The present age of A is 6 years more than that of B and 9 years less than that of C. If the average of the present ages of A, B, and C is 39 years, what will be the ratio of the ages of A and C after 7 years?

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**Solution:**

1. Let the present age of B be *x* years.

2. Then, the present age of A = *x + 6* years (since A is 6 years older than B).

3. The present age of C = *x + 6 + 9 = x + 15* years (since A is 9 years younger than C).

4. The average of their ages is given as 39 years, so:
   
   $$\frac{(x) + (x + 6) + (x + 15)}{3} = 39$$

5. Simplify the equation:
   
   $$\frac{3x + 21}{3} = 39$$
   $$3x + 21 = 117$$
   $$3x = 117 - 21 = 96$$
   $$x = 32$$

6. Therefore, ages are:
   - B = 32 years
   - A = 32 + 6 = 38 years
   - C = 32 + 15 = 47 years

7. After 7 years, their ages will be:
   - A = 38 + 7 = 45 years
   - C = 47 + 7 = 54 years

8. The required ratio of ages of A and C after 7 years is:
   
   $$\frac{45}{54} = \frac{5}{6}$$

**Answer:** 5 : 6

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