A shopkeeper buys a certain of books for Rs 720 . If the cost per book was Rs 5 less, the number of books that could be bought for Rs 720 would be 2 more. Taking the original cost of each book as Rs x, write an equation in x and solve it.
No. of books originally bought=720/x
720/(x-5)=720/x + 2
720/(x-5)=(720+2x)/x
720x=(720+2x)(x-5)
720x=720x-3600+2x2-10x
720x-720x=2x2-10x-3600
0=2x2-10x-3600
x2-5x-1800=0
x2-45x+40x-1800=0
x(x-45)+40(x-45)=0
(x+40)(x-45)=0
so x=-40 and 45
As cost cant be negative we take x = 45
720/(x-5)=720/x + 2
720/(x-5)=(720+2x)/x
720x=(720+2x)(x-5)
720x=720x-3600+2x2-10x
720x-720x=2x2-10x-3600
0=2x2-10x-3600
x2-5x-1800=0
x2-45x+40x-1800=0
x(x-45)+40(x-45)=0
(x+40)(x-45)=0
so x=-40 and 45
As cost cant be negative we take x = 45