Q. 365.0( 3 Votes )

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?

Answer :

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


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