Question

A student buys a certain number of books for rupees 40 less than 1000. If the cost of
each book was ₹ 8 less, the number of books that could be bought for ₹ 960 would
be 4 more. Find the original cost of each book.

Answer 1

SOLUTION :-

Let,

Original cost of each book = x

According to the first condition,

Cost of the books = 1000 - 40

                              = ₹ 960

Number of books for ₹ 960 = $\sf\dfrac{960}{x}$

According to the second condition,

Cost of each book = ₹ ( x - 8 )

Number of books for ₹ ( x - 8 ) = $\sf\dfrac{960}{x-8}$

According to the question,

$\longrightarrow \sf \dfrac{960}{x}+4=\dfrac{960}{x-8}\\\\\longrightarrow \dfrac{960}{x-8}-\dfrac{960}{x}= 4 \\\\\longrightarrow \dfrac{960x-960(x-8)}{x(x-8)}= 4 \\\\\longrightarrow \dfrac{960x-960x+7680}{x^2-8x}= 4 \\\\\longrightarrow 7680 = 4(x^2-8x)\\\\\longrightarrow 7680= 4x^2-32x\\\\\longrightarrow 4x^2-32x-7680= 0 \\\\\longrightarrow x^2-8x-1920 = 0 \\\\\longrightarrow x^2+40x-48x-1920= 0 \\\\\longrightarrow x(x+40)-48(x+40)= 0 \\\\\longrightarrow (x-48)(x+40) = 0$

$\longrightarrow \bf x = 48 \ , \ x= - 40$

Cost cannot be negative.

Original cost of each book = ₹ 48