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A shop keeper buys a number of books for Rs.80. If he had bought 4 more books for the same amount, each book would have cost his Rs.1 less .How many books did he buy? |
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Answer» Let `x` is the number of books that the shopkeeper purchased. Then, price of each book ` = 80/x` Rs If he had bought `4` more books, then each book would have cost `1` rs less. So, he can buy `x+4` books in the same amount. 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` can not be negative so `x=16`. So he bought `16` books. |
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