A shopkeeper buys some book for Rs 80 if he had bought 4 more books for the same amount each book

Let he bought x books for rs 80 So the cost of each book was 80/x

If the cost of each book were rs 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 wouldn’t be negative because quantity of book can’t be negative so x=16 So he bought 16 books

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