & \Rightarrow y=15000 \\
\end{align}$
Hence the cost price of the second scooter on which the seller gets $20\%$ loss is Rs. $15000$.
Now the total selling price of two scooters is
$\begin{align}
  & {{S}_{t}}=12000+12000 \\
 & \Rightarrow {{S}_{t}}=24000 \\
\end{align}$
Now the total cost price of two scooters is
$\begin{align}
  & {{C}_{t}}=10000+15000 \\
 & \Rightarrow {{C}_{t}}=25000 \\
\end{align}$
Here we got the cost price is greater than selling price, so he will get loss by selling the scooters and the loss is given by
$\begin{align}
  & l={{C}_{t}}-{{S}_{t}} \\
 & \Rightarrow l=25000-24000 \\
 & \Rightarrow l=1000 \\
\end{align}$
So, the loss is Rs. $1000$.

So, the correct answer is “Option A”.

Note: We can directly calculate the cost price and selling price of the two scooters without calculating the loss and profit. Let $C.P$ is the cost price and $S.P$ is the selling price with profit percentage $P\%$, then we have the relations
$S.P=\dfrac{100+P\%}{100}\times C.P$ and $C.P=\dfrac{100}{100+P\%}\times S.P$.
Let $C.P$ is the cost price and $S.P$ is the selling price with loss percentage $L\%$, then we have the relations
$S.P=\dfrac{10-L\%}{100}\times C.P$ and $C.P=\dfrac{100}{100-L\%}\times S.P$. From the above formulas we can calculate the Selling Price and Cost Prices when there is a given profit percentage or loss percentage without calculating the profit and loss.