The ratio of the present ages of Aman and David is $2 : 5$. After 10 years, the sum of their ages will be $69$ years. What is the difference between their present ages?

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**Solution:**

1. Let the present ages of Aman and David be $2s$ and $5s$ respectively, based on the given ratio $2 : 5$.

2. After 10 years, their ages will be:
   - Aman: $2s + 10$
   - David: $5s + 10$

3. According to the problem, the sum of their ages after 10 years is $69$:
   $$ (2s + 10) + (5s + 10) = 69 $$

4. Simplify the equation:
   $$ 7s + 20 = 69 $$
   $$ 7s = 69 - 20 = 49 $$
   $$ s = 7 $$

5. Calculate the difference between their present ages:
   $$ (5s - 2s) = 3s = 3 	imes 7 = 21 	ext{ years} $$

**Answer:** $21$ years

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