Question

A man has $60$ pens. He sells some of these at a profit of $12$ $\%$ and the rest at $8$ $\%$ loss. On the whole, he gets a profit of $11$ $\%.$ How many pens were sold at $12$ $\%$ profit:

• A. $47$
• B. $52$
• C. $55$
• D. $57$

Answer 1

The correct option is D $57$

Let us assume that he sells $x$ pens for a profit of $12\%$ and hence $(60-x)$ pens at a loss of $8\%$

Let $C.P$ of a pen be $Rs.1$.

Profit Loss

$CP=x$ $CP=60-x$

$P\%=12\%L\%=8\%$

$SP=CP\left(\frac{100+P\%}{100}\right)SP=(60-x)\left(\frac{100-8}{100}\right)$

$SP=x\left(\frac{100+12}{100}\right)=\frac{92(60-x)}{100}$

$=\frac{112x}{100}=\frac{28x}{25}\frac{23(60-x)}{25}$

Overall

$CP=x+60-x=60$.

$SP=\frac{28x+23(60-x)}{25}=\frac{1380+5x}{25}$

$P\%=\frac{x-24}{5.60}\times 100=11\frac{x-24}{3}=11$

$x-24=33\Rightarrow x=24+33=57$

Hence $57$ pens were sold at a profit $12\%$