Q. 395.0( 2 Votes )

The sum of the reciprocals of Meena's ages (in years) 3 years ago and 5 years hence is 1/3. Find her present age.

Answer :

Let the present age of Meena be x years

Meena’s age three years ago = (x – 3) years


Meena’s age five years hence = (x + 5) years


According to given question





x2 + 2x – 15 = 6x + 6


x2 – 4x – 21 = 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 = – 4 c = – 21


= 1. – 21 = – 21


And either of their sum or difference = b


= – 4


Thus the two terms are – 7 and 3


Sum = – 7 + 3 = – 4


Product = – 7.3 = – 21


x2 – 7x + 3x – 21 = 0


x (x – 7) + 3(x – 7) = 0


(x – 7) (x + 3) = 0


x = – 3 or x = 7


x = 7 age cannot be negative


Hence the present age of Meena is 7 years


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