Ages (chained ratios summing to a total): The ratio Ram : Mohan is 4 : 5, and Mohan : Anil is 5 : 6. If the sum of their ages is 90 years, find Mohan's age.

Introduction / Context:
Linking ratios across three people can be handled by expressing all ages with one common multiplier. The question is a straightforward ratio-sum application aimed at quick, accurate computation.

Given Data / Assumptions:

• Ram : Mohan = 4 : 5.
• Mohan : Anil = 5 : 6.
• R + M + A = 90 years.

Concept / Approach:
Use Mohan as the bridge between the two ratios to put all three in the same scale. With M = 5k, we have R = 4k and A = 6k, so the sum becomes 15k, from which k follows immediately.

Step-by-Step Solution:

Verification / Alternative check:
Check other ages: R = 24, A = 36. Ratios 24 : 30 = 4 : 5 and 30 : 36 = 5 : 6 both hold (✓).

Why Other Options Are Wrong:
They do not yield the correct total of 90 when combined with compatible R and A values preserving both ratios.

Common Pitfalls:
Trying to solve two ratios independently without anchoring on the shared person (Mohan), which leads to inconsistent scaling.

Final Answer:
30 years