Mother–daughters age relation via average and difference: The difference between a mother’s age and the sum of her two daughters’ present ages is 6 years. The average age of the two daughters is 22. What is the mother’s present age?

Introduction / Context:
This problem links average and difference. Convert the average of the two daughters to their sum, add the difference, and obtain the mother’s age directly.

Given Data / Assumptions:

• Average of two daughters = 22 ⇒ sum = 44.
• Mother’s age − (sum of daughters) = 6.

Concept / Approach:
Let M be the mother’s age and S be daughters’ sum. The statement gives M − S = 6, with S = 44. Hence M = 44 + 6.

Step-by-Step Solution:
1) Compute daughters’ sum: 2 × 22 = 44.2) M − 44 = 6 ⇒ M = 50.

Verification / Alternative check:
Check: M − (sum daughters) = 50 − 44 = 6 (correct).

Why Other Options Are Wrong:

• 40/44/46/52 do not meet the exact difference when paired with sum 44.

Common Pitfalls:
Confusing “difference between mother and sum of daughters” with “difference between mother and average” causes wrong results.

Final Answer:
50