Question

On selling each of the two radios for Rs. $5000$ a person neither gained nor lost. If he had sold one radio at $25\%$ gain, then at what percent loss did she sell the $2^{nd}$ radio

• A. $16\frac{2}{3}$ $\%$
• B. $18\frac{2}{9}$ $\%$
• C. $25\%$
• D. $26\frac{2}{3}$ $\%$

Answer 1

Answer: (A)

$16\frac{2}{3}$ $\%$

$1^{st}$ radio S.P. $=$ Rs. $5000$

Gain $=25\%$

$\therefore$ C.P $=$ Rs.$\frac{5000\times 100}{125}=$ Rs. $4000$
$2^{nd}$ radio S.P. $=$ Rs. $5000$, Loss $=x\%$ (say)

$\therefore$ C.P. $=\frac{5000\times 100}{(100-x)}$
Since the person neither gained nor lost Total C.P. $=$ Total S.P
$\Rightarrow 4000+\frac{500000}{(100-x)}=10000$
$\Rightarrow \frac{500000}{(100-x)}=6000\Rightarrow 500000=600000-6000x$
$\Rightarrow 6000x=100000$

$\Rightarrow x=\frac{100}{60}\%=\frac{50}{3}\%=16\frac{2}{3}\%$