Six years ago, the ratio of ages of A to B was $7 : 5$. After 4 years from now, the ratio of their ages will be $11 : 9$. What is A’s present age?

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**Solution:**

1. Let the ages of A and B six years ago be $7x$ and $5x$ respectively.

2. Present ages of A and B are:
   - A's present age = $7x + 6$
   - B's present age = $5x + 6$

3. After 4 years from now, their ages will be:
   - A's age = $7x + 6 + 4 = 7x + 10$
   - B's age = $5x + 6 + 4 = 5x + 10$

4. According to the problem, the ratio of their ages after 4 years is $11 : 9$, so:

$$\frac{7x + 10}{5x + 10} = \frac{11}{9}$$

5. Cross-multiply:

$$9(7x + 10) = 11(5x + 10)$$

$$63x + 90 = 55x + 110$$

6. Simplify:

$$63x - 55x = 110 - 90$$

$$8x = 20$$

$$x = \frac{20}{8} = 2.5$$

7. Calculate A's present age:

$$7x + 6 = 7 	imes 2.5 + 6 = 17.5 + 6 = 23.5 	ext{ years}$$

**Answer:** $23 \frac{1}{2}$ years

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