Let father's age be $F$ and child's age be $C$.

Given $C = \dfrac{F}{2}$

Twenty years ago: $F - 20 = 10(C - 20)$

Substitute $C = \dfrac{F}{2}$:

$F - 20 = 10\left(\dfrac{F}{2} - 20\right)$

$F - 20 = 5F - 200$

$180 = 4F \Rightarrow F = 45$

Answer: $\boxed{45\text{ years}}$ ✅ (Option d)