A man buys a number of pens for Rs. 180. If he had bought 3 more pens for the same amount, each pen would have cost him Rs. 3 less. How many pens did he buy?
Let the total number of pens be x
According to the question – –
taking LCM
540 = 3x2 + 9x cross multiplying
3x2 + 9x – 540 = 0
x2 + 3x – 180 = 0
Using the splitting middle term – the middle term of the general equation 
is divided in two such values that:
Product = a.c
For the given equation a = 1 b = 3 c = – 180
= 1. – 108 = – 180
And either of their sum or difference = b
= 3
Thus the two terms are 15 and – 12
Difference = 15 – 12 = 3
Product = 15. – 12 = – 180
x2 + 15x – 12x – 180 = 0
x(x + 15) – 12(x + 15) = 0
(x + 15)(x – 12) = 0
(x + 15) = 0 or (x – 12) = 0
x = – 15, x = 12
x = 12 (Total number of pens cannot be negative)
Hence the Total number of pens is 12