Question

A shopkeeper buys a number of books for rs. 80. If he had bought 4 more books for the same amount each would have cost him rs.1 less. How many books did he buy.?

Answer 1

Let he bought x books for rs 80

So the cost of each book was 80/x

If the cost of each books were re 1 less then he can buy 4 more books

So, he can buy x+4 books

So the cost of each of the book would be

80/(x+4)

According to the question,

80/x-80/(x+4)=1

(80x+320-80x)/(x^2 +4x)=1

x^2+4x=320

x^2+4x-320=0

x^2+20x-16x-320=0

x(x+20)-16(x+20)=0

(x+20)(x-16)=0

Therefore, x= -20, 16

As x wouldnt be negative because quantity of book cant be negative so x=16

So he bought 16 books