Question

If the price of a book is reduced by Rs.5 ,a person can buy 5 more books for Rs.300 . Find the original list price of the article ?

Answer 1

- Let the original price of the book be Rs. x.

Then the reduced price of the book = Rs. ( x - 5)Total amount = Rs. 300According to the questionOr, Or, Or, 5(x2 - 5x) = 1500Or, x2 - 5x = 300Or, x2 - 5x - 300 = 0Or, x2 - 20x + 15x - 300 = 0Or, x(x - 20) + 15 (x - 20) = 0Or, (x - 20) ( x + 15) = 0x = -15, 20As price can not be negative x = Rs. 20.

Answer 2

Let the original list price of the book = Rs. x

Number of books bought for Rs. 300 = $\sf{\frac{300}{x}}$

Reduced list price of the book = Rs. (x-5)

Number of books bought for Rs. 300 = $\sf{ \frac{300}{x - 5}}$

A/C,

$\sf\red{\frac{300}{x - 5} - \frac{300}{x} = 5}$

$\longrightarrow$$\sf\red{300x - 300(x - 5) = 5x(x - 5)}$

$\longrightarrow$$\sf\red{300 \times 5 - 5x(x - 5) = 0}$

$\longrightarrow$$\sf\red{{x}^{2} - 5x - 300 = 0}$

$\longrightarrow$$\sf\red{(x - 20)(x + 15) = 0}$

$\longrightarrow$$\sf\red{x = 20 \: or \: x = - 15}$

As the price of the book cannot be negative, x ≠ -15 ,so x = 20

Hence, the original list price of the book = Rs. 20