Question

By selling an item for ₹75, the shopkeeper earns the percent profit equal to cost price of the item. The cost price of the item is .

• A. ₹40
• B. ₹50
• C. ₹30

Answer 1

The correct option is B ₹50

Let the cost price = $x$
Profit on the item (S.P - C.P) = $75-x$

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

=$\frac{75-x}{x}\times 100$

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

$\Rightarrow \frac{75-x}{x}\times 100=x$
$\Rightarrow x^2=7500-100x$
$\Rightarrow x^2-7500+100x=0$
$\Rightarrow x^2+150x-50x-7500=0$
$\Rightarrow x(x+150)-50(x+150)=0$
$\Rightarrow (x+150)(x-50)=0$
$\Rightarrow x=-150or50$

Cost price of an item cannot be negative. So, the cost price is ₹50.