Question

if the list price of the toy. is reduced by 2. A person can buy 2 toys more for rupees 360.find the original price of the toy.

Answer 1

let the no of toys be x and price of each toy be y
therefore, xy = 360
and x=360/y  {eg -1}
2nd condition
(x+2)(y-2)=360
xy + 2y - 2x - 4 = 360
2y - 2(360/y) - 4 = 0  { since xy=360 & from eq 1}
$2y^{2}$ - 4y -720 = 0
$y^{2}$ - 2y - 360 =0
$y^{2}$ - 20y +18y -360 =0
y(y-20) +18(y-20) = 0
(y+18)(y-20)=0
therefore y= -18 or y = 20
in this case y=20 since price of quantity cannot e in negative
therefore the original price of toy is 20 rupees

"I hope my answer is correct and is helpful for you"

Answer 2

Answer:

The original price of the toy is Rs. 20.

Step-by-step explanation:

Let us assume the original price of the toy be Rs. x.

The number of toys bought for Rs. 360 = $\frac{360}{x}$

According to the problem, reduced list of the toy is = Rs. (x - 2)

So, the number of toys bought for Rs. 360 will be = $\frac{360}{x - 2}$

It is given that, after the price reduction a person can buy 2 toys more for Rs. 360.

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

⇒ $\frac{720}{(x-2)x}$ = 2

⇒ x² - 2x = 360

⇒ x² + 18x - 20x - 360 = 0

⇒ x (x + 18) - 20 (x + 18) = 0

⇒ (x + 18) (x - 20) = 0

⇒ (x + 18) = 0 or (x - 20) = 0

⇒ x = -18 or 20

Since x can't be negative,

∴ x = 20 is the answer.

Thus, the original price of the toy is Rs. 20.