Question

How much percent above the cost price should a shopkeeper mark his goods so that after allowing a discount of $20\%$ on the marked price, he still has a gain of $10\%$?

• A. $10\%$
• B. $25.5\%$
• C. $30\%$
• D. $37.5\%$

Answer 1

The correct option is D $37.5\%$

Let the cost price of the good be $\text{Rs.}100.$
Selling price when profit is $10\%=(100+\frac{10}{100}\times 100)=\text{Rs.}110$

Let the marked price is $\text{Rs.}x.$
After giving a discount of $20\%$ , the new selling price $=x-\left(\frac{20x}{100}\right)$
The shopkeeper gains $10\%$ after giving the discount. Thus,
$[x-\left(\frac{20x}{100}\right)]=110$
$\Rightarrow \frac{4x}{5}=110$
$\Rightarrow x=\frac{110\times 5}{4}$

$\Rightarrow x=\text{Rs.}137.5$

So. this implies that the marked price of the good is equal to $\text{Rs.}\mathrm{137.5.}$
Hence, the required increase $\text{Rs.}137.5-\text{Rs.}100=\text{Rs.}37.5$.

Or we can say that the required marked price should be $\text{Rs.}37.5\%$ more than that of the cost price.