Finding the Age of A

Video Explanation

Question

A is elder to B by 2 years. A’s father F is twice as old as A. B is twice as old as his sister S. If the ages of the father and sister differ by 40 years, find the age of A.

Solution

Step 1: Let the Variables

Let age of A = \(x\) years

Let age of sister S = \(y\) years

Step 2: Express Other Ages

Age of B = \(x – 2\)

Given: B is twice as old as S

\[ x – 2 = 2y \]

\[ x – 2y = 2 \quad (1) \]

Father’s age:

\[ F = 2x \]

Given difference between father and sister:

\[ 2x – y = 40 \quad (2) \]

Step 3: Solve the Equations

From equation (1):

\[ x = 2y + 2 \]

Substitute into equation (2):

\[ 2(2y + 2) – y = 40 \]

\[ 4y + 4 – y = 40 \]

\[ 3y + 4 = 40 \]

\[ 3y = 36 \]

\[ y = 12 \]

Step 4: Find the Age of A

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

\[ x = 24 + 2 = 26 \]

Conclusion

Age of A:

\[ \boxed{26 \text{ years}} \]