Father–daughter ages: Present ratio is 3:1. Four years ago it was 4:1. What will be the average age of the father and the daughter two years hence?

Introduction / Context:
Age-ratio problems combine present ratios with past ratios to recover exact ages. After solving the present ages, projecting 2 years forward and averaging is straightforward.

Given Data / Assumptions:

• Current ratio father:daughter = 3:1 ⇒ Father = 3x, Daughter = x
• Four years ago ratio = 4:1 ⇒ (3x - 4):(x - 4) = 4:1
• Find the average 2 years hence.

Concept / Approach:
Set up and solve a linear equation from the historical ratio, then add 2 to each age and compute the mean.

Step-by-Step Solution:

Verification / Alternative check:
Check past ratio: 36 - 4 = 32 and 12 - 4 = 8 ⇒ 32:8 = 4:1, as given.

Why Other Options Are Wrong:

• 24 or 25: Underestimates the forward ages.
• 36: That is the father’s present age, not the required average 2 years later.

Common Pitfalls:
Mixing present and past ages or averaging the ratios instead of solving the equation.

Final Answer: