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.

Answer 1

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 = x² - 2x

x² - 2x - 360 = 0

x² + 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 required solution.

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