Use Joule’s law of heating

Thermal energy released in a resistor in time $t$ is $H = Pt$ where power $P = \frac{V^2}{R}$ for a resistor across potential difference $V$.

Parallel connection property

When resistors are connected in parallel, the potential difference across each resistor is the same.

So for resistors $R$ and $3R$ in parallel, both have the same voltage $V$ across them.

Heat produced in each resistor

For resistor $R$: $H_1 = \frac{V^2}{R}t$

For resistor $3R$: $H_2 = \frac{V^2}{3R}t$

Find the ratio

$H_1 : H_2 = \frac{V^2 t}{R} : \frac{V^2 t}{3R}$

Cancelling common terms $V^2 t$ and $R$, $H_1 : H_2 = 1 : \frac{1}{3} = 3 : 1$

Match with options

The ratio of thermal energy released in resistors $R$ and $3R$ is $3:1$

So the correct option is D.