Question

A man marks his goods at a price that would give him $20\%$ profit. He sells $\frac{3}{5}$ of the goods at the marked price and sells the remaining at $20\%$ discount. Find his gain percent on the whole transaction.

• A. $10.4\%$
• B. $12.7\%$
• C. $15.6\%$
• D. $14.36\%$

Answer 1

The correct option is A $10.4\%$

Let cost price (CP) of goods = X Rs

Since, marked price (MP) would give 20% profit.

$\therefore MP=CP+20\%ofCP=X+20\%ofX=1.2X$

Now, $\frac{3}{5}th$ of the goods sold at Marked price.

So, Selling price of $\frac{3}{5}th$ of goods = $\frac{3}{5}\times MP=\frac{3}{5}\times 1.2X=0.72X$

Remaining $(1-\frac{3}{5}=\frac{2}{5}th)$ is sold at 20% discount.

So, Selling price of $\frac{2}{5}th$ of goods $=\frac{2}{5}\times MP-20\%of(\frac{2}{5}\times MP)$

$=\frac{2}{5}\times 1.2X-0.2\times \frac{2}{5}\times 1.2X$

$=0.48X-0.096X=0.384X$

So, Total Selling Price (SP) $=0.72X+0.384X=1.104XRs$

$\therefore Profit=SP-CP=1.104X-X=0.104XRs$

$\Rightarrow Profitpercentage=\frac{profit\times 100}{CP}=\frac{0.104X\times 100}{X}=10.4\%$