Present age of Ram is three times of his son’s present age and two -third of his father’s present age. At present, the average age of all of them is 34 years. What is the difference between present age of Ram’s son and his father’s age?

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The correct option is 42 yrs.

` structure. Let's write down the solution formatting step by step: ```html 42 yrs

The correct answer is 42 yrs.

Step 1: Define variables for the present ages.
Let the present age of Ram's son be $x$ years.

According to the question, Ram's age is three times his son's age:
$\text{Ram's age}=3x$

Ram's age is also two-thirds of his father's age:
$\text{Ram's age}=\frac{2}{3}\times \text{Father's age}$

Therefore, we can find the father's age in terms of $x$:
$3x=\frac{2}{3}\times \text{Father's age}$
$\text{Father's age}=3x\times \frac{3}{2}=\frac{9x}{2}$

Step 2: Form an equation using the average age.
The average age of all three persons is given as 34 years:
$\frac{\text{Son's age}+\text{Ram's age}+\text{Father's age}}{3}=34$

Substitute the ages in terms of $x$ into the equation:
$\frac{x+3x+\frac{9x}{2}}{3}=34$

Multiply both sides by 3:

Combine the terms:
$4x+\frac{9x}{2}=102$
$\frac{8x+9x}{2}=102$
$\frac{17x}{2}=102$

Solve for $x$:
$17x=204$
$x=\frac{204}{17}=12$

Step 3: Calculate the individual ages and the required difference.
Son's present age = $12$ years.
Father's present age = $\frac{9\times 12}{2}=54$ years.

Difference between father's age and son's age:
$\text{Difference}=54-12=42\text{yrs}$

Thus, the required difference between the present age of Ram’s son and his father’s age is 42 yrs.