Age Calculation Steps

Let the age of B be represented by '$x$' years.

According to the question:

• Age of A is 3 times B's age: Age(A) = $3x$ years.
• Age of A is half the age of C: Age(A) = $\frac{\text{Age(C)}}{2}$, which implies Age(C) = $2 \times$ Age(A).
• Substituting Age(A) = $3x$, we get Age(C) = $2 \times (3x) = 6x$ years.

Sum of Ages Equation

The sum of the ages of A, B, and C is given as 120 years.

Age(A) + Age(B) + Age(C) = 120

Substituting the expressions in terms of $x$:

$3x + x + 6x = 120$

Solving for Age of A

Combine the terms involving $x$:

$10x = 120$

Solve for $x$:

$x = \frac{120}{10}$

$x = 12$

Now, calculate the age of A using the value of $x$:

Age(A) = $3x = 3 \times 12 = 36$ years.