If the list price of a toy is reduced by Rs. 2, a person can buy 2 toys more for Rs. 360. Find the original price of the toy.

Given:

If the list price of a toy is reduced by Rs. 2, a person can buy 2 toys more for Rs. 360.

To do:

We have to find the original price of the toy.

Solution:

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

This implies,

Number of toys he can buy at the original price $=Rs. \frac{360}{x}$.

Price of the toy when reduced by $Rs. 2 = Rs. x-2$.

Therefore,

$\frac{360}{x-2}=2+\frac{360}{x}$

$\frac{360}{x-2}=\frac{2x+360}{x}$

$360(x)=(2x+360)(x-2)$

$360x=2x^2-4x+360x-720$

$2x^2-4x-720=0$

$2(x^2-2x-360)=0$

$x^2-2x-360=0$

Solving for $x$ by factorization method, we get,

$x^2-20x+18x-360=0$

$x(x-20)+18(x-20)=0$

$(x+18)(x-20)=0$

$x+18=0$ or $x-20=0$

$x=-18$ or $x=20$

Therefore, the value of $x$ is $20$.   ($x$ cannot be negative)

The original price of the toy is $Rs. 20$.

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Updated on: 10-Oct-2022

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