Question

The sum of the reciprocals of childs age 3 years and 5 years from now is 1/3. Find his present age.

Answer 1

SOLUTION:-

Given:

The sum of the reciprocal 9f childs age 3 years & 5 years from now is 1/3.

To find:

The present age.

Explanation:

Let the present age of the child be R years.

&

•3 years ago, child's age= (R-3) years.

•After 5 years, child's age= (R+5) years.

According to the question:

$= > \frac{1}{R- 3} + \frac{1}{R + 5} = \frac{1}{3} \\ \\ = > \frac{R + 5 + R - 3}{(R - 3)(R + 5)} = \frac{1}{3} \\ \\ = > \frac{2R + 2}{ {R}^{2} + 2R - 15} = \frac{1}{ 3} \\ [cross \: multiplication] \\ = > 6R + 6 = {R}^{2} + 2R - 15 \\ \\ = > 6R - 2R = - 15 - 6 + {R}^{2} \\ \\ = > 4R = - 21 + {R}^{2} \\ \\ = > {R}^{2} - 4r - 21 = 0 \\ \\ = > {R}^{2} - 7R+ 3R- 21 = 0 \\ \\ = > R(R- 7) + 3(R - 7) = 0 \\ \\ = > (R- 7)(R + 3) = 0 \\ \\ = > R- 7 = 0 \: \: \: \: or \: \: \: \: R + 3 = 0 \\ \\ = > R= 7 \: \: \: or \: \: \: R = - 3$

Since, age can't be negative.

So,

R= 7 years

Thus,

The present age of the child is 7 years.

Thank you.

Answer 2

Answer:

Please refer the attachment dear