# The sum of the reciprocals of Rehman’s ages, (in years) 3 years ago and 5 years from now is 1/3. Find his present age

**Solution:**

Let the present age of Rehman be x years.

3 years ago, Rehman’s age was x - 3 years.

5 years from now, his age will be = x + 5

Using this information and the given condition, we can form the following quadratic equation:

1/(x - 3) + 1/(x + 5) = 1/3

[(x + 5) + (x - 3)] / (x - 3)(x + 5) = 1/3

(2x + 2) / x^{2} + 2x - 15 = 1/3

(2x + 2)(3) = x^{2} + 2x - 15

6x + 6 = x^{2} + 2x - 15

x^{2} + 2x - 15 = 6x + 6

x^{2} - 4x - 21 = 0

Let us now find the roots by factorization method:

x^{2} - 7x + 3x - 21 = 0

x(x - 7) + 3(x - 7) = 0

(x - 7) (x + 3) = 0

x - 7 = 0 and x + 3 = 0

x = 7 and x = - 3

But, age can’t be a negative value.

Therefore, Rehman’s present age is 7 years.

**☛ Check: **Class 10 Maths NCERT Solutions Chapter 4

**Video Solution:**

## The sum of the reciprocals of Rehman’s age (in years) 3 years ago and 5 years from now is 1/3. Find his present age

Class 10 Maths NCERT Solutions Chapter 4 Exercise 4.3 Question 4

**Summary:**

The present age of Rehman is 7 years if the sum of the reciprocals of Rehman's age (in years) 3 years ago and 5 years from now is 1/3.

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