Two coils require 20 minutes and 60 minutes respectively to produce same amount of heat energy when…

If $H$ is the heat required to heat the water, then

$P_1\times 60=H\Rightarrow P_1=\frac{H}{60}$ and $P_2\times 20=H\Rightarrow P_2=\frac{H}{20}$

When the coils are connected in parallel their powers will get added. If the required time now is $t$, then

$$\begin{gathered} \left(P_1+P_2\right)t=H \\ \Rightarrow t=\frac{H}{{\displaystyle \frac{H}{60}}+{\displaystyle \frac{H}{20}}}=15 \min \end{gathered}$$