Question

A man sells a TV at a profit of $25\%$ of the cost. Had he sold it at a profit of $25\%$ of the selling price his profit would have increased by $5\%$ of the cost price plus Rs. $100$. Find the cost of the TV?

• A. Rs. $6000$
• B. Rs. $8000$
• C. Rs. $10000$
• D. Rs. $7500$

Answer 1

The correct option is B Rs. $8000$

Let the C.P of the TV $=$ $x$ when $x$ is in Rs.

$\therefore$ $25\%$ profit $=$ $x\times \frac{25}{100}=\frac{x}{4}$ and the S.P. $=$ $x+\frac{x}{4}=\frac{5x}{4}$.

In the second case, by the given condition, the profit is $25\%$ of $\frac{5x}{4}$

$=$ $\frac{5x}{4}\times \frac{25}{100}=\frac{5x}{16}$.

$\therefore$ The difference in profits $=$ $\frac{5x}{16}-\frac{x}{4}=\frac{x}{16}$.

Now $5\%$ of the C.P. $+$ Rs. $100=$ $x\times \frac{5}{100}+100=\frac{x}{20}+100.$

So, by the given condition, we have

$\frac{x}{16}=\frac{x}{20}+100$

$\Rightarrow \frac{x}{16}-\frac{x}{20}=100$

$\Rightarrow \frac{x}{80}=100$

$\Rightarrow x=$ Rs. $8000$

So,the cost price of the TV $=$ Rs. $8000$

Ans- Option B.