Question

Anirudh 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 bought by Anirudh and the price of each book.

Answer 1

Let the number of books be = x.

Total cost of the books = Rs. 60.

$\therefore$ Cost of each book $=Rs.\frac{60}{x}$

If the number of books is (x + 5), then the cost of each book = Rs. $\frac{60}{x+5}$

Difference in cost is one rupee = Cost of each book when number of books is (x) - Cost of each book when number of books is (x + 5)

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

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

$\frac{60x+300-60x}{x^2+5x}=1$

$x^2+5x=300$

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

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

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

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

$x+20=0$ or $x-15=0$

$\therefore x=-20$ or $x=15$

$\therefore$ Number of books = x = 15

Number of books cannot be negative. Hence, -20 is rejected.

$\therefore$ Cost of each book $=\frac{60}{x}=\frac{60}{15}=Rs.4$