Question

A man bought goods worth Rs. $6000$ and sold half of them at a gain of $10\%$. At what gain per cent must the sell the remainder to get a gain of $25\%$ on the whole?

• A. $40\%$
• B. $30\%$
• C. $25\%$
• D. $20\%$

Answer 1

The correct option is A $40\%$

C.P. of $1^{st}$ half of goods $=\frac{1}{2}\times 6000=$ Rs. $3000$
S.P. of $1^{st}$ half of the goods $=\frac{110}{100}\times 3000=$ Rs. $3300$
C.P. of $2^{nd}$ half of goods $=$ Rs. $3000$
Let profit $\%$ $=x$
Then, S.P. of $2^{nd}$ half of goods $=\left(\frac{100+x}{100}\right)\times 3000$
Total CP. $=$ Rs. $6000$, Total gain $=25\%$
$\therefore$ Total S.P. $=\frac{125}{100}\times 6000=$ Rs. $7500$
Given, $3300+30(100+x)=7500$
$\Rightarrow 30(100+x)=4200$
$\Rightarrow 100+x=140$
$\Rightarrow x=40\%$