Question

By selling an item for ₹ 200, if the shopkeeper earns a profit percent equal to the cost price of the item, then the cost price of the item is .

• A. ₹ 50
• B. ₹ 100
• C. ₹ 150

Answer 1

The correct option is B ₹ 100

Let the cost price of the item be $x.$
We have ​$\text{profit \%}=\frac{S.P.-C.P.}{C.P.}\times 100$
$=\frac{200-x}{x}\times 100$
Given that the profit percentage is equal to the cost price.
$\Rightarrow \frac{200-x}{x}\times 100=x$
$\Rightarrow x^2=20000-100x$
$\Rightarrow x^2+100x-20000=0$
$\Rightarrow x^2+200x-100x-20000=0$
$\Rightarrow x(x+200)-100(x+200)=0$
$\Rightarrow (x-100)(x+200)=0$
$\Rightarrow x=100\text{or}-200$
The roots of the equation are -200 and 100.
But since the cost price of an item cannot be negative, we must have $x=₹100.$