In an electric circuit, two resistances R and 2R are wired in...

When two resistances are connected in parallel, the potential difference $V$ across them is the same.

The thermal energy developed in a resistance $R$ in time $t$ is given by $H = \dfrac{V^2}{R} t$

For the first resistance $R_1 = R$, the thermal energy is $H_1 = \dfrac{V^2}{R} t$

For the second resistance $R_2 = 2R$, the thermal energy is $H_2 = \dfrac{V^2}{2R} t$

The ratio of the thermal energy developed in $R$ to that in $2R$ is

$\dfrac{H_1}{H_2} = \dfrac{\dfrac{V^2}{R} t}{\dfrac{V^2}{2R} t} = \dfrac{2R}{R} = 2$

Thus, the ratio is $2 : 1$