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 15 and the price of each book is Rs.4

Step-by-step explanation:

Arun bought some books for Rs. 60

Let number of books bought by Arun = x

Let cost for each book = Rs. y

Total cost = 60

=> xy = 60......................(i)

If he had bought 5 more books for the same amount each book would have cost him one rupee less.

So, (x + 5)(y - 1) = 60

=> xy - x + 5y - 5 = 60

=> 60 - x + 5$(\frac{60}{x})$ = 60 + 5 = 65

=> -x² + 300 - 5x = 0

=> x² + 5x - 300 = 0

=> x² + 20x - 15x - 300 = 0

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

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

=> x = -20, 15.

Number of books cannot be negative. So, x = 15

Plug the value of x in equation(i),

xy = 60

=> 15y = 60

=> y = Rs. $\frac{60}{15}$ = Rs. 4

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