Question

A shop keeper buys some books for RS80.If he had bought 4 more books for the same amount,each book would've cost RS1 less .What is the number of books he bought?  

Answer 1

HI ,
Let the total  number of pens bought by a man be x
Total cost of pen = Rs 80
Cost of each pen = RS 80 / x
Condition :
Number one pens = (x +4)
Cost of each pen = Rs 80 / x +4
According to question
80 / x - 80 / x +4 =1
80(1/ x - 1/ x+4)=1
x+4- x / x (x+4) = 1/80
4 / x2 + 4x = 1/80
80 (4)=1(x2 + 4x)... (by cross multiplication)
320 =x 2 +4x.
x 2 +4x - 320 =0 ...(taking R.H.S. to L.H.S )
x 2 +20x -16x - 320 = 0
(x 2 +20 x) - (16x-320)=0
x (x+20)-16 (x+20) = 0
(x-16) (x+20) =0
either x-16 =0 or x +20 =0
x =16 or x = -20
Since we had assumed the total number of  pen to be  x
here x = 16  (x does not equal to -20 as the number of pen is never negative)So the total number of pen bought by a man is 16.

Answer 2

Assume the shopkeeper buys x number of books for Rs 80.

Cost per book = 80/x

80/x -80/(x+4) = 1

80 (x+4 -x)  /x(x+4) = 1

80x4  = x(x+4)

320  = x2 + 4x

x2 + 4x - 320 =0

x2 + 20x -16x- 320 =0

x(x+20) -16(x+20) =0

(x+20) (x-16) = 0

Hence number of books shopkeeper buys x = 16.