Problems on Ages — “Shyam’s age is 1/3 of his mother’s. He is 2 years older than his sister. If the sister is 8 years old, find the mother’s age.”

Introduction / Context:
Chain relations allow you to work from the known youngest age upward. Once Shyam’s age is deduced from his sibling difference, scale up using the stated fraction to get the mother’s age.

Given Data / Assumptions:

• Sister = 8 years.
• Shyam is 2 years older than his sister ⇒ Shyam = 10 years.
• Shyam is 1/3 of his mother’s age ⇒ Mother = 3 * Shyam.

Concept / Approach:
Compute Shyam first, then multiply by 3 for the mother’s age.

Step-by-Step Solution:

Verification / Alternative check:
Check fraction: 10 is indeed one-third of 30; sibling difference satisfied.

Why Other Options Are Wrong:
25/48/60/36 break either the 1/3 relation or the 2-year sibling gap.

Common Pitfalls:
Reversing the fraction (taking mother as 1/3 of Shyam) or misapplying the +2 to the wrong person.

Final Answer:
30 years