Question

the price of a toy is reduced by Rs2, he can purchase 2 more toys with an amount of Rs360, find the price of the toy


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Answer 1

Step-by-step explanation:

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 - (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.

Answer 2

The person has Rs 360 with him. If the price of the toy is Rs x, then he can buy a total of 360/x toys.

Now said that he can buy two more toys if the price is reduced by Rs 2. So, if the price was Rs (x-2), then he could have bought $(\frac{360}{x}+2)$ toys. But since he has Rs 360, we can also say that if the price of the toy is Rs (x-2), then he could have bought $\frac{360}{x-2}$ toys. That means

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

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

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

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

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

x = 20      OR      x = -18(rejected)

So actual price of toy is Rs 20