Question

A shopkeeper buys a number of books for ₹ 80. If he had bought 4 more books for the same amount, each book would cost ₹ 1 less. How many books did he buy?

Answer 1

Let the number of books bought by shopkeeper =  x

Cost of x books = ₹ 80
Cost of one book= ₹ 80/x

If the number of books bought is(x+4),
Cost of one book=  ₹ 80/x+4

Given: cost of one book is reduced by ₹ 1.
ATQ
80/x - 80/x + 4 = 1
80(1/x - 1/(x+4) = 1
80( x +4 - x )/x(x + 4)= 1
80 × 4 /(x² + 4x) = 1
320 / x² + 4x = 1
x² + 4x = 320
x² + 4x -  320 = 0
x² + 20x - 16x - 320 = 0
x(x+20) -16 (x+20) = 0
(x+20) (x- 16) = 0
(x+20) =0 or (x- 16) = 0
x = -20 or x = 16

x = -20 ,x  not possible because the number of books Can't be negative .

so, number of books (x) = 16

Hence the number of books is 16.

HOPE THIS WILL HELP YOU...

Answer 2

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Let the number of books purchased for Rs.80 = x
Then cost of each books = 80/x
If he buys for more books, the number of books = x+4
Cost of each book = 80/x+4
(80/x)-[80/(x+4)]=1
Solve x=-20 and x = 16
Rejecting x = -20
The number of books purchased = 16
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