Question

The percentage of loss when an article is sold at Rs. $50$ is the same as that of the profit when it is sold at Rs. $70$. The above mentioned percentage of profit or loss on the article is

• A. $10\%$
• B. $12\%$
• C. $16\frac{2}{3}\%$
• D. $8\frac{1}{3}\%$

Answer 1

The correct option is C $16\frac{2}{3}\%$

Let the percentage of profit or loss on the article be $x$.
C.P. at $x\%$ loss when S.P. is Rs. $50$ $=$ Rs. $\frac{50\times 100}{(100-x)}$

C.P. at $x\%$ profit when S.P. is Rs. $70$ $=$ Rs. $\frac{70\times 100}{(100+x)}$

$\therefore \frac{50\times 100}{(100-x)}=\frac{70\times 100}{(100+x)}$

$\Rightarrow 5(100+x)=7(100-x)$
$\Rightarrow 500+5x=700-7x\Rightarrow 12x=200$
$\Rightarrow x=\frac{200}{12}=16\frac{2}{3}\%$