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

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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