The present age of X is 50\% more than that of Y, and the present age of Z is the average of the present ages of X and Y. If the difference between the age of Z after 5 years and the age of Y 3 years ago is 10 years, what will be the age of X after 6 years?

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**Solution:**

1. Let the present age of Y be *y* years.

2. Since X's present age is 50\% more than Y's, we have:
   $$X = y + 0.5y = 1.5y$$

3. The present age of Z is the average of X and Y:
   $$Z = \frac{X + Y}{2} = \frac{1.5y + y}{2} = \frac{2.5y}{2} = 1.25y$$

4. According to the problem, the difference between Z's age after 5 years and Y's age 3 years ago is 10 years:
   $$ (Z + 5) - (Y - 3) = 10 $$

Substitute values:
   $$ (1.25y + 5) - (y - 3) = 10 $$

Simplify:
   $$ 1.25y + 5 - y + 3 = 10 $$
   $$ 0.25y + 8 = 10 $$
   $$ 0.25y = 2 $$
   $$ y = 8 $$

5. Now, find X's present age:
   $$ X = 1.5y = 1.5 	imes 8 = 12 $$

6. The age of X after 6 years will be:
   $$ 12 + 6 = 18 $$

**Answer:** 18 years

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