Question

Arun bought some books for Rs. 60. Had he bought 5 more books for the sameamount each book would have cost him one rupee less. Find the number ofbooks bought by Arun and the price of each book.​

Answer 1

The number of books bought by Arun is 4 and the price of each book is Rs. 15.

Step-by-step explanation:

Let, Arun bought x number of books for Rs. 60.

So, the cost per book is $\frac{60}{x}$ Rs.

Now, if he bought 5 more books i.e. (x + 5) books for Rs. 60, then per book cost will be $\frac{60}{x + 5}$ Rs.

Therefore, from the given conditions we can write

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

⇒ 60(x + 5 - x) = x(x + 5)

⇒ 300 = x² + 5x

⇒ x² + 5x - 300 = 0

⇒ x² + 20x - 15x - 300 = 0

⇒ (x - 15)(x + 20) = 0

⇒ x = 15 Rs. as x can not be negative.

Therefore, the number of books bought by Arun is $\frac{60}{15} = 4$ and the price of each book is Rs. 15. (Answer)