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Amita buys some books for Rs 1920 . . .

Question : Amita buys some books for ₹1920. If she had bought 4 more books for the same
amount each book would cost her ₹ 24 less. How many books did she buy? What was the initial price of one book?

Doubt by Yana

Solution : 

Let the original number of books purchased be x. 
Cost of each book = 1920/x

Number of books when she bought 4 more books = x+4

New cost of each book = 1920/(x+4)

ATQ 
1920/x-
1920/(x+4)=24
1920[1/x-1/(x+4)]=24
[(x+4)-x]/[x(x+4)]=24/1920
4/[x²+4x]=1/80
x²+4x=320
x²-4x-320=0
x²+(20-16)x-320=0
x²+20x-16x-320=0
x(x+20)-16(x+20)=0
(x-16)(x+20)=0
x-16=0 OR x+20=0
x=+16 OR x=-20
Number of books can't be negative. 
So, x=-20 (Rejected)
x=16
Hence, she bought 16 Books.
Initial Price of each Book = 1920/x = 1920/16 
=₹120