Finding the Age of the Father

Video Explanation

Question

The age of the father is twice the sum of the ages of his two children. After 20 years, his age will be equal to the sum of the ages of his children. Find the present age of the father.

Solution

Step 1: Let the Variables

Let present age of father = \(x\) years

Let present sum of ages of two children = \(y\) years

Step 2: Form the Equations

Given:

\[ x = 2y \]

\[ x – 2y = 0 \quad (1) \]

After 20 years:

Father’s age = \(x + 20\)

Each child gains 20 years, so total increase = \(40\)

New sum of children’s ages = \(y + 40\)

According to condition:

\[ x + 20 = y + 40 \]

\[ x – y = 20 \quad (2) \]

Step 3: Solve by Elimination

Subtract equation (1) from equation (2):

\[ (x – y) – (x – 2y) = 20 – 0 \]

\[ x – y – x + 2y = 20 \]

\[ y = 20 \]

Step 4: Find the Value of x

\[ x = 2y = 2(20) \]

\[ x = 40 \]

Conclusion

Present age of the father:

\[ \boxed{40 \text{ years}} \]