The ratio of the present ages of Maala and Kala is 4 : 3. The sum of their present ages is 2.8 decades, that is 28 years. What will be the ratio of their ages after 0.8 decades, that is after 8 years?

Introduction / Context:
This problem deals with age ratios and their change over time. We are given a present ratio, the total of the ages now, and asked to find the ratio after a certain number of years. It tests understanding of ratios, basic algebra, and the idea that each person age increases by the same fixed amount over time.

Given Data / Assumptions:

• Present ratio of ages of Maala and Kala is 4 : 3.
• The sum of their present ages is 2.8 decades, which equals 28 years.
• We need the ratio of their ages after 0.8 decades, that is after 8 years.
• All ages are in years and non-negative.

Concept / Approach:
When two ages are in a given ratio, we express them as multiples of a common variable. Using the sum of the ages, we solve for that variable and get the actual ages. Then we add the given future time to each age and compute the new ratio. Age ratios change when equal years are added to each person, but the age difference remains constant.

Step-by-Step Solution:
Let the present age of Maala be 4 * x years and the present age of Kala be 3 * x years.Given that their total age is 28 years, so 4 * x + 3 * x = 28.This simplifies to 7 * x = 28.So x = 28 / 7 = 4.Present age of Maala = 4 * 4 = 16 years.Present age of Kala = 3 * 4 = 12 years.After 8 years, Maala age will be 16 + 8 = 24 years.After 8 years, Kala age will be 12 + 8 = 20 years.The required ratio after 8 years is 24 : 20.Simplify by dividing by 4: 24 : 20 = 6 : 5.

Verification / Alternative check:
Check the sum now: 16 + 12 = 28 years, which matches the given total.Check the ratio now: 16 : 12 simplifies to 4 : 3, which matches the given ratio.After 8 years, 24 : 20 simplifies to 6 : 5, confirming that 6 : 5 is the correct future ratio.

Why Other Options Are Wrong:
4 : 3: This is the present ratio, not the ratio after 8 years. The ratio changes when equal years are added to two different ages.12 : 11: There is no combination of 16 and 12 increased by the same amount that gives this ratio.7 : 4: This does not match 24 : 20 or any reasonable simplification from the correct ages.

Common Pitfalls:
Forgetting to convert decades to years can lead to wrong calculations. Here 0.8 decades means 8 years.Some students incorrectly keep the ratio constant over time without adding the extra years to each age.Errors sometimes occur when simplifying the final ratio, such as dividing by different numbers.

Final Answer:
The ratio of their ages after 8 years will be 6 : 5.