Ratio of thermal energy released in two resistor R and 3R connected...

In parallel connection, potential difference across resistors remains the same.

Thermal energy released in resistor is given by $H = \dfrac{{V}^{2}}{R} \times t$

So, the ratio is $\dfrac{{H}_{1}}{{H}_{2}} = \dfrac{\dfrac{{V}^{2}t}{R}}{\dfrac{{V}^{2}t}{3R}} = \dfrac{3R}{R} = 3: 1$.