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 = 3x^{2} + 9x cross multiplying

3x^{2} + 9x – 540 = 0

x^{2} + 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

x^{2} + 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

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