Ages — father, mother and son ratios with a future ratio condition: Present son:father = 1:5 and mother:father = 4:5. After 2 years, son:mother becomes 3:10. Find the present age of the father.

Introduction / Context:This is a multi-ratio age problem linking present ratios to a future ratio. We convert all given ratios into algebraic relations and solve consistently.

Given Data / Assumptions:

• Present son:father = 1:5.
• Present mother:father = 4:5 ⇒ mother:son = 4:1.
• After 2 years, (son + 2) : (mother + 2) = 3 : 10.

Concept / Approach:Let present son age be s, then father = 5s; mother = 4s (since mother:son = 4:1). Use the future ratio to determine s, then compute the father’s present age 5s.

Step-by-Step Solution:

Verification / Alternative check:

Why Other Options Are Wrong:

• 30, 28, 27 years do not match the computed father’s age (35 years).
• Hence the only correct choice is “None of these.”

Common Pitfalls:

• Assuming mother:father = 4:5 implies a fixed difference; it is a ratio, not a difference.
• Forgetting to add 2 to both ages in the future ratio.

Final Answer:None of these (father is 35 years)