Vanraj Age Calculation Setup

Let the present age of Vanraj's son be represented by $S$ years.

• Vanraj's present age is three times his son's age: Vanraj's age = $3S$.
• Vanraj's daughter is 3 years younger than the son: Daughter's age = $S - 3$.

Ages 3 Years Ago

We need to determine their ages 3 years prior to the present:

• Vanraj's age 3 years ago = $(3S - 3)$ years.
• Son's age 3 years ago = $(S - 3)$ years.
• Daughter's age 3 years ago = $((S - 3) - 3) = (S - 6)$ years.

Formulating the Age Sum Equation

The problem states that the sum of their ages 3 years ago was 58 years.

Equation:

$(3S - 3) + (S - 3) + (S - 6) = 58$

Solving for Son's Age

Combine like terms to solve the equation for $S$:

$3S + S + S - 3 - 3 - 6 = 58$

$5S - 12 = 58$

$5S = 58 + 12$

$5S = 70$

$S = \frac{70}{5}$

$S = 14$

So, the son's present age is 14 years.

Calculating Vanraj's Present Age

Vanraj's present age is $3S$. Substitute the value of $S$:

Vanraj's present age = $3 \times 14 = 42$ years.