Problems on Ages — “The sum of the ages of Ram, Shyam and Mohan is 93. Ten years ago their ratio was 2 : 3 : 4. Find Mohan’s present age.”

Introduction / Context:
A common structure is a present total with a ratio given at an earlier time. Represent past ages via parts, advance them by the elapsed years to the present, and match the current total.

Given Data / Assumptions:

• Ten years ago: Ram : Shyam : Mohan = 2 : 3 : 4 ⇒ let past ages be 2k, 3k, 4k.
• Now: each has aged 10 years, and the present total = 93.

Concept / Approach:
Present ages are (2k + 10), (3k + 10), (4k + 10). Sum and solve for k, then compute Mohan’s present age (the third term).

Step-by-Step Solution:

Verification / Alternative check:
Present ages become (24, 31, 38); ten years ago they were (14, 21, 28) = 2 : 3 : 4 ✓; present sum 24 + 31 + 38 = 93 ✓.

Why Other Options Are Wrong:
34/32/24/36 do not align with both the past ratio and the present total when back-checked.

Common Pitfalls:
Applying the +10 only once to the total instead of per person (+30 overall); mixing present and past parts in the same equation.

Final Answer:
38 years