Ayush was born two years after his father's marriage. His mother is five years younger than his father but 20 years older than Ayush, who is now 10 years old. At what age did the father get married?

Introduction / Context:
This age puzzle involves three family members: Ayush, his father, and his mother. You are given information about age differences and the timing of Ayush's birth relative to his father's marriage. The goal is to compute the father's age at the time of marriage. Such questions test your ability to manipulate age differences and timelines logically.

Given Data / Assumptions:

• Ayush is currently 10 years old.
• His mother is 20 years older than Ayush, so her present age is 10 + 20 = 30 years.
• His mother is five years younger than his father, so the father's present age is 30 + 5 = 35 years.
• Ayush was born two years after his father's marriage.
• All ages are in complete years, and we ignore months for this calculation.

Concept / Approach:
Once we determine the present ages of the parents, we can work backwards. If the father is 35 years old now and Ayush is 10, then the father's age when Ayush was born was 35 - 10 = 25 years. Since the marriage took place two years before Ayush was born, the father must have been two years younger at that time. Therefore, we subtract two more years from 25 to obtain the father's age at marriage.

Step-by-Step Solution:
Step 1: Ayush is 10 years old at present.Step 2: Mother is 20 years older than Ayush, so mother's present age = 10 + 20 = 30 years.Step 3: Mother is five years younger than father, so father's present age = 30 + 5 = 35 years.Step 4: When Ayush was born 10 years ago, father's age was 35 - 10 = 25 years.Step 5: Ayush was born two years after father's marriage, so at the time of marriage father was 25 - 2 = 23 years old.Step 6: Therefore, the father got married at the age of 23 years.

Verification / Alternative check:
We can check the overall consistency: if father married at 23 years, then two years later at age 25 he had Ayush. Ten years after that, he would be 35, matching the computed present age. At that same present time, mother is 5 years younger, so she is 30, which is also 20 years older than Ayush (10). All conditions in the problem are satisfied, confirming that the calculation is correct.

Why Other Options Are Wrong:
Option B (25 years): This would suggest father's age at marriage equals his age at Ayush's birth, which contradicts the condition that Ayush was born two years after the marriage.
Option C (33 years) and Option D (35 years): These ages are too high and do not align with the given age differences and birth timelines when checked systematically.

Common Pitfalls:
A common mistake is to misinterpret the phrase “two years after his father's marriage” and either add or subtract incorrectly. Another frequent error is forgetting to use the mother's age relationship to verify or calculate the father's present age. Carefully drawing a time line for birth events and marriage often helps avoid such confusion and leads to a quick and correct solution.

Final Answer:
Ayush's father got married at the age of 23 years.