#### Question

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.

#### Solution

Let the original list price of the toy be Rs. *x *.

Then, the number of toys brought for Rs.360 `=360/x`

According to question, reduced list price of the toys = Rs. (x - 2).

Therefore, the number of toys brought for Rs.360 `=360/(x-2)`

It is given that

`360/(x-2)-360/x=2`

`360x-360(x-2)/((x-2)x)=2`

`(360x-360x+720)/(x^2-2x)=2`

`720/(x^2-2x)=2`

`720/2=x^2-2x`

360 = x^{2} - 2x

x^{2} - 2x - 360 = 0

x^{2} + 18x - 20x - 360 = 0

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

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

x + 18 = 0

x = -18

Or

x - 20 = 0

x = 20

Because *x *cannot be negative.

Thus,* x = 20 *is the require solution.

Therefore, the original list price of the toy be x = Rs. 20

Is there an error in this question or solution?

#### APPEARS IN

Solution 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. Concept: Solutions of Quadratic Equations by Factorization.