Question

if the list price of a toy is reduced by $2,a person can buy 2 toys more for $360. find the orginal price of toy

Answer 1

Answer:

⇢ $20

Explanation:

Given:-

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

Find:-

⇢ Find the orginal price of toy.

Calculations:-

• Let x be the number of toys.
• Let y be the price of each toy.

As per the given chase:

⇢ xy = $360

⇢ x = 360/y

Adding values from the above equation:

⇢ (x + 2) (y - 2) = 360

⇢ 2y - 2(360/y) - 4 = 0

⇢ 2y² - 4y - 720 = 0

⇢ y² - 2y - 360 = 0

⇢ y(y - 20) + 18(y - 20) = 0

⇢ (y + 18) (y - 20) = 0

Therefore,

• x = -18 or
• y = 20

But the price/cost of toy couldn't be negative as the negative price doesn't have any value in the cost price of selling objects we can consider that 20 is the cost price of the toy.

Answer 2

Answer:

Let the original price of the book be ₹ x.

Number of books bought for ₹ 360 = 360/x  

Reduced list price of the book = ₹ (x - 2)

Number of books bought for ₹ 360 = 360/(x - 2)

A.T .Q

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

360[1/(x -2) - 1/x ] = 2

[1/(x -2) - 1/x ] = 2/360

[x - ( - 2)] /x(x - 2) = 1/180

[By taking LCM]

(x - x + 2)/x² - 2x = 1/180

2/x² - 2x = 1/180

x² - 2x = 2 × 180

x² - 2x = 360

x² - 2x  - 360 = 0

x² - 20x + 18x - 360 = 0

[By middle term splitting]

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

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

(x - 20) = 0  or  (x + 18) = 0

x = 20 or x = - 18  

Since, the price of the book can't be negative, so x ≠ - 18  

Therefore , x = 20  

Hence, the original  price of the book is ₹ 20.