Question

A man bought two old scooters for Rs. $18000$. By selling one at a profit of $25\%$ and the other at a loss of $20\%$, he neither gains nor loses. Find the cost price of each scooter.

• A. $12000,6000$
• B. $8000,10000$
• C. $11000,7000$
• D. $13000,5000$

Answer 1

The correct option is B $8000,10000$

Let the C.P. of the $1^{st}$ scooter $=$ Rs. $x$.

Then, C.P. of the $2^{nd}$ scooter $=$ Rs. $(18000-x)$

By selling one scooter he gets $25\%$ profit, then
S.P. of $1^{st}$ scooter $=$ Rs. $x\times \frac{125}{100}=$ Rs. $\frac{5x}{4}$

By selling $2^{nd}$ scooter he gets $20\%$ loss, then S.P. of $2^{nd}$ scooter $=$ Rs. $(18000-x)\times \frac{80}{100}$
$=$ Rs. $\frac{4}{5}(18000-x)$
Since Mohan neither gains nor loses, his
Total S.P. $=$ Total C.P.
$\Rightarrow \frac{5x}{4}+\frac{4}{5}(18000-x)=18000$
$\Rightarrow \frac{5x}{4}-\frac{4x}{5}=18000-14400=3600$
$\Rightarrow \frac{25x-16x}{20}=3600$

$\Rightarrow 9x=3600\times 20$
$\Rightarrow x=\frac{3600\times 20}{9}=8000$
$\therefore$ C.P. of 1st scooter $=$ Rs. $8000$
C.P. of $2^{nd}$ scooter $=18000-8000=$ Rs. $10,000$.