Ayush was born two years after his father's marriage. Ayush's 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 problem links the ages of Ayush, his father, and his mother with information about the father's age at the time of marriage. By carefully using the given age differences, we can determine how old the father was when he got married.

Given Data / Assumptions:

- Ayush is currently 10 years old.
- Ayush's mother is 20 years older than Ayush.
- Ayush's mother is five years younger than his father.
- Ayush was born two years after his father's marriage.
- We must find the father's age at the time of marriage.

Concept / Approach:
We first compute the mother's present age using the information about Ayush's age. Then we use the age difference between the mother and father to find the father's present age. Finally, we use the timing between the father's marriage and Ayush's birth to determine how many years ago the marriage took place and subtract this from the father's present age to get his age at marriage.

Step-by-Step Solution:
Step 1: Ayush's present age is 10 years. Step 2: The mother is 20 years older than Ayush, so mother's present age = 10 + 20 = 30 years. Step 3: The mother is five years younger than the father. Let the father's present age be F years. Then F − 5 = 30. Step 4: Solving gives F = 30 + 5 = 35 years. Step 5: Ayush was born two years after his father's marriage, and Ayush is now 10 years old. Step 6: Therefore, the marriage took place 10 + 2 = 12 years ago. Step 7: Father's age at the time of marriage = present age − years since marriage = 35 − 12 = 23 years.

Verification / Alternative check:
If the father is 35 now and was 23 at the time of marriage, then the marriage happened 12 years ago. Since Ayush is 10 years old now, he was born 10 years ago, which is 2 years after the marriage, consistent with the problem statement. The mother's present age is 30, which is both 20 years more than Ayush's age and 5 years less than the father's age. All conditions are satisfied.

Why Other Options Are Wrong:
Options such as 22, 24, 25, or 26 years lead to inconsistencies when we calculate the father's present age and compare it with the given age differences. They do not simultaneously satisfy the facts that the mother is 5 years younger than the father, 20 years older than Ayush, and that Ayush was born 2 years after the marriage.

Common Pitfalls:
Students sometimes mix up the directions of the age differences or miscalculate the timing between the marriage and Ayush's birth. Another common error is to forget to add the 2-year gap between the marriage and birth when counting back from the father's present age. Drawing a simple timeline is helpful in avoiding such mistakes.

Final Answer:
The father got married at the age of 23 years.