Question

A dealer sells a toy for Rs. $24$ and gains as much percent as the cost price of the toy. Find the cost price of the toy.

Answer 1

Let the cost price of the toy be Rs. $x$.

Then gain $x$% Gain $Rs.(x\times \frac{x}{100})=Rs.\frac{x^2}{100}$

$S.P=C.P+Gain$ $=x+\frac{x^2}{100}$

But $S.P=Rs.24$

$\Rightarrow x+\frac{x^2}{100}=24$

$\Rightarrow 100x+x^2=2400\Rightarrow x^2+100x-2400=0$

$\Rightarrow x^2+120x-20x-2400=0\Rightarrow x(x+120)-20(x+120)=0$

$\Rightarrow (x+120)(x-20)=0\Rightarrow x=20,-120\Rightarrow x=20$

Hence the cost price of the toy is Rs. $20$