Age ratio and difference: Laxmi’s present age and her mother’s present age are in the ratio 3 : 11. The difference of their ages is 24 years. What will be the ratio of their ages after 3 years?

Introduction / Context:
This problem uses basic age-ratio algebra. When a ratio and a difference are both given, we can find actual ages by interpreting each ratio “part” as an equal number of years. We then project both ages forward equally to get the required future ratio.

Given Data / Assumptions:

• Laxmi : Mother = 3 : 11 (now)
• Age difference = 24 years
• Find ratio after 3 years

Concept / Approach:
If present ages are 3k and 11k, the difference 11k − 3k equals 24, which gives k. Once actual ages are known, add the same increment (3 years) to both to compute the future ratio.

Step-by-Step Solution:

Verification / Alternative check:
Difference remains 24 both now and in future (36 − 12), consistent with equal increments. The ratio simplifies cleanly to 1 : 3.

Why Other Options Are Wrong:
2 : 3 and 3 : 5 do not match the computed future ages 12 and 36. “None of these” is unnecessary because 1 : 3 fits exactly.

Common Pitfalls:
Using 24 directly as a current age; forgetting that both ages increase equally when projecting forward; or mis-simplifying the final ratio.

Final Answer:
1 : 3