The average age of three girls is 20 years, and their ages are in the proportion 3 : 5 : 7. What is the age of the youngest girl?

Introduction / Context: We are given an average age and a ratio of ages. The task is to convert the ratio into actual ages using the average to find total and then allocate by ratio parts.

Given Data / Assumptions:

• Average of 3 girls = 20 years ⇒ total = 60 years.
• Proportion of ages = 3 : 5 : 7.
• Find the youngest girl’s age.

Concept / Approach: Sum of ratio parts is 3 + 5 + 7 = 15. Each part equals total/15. Multiply each part by the corresponding ratio number to get individual ages.

Step-by-Step Solution: Total age = 3 * 20 = 60. Sum of parts = 15 ⇒ one part = 60 / 15 = 4. Ages: 3*4 = 12; 5*4 = 20; 7*4 = 28. Youngest = 12 years.

Verification / Alternative check: Average of 12, 20, 28 is (60/3) = 20, which matches the given average.

Why Other Options Are Wrong: 4 years, 6 years 8 months, and 8 years 3 months are inconsistent with both the total sum and the given ratio.

Common Pitfalls: Forgetting to multiply the unit part properly or miscomputing the total (average * count). Ratio problems require careful handling of parts.

Final Answer: 12 years