Question

Aniruddha bought some books for Rs. $60$. Had he bought $5$ more books for the same amount, each book would have cost him $1$ rupee less. Find the number of books by Aniruddha.

Answer 1

Solution:

Let the number of books purchased for Rs. $60=x.$

Then cost of each book $=\frac{60}{x}$

If he buys five more books, then the number of books$=x+5$

Cost of each book$=\frac{60}{x+5}$

According to question,

$\frac{60}{x}-\frac{60}{x+5}=1$

or, $60(x+5-x)=x(x+5)$

or, $300=x^2+5x$

or, $x^2+5x-300=0$

or, $x^2+20x-15x-300=0$

or, $x(x+20)-15(x+20)=0$

or, $(x-15)(x+20)=0$

or, $x=15$ or $x=-20$

$x$ can't be negative. So, $x=15$ is the feasible solution.

Therefore, number of books by Aniruddha $=15.$