Question

A shopkeeper buys a certain no. of books for Rs. $960$. If the cost per book was Rs. $8$ less, the no. of books that could be bought for Rs. $960$ would be 4 more. Taking the original cost of each book to be Rs. $x$, write an equation in $x$ and solve it.

• A. Rs. $48$
• B. Rs. $24$
• C. Rs. $40$
• D. Rs. $14$

Answer 1

The correct option is A Rs. $48$

Let orignal cost of each book $=x$
No. of books bought for Rs. 960 $=\frac{960}{x}$
The cost of each book was Rs. 8 less, then the cost of book $=x-8$
Difference in the no. of books bought $=\frac{960}{x-8}-\frac{960}{x}=4$
$\frac{240}{x-8}-\frac{240}{x}=1$
$240x-240(x-8)=x(x-8)$
$x^2-8x-1920=0$
$x^2-48x+40x-1920=0$
$x(x-48)+40(x-48)=0$
$(x+40)(x-48)=0$
$x=-40\left(impossible\right)$and $x=48$
Orignal cost of each book is $48$
Option A is correct.