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