A shopkeeper buys a number of books for 80. If he had bought 4 morebooks for the same amount, each book would have cost 1 less. Howmany books did he buy ?

A shopkeeper buys a number of books for 80. If he had bought 4 moreboo

1.	A shopkeeper buys a number of books for 80. If he had bought 4 morebooks for the same amount, each book would have cost 1 less. Howmany books did he buy ?
Answer» Let he bought x books for rs 80So the cost of each book was 80/xIf the cost of each books were re 1 less then he can buy 4 more booksSo, he can buy x+4 booksSo 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)=1x^2+4x=320x^2+4x-320=0x^2+20x-16x-320=0x(x+20)-16(x+20)=0(x+20)(x-16)=0Therefore, x= -20, 16As x wouldnt be negative because quantity of book cant be negative so x=16So he bought 16 books