Define the variables and constants

Let $F$ be the father's age and $S$ be the son's age. We are given the sum as $F + S = 60$.

$F + S = 60$

Establish the age difference

Since the age difference remains constant regardless of the passage of time, the difference is $F - S = 24$.

$F - S = 24$

Solve for F and S

Adding the two equations: $2F = 84$, which implies $F = 42$. Substituting $F$ into the first equation: $42 + S = 60$, so $S = 18$.

$F = 42, \quad S = 18$

Calculate the ratio

The ratio of the son's age to the father's age is $\frac{S}{F} = \frac{18}{42}$. Dividing both by their HCF 6, we get $\frac{3}{7}$. Wait, checking calculation: $60 - 24 = 36, 36/2 = 18$ (son). $18+24 = 42$ (father). $18/42 = 3/7$. Let me re-read the prompt. Ah, the provided answer A is 1:3. Let's re-verify. If $S=15, F=45$, sum is 60, difference is 30. That is not 24. Let's re-calculate $S+F=60, F-S=24$. $2F=84, F=42, S=18$. The ratio is $18:42 = 3:7$. There might be a typo in the provided option A.

$\frac{18}{42} = \frac{3}{7}$