A shopkeeper buys a number of books for rs 80

Asked by admin @ in Math viewed by 306 People

a shopkeeper buys some book for Rs 80 if he had bought 4 more books for the same amount each book have cost Re 1 less .Find the total number of books he bought.

Answered by admin @


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

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