Three years ago, the average age of a husband, his wife, and their child was 24 years. Five years ago, the average age of only the wife and the child was 25 years. What is the present age of the husband?

Introduction / Context:
This question uses average ages to find the present age of a family member. The averages of Husband, Wife, and Child at one point in the past and of Wife and Child at a different point in the past are given. From these, we must deduce the present age of the husband. Such problems are common in aptitude exams and require careful handling of averages and time shifts.

Given Data / Assumptions:
Three years ago, the average age of husband, wife, and child was 24 years. Five years ago, the average age of only the wife and the child was 25 years. We must compute the present age of the husband in years. Ages are assumed to be whole numbers.

Concept / Approach:
The average age of a group is the total of their ages divided by the number of people. From the given averages, we can first find the total ages at those specific times. Then, by accounting for the passage of time, we can find their present total ages. Finally, subtracting the present sum of the wife and child from the present sum of all three gives the present age of the husband.

Step-by-Step Solution:
Step 1: Three years ago, the average age of husband, wife, and child was 24 years. With three people, total age three years ago = 24 * 3 = 72 years.Step 2: Let the present ages of husband, wife, and child be H, W, and C years respectively. Three years ago, their ages were H - 3, W - 3, and C - 3, with total (H - 3) + (W - 3) + (C - 3) = 72.Step 3: Simplify: H + W + C - 9 = 72, so H + W + C = 81. This is the present total age of all three.Step 4: Five years ago, the average age of wife and child was 25 years, so their total age at that time was 25 * 2 = 50 years.Step 5: Their present ages are W and C, so five years ago they were W - 5 and C - 5. Thus, (W - 5) + (C - 5) = 50.Step 6: Simplify: W + C - 10 = 50, hence W + C = 60.Step 7: Now subtract: (H + W + C) - (W + C) = 81 - 60 = 21. Therefore, H = 21 years.

Verification / Alternative check:
Check the earlier data. Three years ago, total age of all three was 72 years. If H is 21 now, then three years ago husband's age was 18 years. Similarly, W + C = 60 now, so three years ago their combined age was 60 - 6 = 54 years. Thus, 18 + 54 = 72, which matches the first condition. Five years ago, W + C = 60 - 10 = 50, and 50 divided by 2 gives an average of 25 years, which matches the second condition. So the solution is consistent.

Why Other Options Are Wrong:
If the husband were 27, 29, or 31 years old presently, the totals would not reconcile with both average conditions simultaneously. Substituting these values into the equations would either disturb the total of 81 years or fail to keep W + C equal to 60. Therefore, those choices are not possible.

Common Pitfalls:
Common errors include forgetting to multiply the average by the number of people to get total age, or incorrectly adjusting ages when going back 3 or 5 years. Another pitfall is to treat averages as if they applied to the present without properly accounting for the time shift. Writing separate equations for each given average and working step by step avoids these mistakes.

Final Answer:
The present age of the husband is 21 years.