Question

A man purchased a scooter for Rs. 6250 and sold it at 8% profit. He purchased another scooter for Rs. 3750. After selling it he found that he has gained 2% on the whole. Then in the sale of the second scooter, he has
a) 8% loss
b) 8% gain
c) 10% gain
d) 6% loss

Answer 1

Hint: We are having the cost price of scooter 1 as $C{{P}_{1}}=Rs.6250$ with 8% profit. By using the formula for % profit: $\%profit=\dfrac{SP-CP}{CP}\times 100$, find the selling price of scooter 1. Also, we have the cost price of scooter 2 as $C{{P}_{2}}=Rs.3750$, and the net % profit is 2%. So, by using the % profit formula for a net gain, find the total selling price of both the scooters, where CP is the total cost price of scooters. Now, subtract the selling price of scooter 1 from the total selling price to get the selling price of scooter 2. Now, check if the selling price of scooter 2 is greater than the cost price. If yes then apply % profit formula else apply % loss formula: $\%loss=\dfrac{CP-SP}{CP}\times 100$.

Complete step-by-step solution:
As we have:
The cost price of scooter 1 is $C{{P}_{1}}=Rs.6250$
The Selling price of scooter 1 is $S{{P}_{1}}$
% profit on scooter 1 = 8%
So, by applying % profit formula $\%profit=\dfrac{SP-CP}{CP}\times 100$ for scooter 1, we have:
$\begin{align}
  & \Rightarrow \dfrac{S{{P}_{1}}-6250}{6250}\times 100=8 \\
 & \Rightarrow S{{P}_{1}}-6250=500 \\
 & \Rightarrow S{{P}_{1}}=Rs.6750......(1) \\
\end{align}$
Now, we have cost price of scooter 2 is $C{{P}_{2}}=Rs.3750$
So, total cost price of both scooters is:
$\begin{align}
  & CP=C{{P}_{1}}+C{{P}_{2}} \\
 & =6250+3750 \\
 & =Rs.10000
\end{align}$
Also, % profit for both scooters is 2 %
So, by applying % profit formula for both the scooters, we get total selling price of scooters as:
$\begin{align}
  & \Rightarrow \dfrac{SP-10000}{10000}\times 100=2 \\
 & \Rightarrow SP-10000=200 \\
 & \Rightarrow SP=Rs.10200 \\
\end{align}$
So, we can say that, selling price of scooter 2 is:
$\begin{align}
  & SP=S{{P}_{1}}+S{{P}_{2}} \\
 & S{{P}_{2}}=SP-S{{P}_{1}} \\
 & =10200-6750 \\
 & =Rs.3450
\end{align}$
Since selling price of scooter 2 is less than cost price of scooter 2, so we will % loss.
So, by applying % loss formula for scooter 2, we get:
$\begin{align}
  & \%loss=\dfrac{3750-3450}{3750}\times 100 \\
 & =\dfrac{300}{3750}\times 100 \\
 & =8\%
\end{align}$
Hence, option (a) is the correct answer.

Note: While applying % profit or % loss formula, always remember that gain or loss has to be divided by cost price only. Students might think to use the selling price instead of the cost price in the denominator but that would be wrong as loss and profit percentage always calculated respect to cost price unless it is not given in the problem to find this w.r.t selling price.