Present age of Ram is three times his son's present age and two-thirds of his father's present age. The average age of Ram, his son, and his father is 34 years. What is the difference between the present age of Ram's son and his father's age?

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**Solution:**

1. Let the present age of Ram's son be *x* years.

2. Then, Ram's present age = 3 *x* (since Ram is three times as old as his son).

3. Ram's present age is also two-thirds of his father's present age. Let father's age be *F*.

So, $ $3x = \frac{2}{3} F$ $  
   $ $\Rightarrow F = \frac{3}{2} \times 3x = \frac{9}{2} x = 4.5x $$

4. The average age of Ram, his son, and his father is 34 years:

$$ $\frac{x + 3x + 4.5x}{3} = 34$ $$

$$ $\frac{8.5x}{3} = 34 $$$

$$ 8.5x = 102 $$

$$$ x = \frac{102}{8.5} = 12$ $$

5. Now, son's age = 12 years

Father's age = $$4.5 \times 12 = 54$$ years

6. Difference between father's age and son's age:

$$ 54 - 12 = 42 $$ years

**Answer:** 42 years

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