Question

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

Answer 1

Eq no 1:- total books purchased = x
Therefore unit price = 80/ x
Eq no 2:- 4 extra book purchased on same price = ×+4 =80
Therefore unit price = 80/(×+4)
Difference of price is Rs. 1
Hence 80/× - 80/(x-4) =1

By solving the equation
320/ (xpower2 + 4x)=0
Xpower2+4x-320=0

X(X+20) -16(X+20)=0
(X+20) (X-16)=0
X=-20, X=16

We negate negative answer
Therefore no of books brought =16

Answer 2

Answer: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.