Finding the Age of the Father

Video Explanation

Question

Father’s age is three times the sum of ages of his two children. After 5 years, his age will be twice the sum of ages of the two 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:

\[ x = 3y \]

\[ x – 3y = 0 \quad (1) \]

After 5 years:

Father’s age = \(x + 5\)

Each child gains 5 years, so total increase = \(10\)

New sum of children’s ages = \(y + 10\)

According to condition:

\[ x + 5 = 2(y + 10) \]

\[ x + 5 = 2y + 20 \]

\[ x – 2y = 15 \quad (2) \]

Step 3: Solve by Elimination

Subtract equation (1) from equation (2):

\[ (x – 2y) – (x – 3y) = 15 – 0 \]

\[ x – 2y – x + 3y = 15 \]

\[ y = 15 \]

Step 4: Find the Value of x

Substitute \(y = 15\) in equation (1):

\[ x = 3(15) \]

\[ x = 45 \]

Conclusion

Present age of father:

\[ \boxed{45 \text{ years}} \]