The ratio of Sumit’s and Prakash’s present ages is 2 : 3. Sumit is 6 years younger than Prakash. What will be the ratio of their ages after 6 years?

Introduction / Context:
This age problem uses ratios and a known difference between two people. We determine current ages from ratio plus difference, then project forward to find the future ratio.

Given Data / Assumptions:

• Sumit : Prakash = 2 : 3 at present.
• Sumit is 6 years younger than Prakash.
• Find ratio after 6 years.

Concept / Approach:
Express ages as 2k and 3k. Use the given difference (3k − 2k = 6) to find k. Then add 6 years to each and form the new ratio.

Step-by-Step Solution:
Let Sumit = 2k, Prakash = 3k. Given 3k − 2k = 6 ⇒ k = 6. Present ages: Sumit = 12, Prakash = 18. After 6 years: Sumit = 18, Prakash = 24. Required ratio = 18 : 24 = 3 : 4.

Verification / Alternative check:
The difference remains 6 years before and after. The ratio after 6 years simplifies cleanly to 3 : 4, confirming the calculation.

Why Other Options Are Wrong:
1 : 2 and 2 : 3 do not reflect the correct future ages. 3 : 8 is far too skewed considering the fixed 6-year gap.

Common Pitfalls:
Confusing which person is older, or forming the future ratio using wrong present values. Always compute k from the difference first, then update ages.

Final Answer:
3 : 4