## Book: RS Aggarwal - Mathematics

#### Subject: Maths - Class 10th

##### Q. No. 39 of Exercise 10E

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39
##### 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.

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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