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Question

A SHOPKEEPER BUYS A NUMBER OF BOOKS FOR RS.1200.IF HE HAD BOUGHT 10 MORE BOOKS FOR THE SAME AMOUNT,EACH BOOK WOULD HAVE COST HIM RS.20 LESS..HOW MANY BOOKS DID HE BUY?


Solution

Let the no. of books he bought = x , and cost of each book = Rs. y
xy  = 1200           ------------------           eq 1
(x+10)(y - 20) = 1200
xy - 20x + 10y - 200 = 1200 (from eq - 1)
20x - 10y + 200 = 0
2x - y + 20 = 0
y = 2x + 20
Put this value in eq - 1 
x(2x + 20) = 1200
2x2 + 20x - 1200 = 0
x2 + 10x - 600 = 0
x2 + 30x - 20x - 600 = 0
x(x + 30) - 20(x + 30) = 0
(x - 20)(x + 30) = 0
x = 20 or -30
So, No. of books he bought = 20 (as books cannot be -ve)

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