Three-person sum with given ratios: Ram's age is double Shyam's and half Suresh's. If the sum of their ages is 70, what is Ram's age?

Introduction / Context:Sum with linked ratios is reduced to one variable by expressing all ages in terms of the same unknown. Then a single equation in that unknown yields the answer.

Given Data / Assumptions:

• Let Ram = R.
• Shyam = R / 2 (since R is double Shyam).
• Suresh = 2R (since R is half Suresh).
• R + R/2 + 2R = 70.

Concept / Approach:Combine like terms; solve for R.

Step-by-Step Solution:1) Total = 3.5R = 70.2) R = 70 / 3.5 = 20.

Verification / Alternative check:Check: Shyam = 10, Suresh = 40; sum = 20 + 10 + 40 = 70; all relations hold.

Why Other Options Are Wrong:They do not satisfy both ratio statements and the total simultaneously.

Common Pitfalls:Misreading “half” and “double,” or forgetting to include all three in the sum.

Final Answer:20