Problems on Ages — “The average age of a woman and her daughter is 42 years. Their age ratio is 2 : 1. Find the daughter’s age.”

Introduction / Context:This mixes average and ratio. Average of two gives the total; the ratio divides that total into parts. Converting to “total parts” makes the calculation direct and error-free.

Given Data / Assumptions:

• Average (woman + daughter) = 42 years.
• Ratio woman : daughter = 2 : 1 (total parts = 3).

Concept / Approach:Sum = average * number of persons = 42 * 2 = 84. One “ratio part” equals 84/3 = 28. Daughter’s share is 1 part; mother’s is 2 parts (56 years).

Step-by-Step Solution:

Verification / Alternative check:(56 + 28)/2 = 84/2 = 42 ✓; 56 : 28 = 2 : 1 ✓.

Why Other Options Are Wrong:24/26/30/32 do not satisfy both the total 84 and the 2:1 split simultaneously.

Common Pitfalls:Confusing “average of two” (sum/2) with ratio distribution; forgetting to multiply the average by the count to recover the sum first.

Final Answer:28 years