Ages in a given ratio with known total; future ratio requested: Shami, Nammi and Pammi are currently in the age ratio 3 : 4 : 5. Their total age is 48 years. What will be the ratio of their ages 8 years from now?

Introduction / Context:
When a ratio and total are given, compute the common unit, obtain actual present ages, then add the future increment to each and reduce to the simplest ratio for the future time.

Given Data / Assumptions:

• Present ratio = 3 : 4 : 5.
• Total = 48 years.
• Future time shift = +8 years for each person.

Concept / Approach:
The sum of ratio parts is 3 + 4 + 5 = 12. One unit equals 48 / 12 = 4. Present ages are 12, 16, and 20. Add 8 to each and reduce.

Step-by-Step Solution:
1) Present ages: 3×4 = 12; 4×4 = 16; 5×4 = 20.2) After 8 years: 20, 24, 28.3) Simplify 20 : 24 : 28 by dividing by 4 ⇒ 5 : 6 : 7.

Verification / Alternative check:
All three increased equally by 8, so internal differences remain consistent; the simplified ratio is correct.

Why Other Options Are Wrong:

• 4:5:6 and 6:7:8 correspond to different increments; 5:7:8 changes differences improperly; 3:5:7 is unrelated.

Common Pitfalls:
Forgetting to simplify the final ratio or incorrectly applying the total to find the unit are common issues.

Final Answer:
5 : 6 : 7