The average age of Hari, his wife and their two children is 23 years. His wife is 4 years younger than Hari. She was 20 years old when their daughter was born, and Hari was 28 years old when their son was born. What is the sum of the present ages, in years, of Hari and his daughter?

Introduction / Context:
This problem combines average age concepts with age differences between family members and information about how old the parents were when their children were born. It is a classic mixed age problem seen in aptitude tests that checks your ability to set up equations from several related statements and derive the required sum of ages.

Given Data / Assumptions:

• The family consists of Hari, his wife, their daughter and their son, four people in total.
• The average age of these four family members is 23 years.
• Hari wife is 4 years younger than Hari.
• Hari wife was 20 years old when their daughter was born.
• Hari was 28 years old when their son was born.
• We need the sum of the present ages of Hari and his daughter.

Concept / Approach:
First, we use the average age to get the total of all four present ages. Next, we represent Hari age as a variable and use the information about age differences and birth times to express the ages of his wife, daughter and son in terms of the same variable. This leads to one equation in one unknown, which we solve to get Hari present age. Then we find the daughter present age and add it to Hari age to obtain the required sum.

Step-by-Step Solution:
Step 1: Let Hari present age be H years. Step 2: His wife is 4 years younger, so her present age is H - 4 years. Step 3: She was 20 years old when their daughter was born, so the daughter present age is (H - 4) - 20 = H - 24 years. Step 4: Hari was 28 years old when their son was born, so the son present age is H - 28 years. Step 5: The family has four members and their average age is 23 years, so the total of their present ages is 4 * 23 = 92 years. Step 6: The sum of their present ages in terms of H is H + (H - 4) + (H - 24) + (H - 28) = 4H - 56. Step 7: Set this equal to 92: 4H - 56 = 92. Step 8: Add 56 to both sides to get 4H = 148. Step 9: Divide both sides by 4 to obtain H = 37. Step 10: Therefore, Hari present age is 37 years and the daughter present age is H - 24 = 37 - 24 = 13 years. Step 11: The sum of the present ages of Hari and his daughter is 37 + 13 = 50 years.

Verification / Alternative check:
Let us verify by computing all four ages. Hari is 37 years old, his wife is 37 - 4 = 33 years old, their daughter is 13 years old and their son is 37 - 28 = 9 years old. The total of the four ages is 37 + 33 + 13 + 9 = 92 years. Dividing by 4 gives an average of 92 / 4 = 23 years, which matches the given average. The ages are also consistent with the birth information, confirming that our calculation is correct.

Why Other Options Are Wrong:
Option A (53 years) does not match the sum 37 + 13 and would require different ages which would break the given average or birth conditions.
Option B (55 years) similarly does not correspond to any consistent set of ages satisfying all the given statements.
Option C (56 years) is also inconsistent with the required average age and age differences among family members.

Common Pitfalls:
Students may misinterpret statements like “she was 20 years old when their daughter was born” and incorrectly add or subtract years. Another common mistake is to forget that the average applies to the total of all four members. Using a clear variable for Hari age and writing each family member age in terms of this variable prevents such errors and leads to a systematic solution.

Final Answer:
The sum of the present ages of Hari and his daughter is 50 years.