# Q1.A shopkeeper buys a number of pens for Rs80.If he had bought 4 more pens for the same amount , each pen would have cost him Rs 1 less. How many pens did he buys?

1
by shab

2015-02-28T17:42:22+05:30
No. of pens bought=16

A shopkeeper buys a number of pens 4 rs. 80.
If he had bought 4 more pens for the same amount,
each pen would have cost him 1 less.
How many pens did he buy?
Let the total number of pens bought by a man be x
Total cost of pen = Rs 80 / x
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 / x^2 + 4x = 1/80
80 (4) = 1(x^2 + 4x)... (by cross multiplication)
320 = x^2 + 4x x^2 + 4x - 320 = 0 ...(ta
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 + 20x ) - (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 pens is never negative)
So the total number pens bought by a man is 16
this is how you will solve