Relative ages and eldest identification: Ram is twice the age of Shyam and half the age of Sohan. Shyam is older than Mohan. Who is the eldest among Ram, Shyam, Sohan, and Mohan?

Introduction / Context:
Ranking-test problems with ages usually give proportional relations (e.g., “twice,” “half”) and a couple of comparative statements. The task is to translate the language into simple algebra or consistent ordering and then identify the extreme (eldest or youngest).

Given Data / Assumptions:

• Ram = 2 * Shyam.
• Ram = (1/2) * Sohan ⇒ Sohan = 2 * Ram.
• Shyam is older than Mohan.
• All ages are positive and measured at the same time (no time shift).

Concept / Approach:
Convert each sentence to a relation. From Ram = 2*Shyam, Ram is older than Shyam. From Sohan = 2*Ram, Sohan is older than Ram (and hence older than Shyam). The note that Shyam is older than Mohan only affects the lower end of the order; it does not challenge Sohan’s status at the top.

Step-by-Step Solution:

Verification / Alternative check:
Pick an easy numeric example for intuition: let Shyam = 10. Then Ram = 20, Sohan = 40, and Mohan < 10 (say 9). Clearly, 40 (Sohan) is the maximum age. Any positive scaling preserves the order.

Why Other Options Are Wrong:

• Mohan: Explicitly younger than Shyam, so cannot be eldest.
• Shyam: Half of Ram; cannot exceed Ram or Sohan.
• Ram: Half of Sohan; therefore younger than Sohan.
• None of these: Incorrect because Sohan fits and is in the list.

Common Pitfalls:
Confusing “twice” and “half,” or treating “Shyam older than Mohan” as impacting who is eldest at the top. Proportional relations dominate extremes here.

Final Answer:
Sohan