Q. 194.7( 3 Votes )

Divide 27 into two parts such that the sum of their reciprocals is 3/20.

Answer :

Let the two parts be x and (27 – x)

According to given condition,




On taking the LCM




On Cross multiplying



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 = – 27 c = 180


= 1. – 180 = – 180


And either of their sum or difference = b


= – 27


Thus the two terms are – 15 and – 12


Sum = – 15 – 12 = – 27


Product = – 15. – 12 = 180



x (x – 15) – 12(x – 15) = 0


(x – 15) (x – 12) = 0


(x – 15) = 0 or (x – 12) = 0


x = 15 or x = 12


Case I: when x = 12


27 – x = 27 – 12 = 15


Case II: when x = 15


27 – x = 27 – 15 = 12


Hence required numbers are 12 and 15.


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