If 6 years are subtracted from the present age of Ayush and 25 percent of the remaining value is taken, we get the present age of his only son. Four years ago, the present age of his daughter was 7 years more than the age of his son at that time. The sum of the present ages of the daughter and the wife of Ayush is 10 years more than Ayush present age. If the average of the present ages of the entire family (Ayush, his wife, his son and his daughter) is 30.25 years, what is the present age, in years, of Ayush?

Introduction / Context:
This is a multi step age problem involving four members of a family: Ayush, his wife, his son and his daughter. It combines percentages, average age, and age relations at different times. Such questions are considered challenging in aptitude exams because they require setting up several equations from a dense verbal description and solving them logically without losing track of the relationships.

Given Data / Assumptions:

• Let Ayush present age be A years.
• If 6 years are subtracted from A and 25 percent of the result is taken, that value equals the present age of his son.
• Four years ago, the daughter age was 7 years more than the son age at that time.
• The sum of the present ages of the daughter and Ayush wife is 10 years more than Ayush present age.
• The family consists of four people and the average of their present ages is 30.25 years.
• All ages are in years.

Concept / Approach:
We proceed by expressing each family member age in terms of Ayush age A. First, we convert the percentage relation into an algebraic expression for the son age. Next, we use the information from four years ago to express the daughter age in terms of the son age. Then we express the wife age from the given sum with the daughter. Finally, we use the average to get the total sum of all ages and form an equation in A. Solving this equation gives Ayush present age, which we can then verify against all conditions.

Step-by-Step Solution:
Step 1: Let Ayush present age be A years. Step 2: After subtracting 6 years from A, we get A - 6. The present age of the son is 25 percent of this, so son age S = 25 percent of (A - 6) = (A - 6) / 4. Step 3: Four years ago, the son age was S - 4 and the daughter age was D - 4, where D is the daughter present age. Step 4: At that time, the daughter age was 7 years more than the son age, so D - 4 = (S - 4) + 7, which simplifies to D = S + 7. Step 5: The sum of the present ages of the daughter and the wife is 10 years more than Ayush present age, so D + W = A + 10, where W is the wife present age. Step 6: Substitute D = S + 7 into this to get S + 7 + W = A + 10, which gives W = A + 3 - S. Step 7: The average age of the four family members is 30.25 years, so the total of their present ages is 4 * 30.25 = 121 years. Step 8: The total sum is A (Ayush) + W (wife) + S (son) + D (daughter) = 121. Step 9: Substitute W = A + 3 - S and D = S + 7 into this total: A + (A + 3 - S) + S + (S + 7) = 121. Step 10: Simplify: A + A + 3 - S + S + S + 7 = 2A + S + 10 = 121. Step 11: So 2A + S = 111. Step 12: But S = (A - 6) / 4, so substitute to get 2A + (A - 6) / 4 = 111. Step 13: Multiply through by 4 to clear the denominator: 8A + (A - 6) = 444. Step 14: Combine like terms: 9A - 6 = 444, giving 9A = 450. Step 15: Divide both sides by 9 to obtain A = 50. Step 16: Therefore Ayush present age is 50 years.

Verification / Alternative check:
Let us verify all relations. If A = 50, then S = (50 - 6) / 4 = 44 / 4 = 11 years. The daughter age is D = S + 7 = 11 + 7 = 18 years. The wife age is W = A + 3 - S = 50 + 3 - 11 = 42 years. Total present ages are 50 + 42 + 11 + 18 = 121 years, and the average is 121 / 4 = 30.25 years, as specified. Four years ago, the son was 7 years old and the daughter was 14 years old, so the daughter was indeed 7 years older than the son. All conditions are satisfied, confirming the correctness of the solution.

Why Other Options Are Wrong:
Option A (45 years) fails to produce an average of 30.25 years when the corresponding family ages are calculated from the given relations.
Option C (60 years) leads to inconsistent values for the son or daughter ages or breaks the condition about the daughter and wife sum.
Option D (40 years) similarly does not satisfy all the given relations and the average simultaneously.

Common Pitfalls:
This question contains many statements, so it is easy to lose track of the relationships or to misinterpret the percentage condition. Some students also incorrectly apply the average formula, forgetting that it is the total divided by the number of people. To avoid these pitfalls, write each relation algebraically step by step, keep all expressions in terms of a single variable and only then solve the final equation. Checking all conditions at the end is essential to ensure there are no hidden mistakes.

Final Answer:
The present age of Ayush is 50 years.