Average and difference – The average of Amit’s and Anil’s present ages is 32 years. If Amit is 6 years older than Anil, what is Anil’s present age?

Introduction / Context:
Average of two numbers and their difference uniquely determine each number. Convert the average to a sum and split using the half-difference idea.

Given Data / Assumptions:

• (Amit + Anil) / 2 = 32 ⇒ Amit + Anil = 64.
• Amit = Anil + 6.

Concept / Approach:
Substitute into the sum to solve for Anil first, then compute Amit if needed. We only need Anil.

Step-by-Step Solution:
(Anil + 6) + Anil = 64.2·Anil + 6 = 64 ⇒ 2·Anil = 58 ⇒ Anil = 29.

Verification / Alternative check:
Amit = 35; average = (35 + 29) / 2 = 32, as stated.

Why Other Options Are Wrong:
They do not satisfy both the sum and the 6-year difference simultaneously.

Common Pitfalls:
Using 32 directly for one of the ages or halving the difference incorrectly.

Final Answer:
29 years