The current age of Y is $28$ years. Four years from now, the ratio of the ages of X to Y will be $7 : 8$. If the present age of Z is $25\%$ more than the current age of X, what was the age of Z six years ago?

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**Solution:**

1. Calculate Y's age after 4 years:
   - Current age of Y = $28$ years
   - After 4 years, age of Y = $28 + 4 = 32$ years

2. Using the given ratio of ages of X to Y after 4 years as $7 : 8$, find X's age after 4 years:
   - Let X's age after 4 years be $x$
   - Then, $\frac{x}{32} = \frac{7}{8}$
   - Solving for $x$, we get $x = 32 	imes \frac{7}{8} = 28$ years

3. Find the present age of X:
   - Since $x$ is X's age after 4 years, present age of X = $28 - 4 = 24$ years

4. Calculate the present age of Z:
   - Z's present age is $25\%$ more than X's present age
   - So, present age of Z = $24 + 0.25 	imes 24 = 24 	imes 1.25 = 30$ years

5. Find Z's age 6 years ago:
   - Age of Z six years ago = $30 - 6 = 24$ years

**Answer:** $24$ years

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