Question

A man marks his goods at a price that would give him 20% profit. He sells $\frac{1}{5}$ of the goods at the marked price and sells the remaining at $20\%$ discount. Find his gain per cent on the whole transaction.

• A. $0.8$%
• B. $0.7$%
• C. $0.6$%
• D. $0.5$%

Answer 1

The correct option is A $0.8$%

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, $\frac{1}{5}th$ of the goods sold at Marked price.

So, Selling price of $\frac{1}{5}th$ of goods = $\frac{1}{5}\times MP=\frac{1}{5}\times 1.2X=0.24X$

Remaining $(1-\frac{1}{5}=\frac{4}{5}th)$ is sold at 20% discount.

So, Selling price of $\frac{4}{5}th$ of goods $=\frac{4}{5}\times MP-20\%of(\frac{4}{5}\times MP)$

$=\frac{4}{5}\times 1.2X-0.2\times \frac{4}{5}\times 1.2X$

$=0.96X-0.192X=0.768X$

So, Total Selling Price (SP) $=0.24X+0.768X=1.008XRs$

$\therefore Profit=SP-CP=\mathrm{1..008}X-X=0.008XRs$

$\Rightarrow Profitpercentage=\frac{profit\times 100}{CP}=\frac{0.008X\times 100}{X}=0.8\%$