Aman was born three years after the marriage of his parents. Aman’s mother is three years younger than his father. At present, Aman is 20 years younger than his mother. After three years, the ratio of the age of Aman’s father to his mother will be 11:10. Find how many years before Aman was born did his parents get married?

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**Solution:**

1. Let the age of Aman’s father at the time of marriage be $x$ years.

2. Then, Aman’s mother’s age at marriage = $(x - 3)$ years (since mother is 3 years younger).

3. Aman was born 3 years after marriage, so at Aman’s birth:
   - Father’s age = $x + 3$
   - Mother’s age = $x$

4. Let Aman’s current age be $y$ years.

5. Present ages:
   - Father = $x + 3 + y$
   - Mother = $x + y$

6. Given Aman is 20 years younger than his mother:
   $$y = (x + y) - 20 \ \Rightarrow x = 20$$

7. So, father’s present age = $20 + 3 + y = 23 + y$

8. Mother’s present age = $20 + y$

9. After 3 years, the ratio of father’s age to mother’s age is 11:10:
   $$\frac{(23 + y) + 3}{(20 + y) + 3} = \frac{11}{10} \ \Rightarrow \frac{26 + y}{23 + y} = \frac{11}{10}$$

10. Cross multiply:
    $$10(26 + y) = 11(23 + y) \ 260 + 10y = 253 + 11y \ 260 - 253 = 11y - 10y \ 7 = y$$

11. Aman’s age is 7 years.

12. Since Aman was born 3 years after marriage, the marriage was $7 + 3 = 10$ years ago.

**Answer:** 10 years

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