Question

By selling an item for Rs. 24, the shopkeeper earns the percent profit equal to cost price of the item. Find the cost price of the item.

• A. Rs. 120
• B. Rs. 60
• C. Rs. 45
• D. Rs. 20

Answer 1

The correct option is D

Rs. 20

Let the cost price be $x$
Profit on the item is $24-x$

Profit % = $\frac{S.P-C.P}{C.P}\times 100$

=$\frac{24-x}{x}\times 100$

Given that the profit percentage is equal to the cost price.

$\Rightarrow \frac{24-x}{x}\times 100=x$
$\Rightarrow x^2=2400-100x$
$\Rightarrow x^2-2400+100x=0$
$\Rightarrow x^2+120x-20x-2400=0$
$\Rightarrow (x+120)(x-20)=0$
$\Rightarrow x=-120or20$

Cost price of an item cannot be negative. So, the cost price is Rs. 20