Relative ages and ordering – Ram's age is double Shyam's age and half of Sohan's age. Shyam is older than Mohan. Based on these relations, who is the oldest among the four?

Introduction / Context:This is a classic “problems on ages” ordering question. We are not asked for numerical ages; instead, we must use the given multiplicative relationships to rank the people from oldest to youngest and identify the oldest individual.

Given Data / Assumptions:

• Ram's age is double Shyam's age.
• Ram's age is half of Sohan's age.
• Shyam is older than Mohan.
• All ages are present ages and positive integers are not required; only ordering matters.

Concept / Approach:Translate words to proportional relations. If Shyam = s, then Ram = 2s. If Ram is half of Sohan, then Sohan = 2 * Ram = 4s. The statement “Shyam is older than Mohan” only says Mohan is below Shyam; it does not change who is overall oldest because the Sohan–Ram–Shyam chain already fixes the top end of the order.

Step-by-Step Solution:Let Shyam = s.Then Ram = 2s (given).Since Ram is half of Sohan, Sohan = 2 * (2s) = 4s.Therefore, in descending order: Sohan (4s) > Ram (2s) > Shyam (s) > Mohan (below Shyam).Hence, Sohan is the oldest.

Verification / Alternative check:Pick a simple number: let Shyam = 10. Then Ram = 20 and Sohan = 40. Any Mohan that is younger than Shyam (say, 9) maintains the order. The oldest remains Sohan (40).

Why Other Options Are Wrong:

• Ram and Shyam are strictly younger than Sohan by the relations.
• Mohan is explicitly younger than Shyam, so he cannot be the oldest.
• “None of these” is incorrect because Sohan is determinable.

Common Pitfalls:Confusing “double” and “half,” or assuming “older than Mohan” implies Mohan could be the oldest; that statement only places Mohan below Shyam.

Final Answer:Sohan