Question

A man sells two scooters at $\text{Rs.}36000$ each. On one scooter he makes $15\%$ profit and on the other, he makes $15\%$ loss. Find the profit or loss percentage in the whole transaction.

• A. $2.25\%$ Loss
• B. $2.25\%$ Profit
• C. $22.5\%$ Loss
• D. $22.5\%$ Profit

Answer 1

The correct option is A $2.25\%$ Loss

Let the CP for the first and second scooter be $x$ and $y$ respectively.

For the first scooter,
$SP=\text{Rs.}36,000$

$CP=x$
$Profit=15\%$

$\begin{array}{cc}\frac{SP-CP}{CP}\times 100& =15\\ \frac{36,000-x}{x}\times 100& =15\\ 36,000-x& =0.15x\\ 1.15x& =36,000\\ x& =\frac{36000}{1.15}\\ & =\frac{7,20,000}{23}\end{array}$
For the second article,
$SP=\text{Rs.}36,000$

$CP=y$

$Loss=15\%$

$\begin{array}{cc}\frac{CP-SP}{CP}\times 100& =15\\ \frac{y-36,000}{y}\times 100& =15\\ y-36,000& =0.15y\\ 0.85y& =36,000\\ y& =\frac{36,000}{0.85}\\ & =\frac{7,20,000}{17}\end{array}$
So, Total SP of the two articles $=\text{Rs.}36,000+\text{Rs.}36,000$

$=\text{Rs.}72,000$

Total CP of the two articles $=\text{Rs.}\frac{7,20,000}{23}+\text{Rs.}\frac{7,20,000}{17}$

$=\text{Rs.}\frac{2,88,00,000}{17\times 23}$

$=\text{Rs.}73,657.29$
The total $CP>SP$, there is a loss

So,

$\begin{array}{cc}Loss& =\frac{CP-SP}{CP}\times 100\\ & =\frac{73,657.29-72,000}{73,657.29}\times 100\\ & =2.25\%\end{array}$