Question

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

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Answer 1

Given :-

• Selling price of the toy = Rs. 24
• The dealer gains as much per cent as the cost price of the toy.

To Find :-

• Cost price(C.P) of the toy.

Solution :-

Suppose the cost price of the toy be Rs. x. Then, According to the question,

$\implies\rm{Gain=x\%}$

$\implies\rm{Gain=Rs.\left(x\times{}\dfrac{x}{100}\right)=Rs.\dfrac{x^2}{100}}$

We know, S.P = C.P + Gain

$\implies\rm{x+\dfrac{x^2}{100}=24\quad\quad\quad[{\because}\:S.P=Rs.24]}$

$\implies\rm{100x+x^2=2400}$

$\implies\rm{x^2+100x-2400=0}$

Splitting the middle term, we get,

$\implies\rm{x^2+120x-20x-2400=0}$

$\implies\rm{x(x+120)-20(x+120)=0}$

$\implies\rm{(x+120)(x-20)=0}$

$\implies\rm{x=20,-120}$

Neglecting negative value, we get,

$\implies\bold{x=20}$

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