Question

A man sells a TV set for $Rs.6,900$ and makes a profit of $15\%.$ He sells a second TV set at a loss of $10\%.$ If on the whole, he neither gains nor loses, find the cost price of the second TV set.

• A. $Rs.9,000$
• B. $Rs.10,000$
• C. $Rs.11,000$
• D. $Rs.12,000$

Answer 1

The correct option is A $Rs.9,000$

For first TV:
$SP=Rs.6,900$
$\text{Profit}=15\%$

Now, with this $SP$,

$\text{Profit}\%=\frac{SP-CP}{CP}\times 100$

$\Rightarrow 15=\frac{6900-CP}{CP}\times 100$

$\Rightarrow 6,900-CP=0.15CP$

$\Rightarrow 1.15CP=6900$

$\Rightarrow CP=Rs.6000$

Let the cost price of the second TV be $x$ and it is given that there is a loss of $10\%$

So,

$\text{Loss}\%=\frac{CP-SP}{CP}\times 100$

$\Rightarrow 10=\frac{x-SP}{x}\times 100$

$\Rightarrow x-SP=0.10x$

$\Rightarrow 0.9x=SP\dots \left(i\right)$

Given, there is no profit or loss in the whole transaction that means total sales are equal to the total cost price of TV sets. So,

Total $SP=$ Total $CP$

$\Rightarrow 6900+0.9x=6000+x$ [From equation $\left(i\right)$]

$\Rightarrow 6900-6000=x-0.9x$

$\Rightarrow 900=0.1x$

$\Rightarrow x=Rs.9000$

Thus, the cost price of the second TV is $Rs.9,000.$