Finding the Present Ages of Father and Son

Video Explanation

Question

A father is three times as old as his son. In 12 years, he will be twice as old as his son. Find their present ages.

Solution

Step 1: Let the Variables

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

Let present age of son = \(y\) years

Step 2: Form the Equations

Father is three times son:

\[ x = 3y \]

\[ x – 3y = 0 \quad (1) \]

After 12 years:

\[ x + 12 = 2(y + 12) \]

\[ x + 12 = 2y + 24 \]

\[ x – 2y = 12 \quad (2) \]

Step 3: Solve by Elimination Method

Subtract equation (1) from equation (2):

\[ (x – 2y) – (x – 3y) = 12 – 0 \]

\[ x – 2y – x + 3y = 12 \]

\[ y = 12 \]

Step 4: Find the Value of x

Substitute \(y = 12\) in equation (1):

\[ x – 3(12) = 0 \]

\[ x = 36 \]

Conclusion

Present age of father:

\[ \boxed{36 \text{ years}} \]

Present age of son:

\[ \boxed{12 \text{ years}} \]