Two identical heater filaments are connected first in parallel and then in series. At the same applied…

Let the resistance of the filaments be $R$ and the voltage be $V$.

For the series combination the power is 

$P_1=\left(\frac{V^2}{2R}\right)$ 

For parallel combination,

$P_2=\frac{V^2}{\left(\frac{R}{2}\right)}=\left(\frac{2V^2}{R}\right)$

Hence, the ratio is

$\Rightarrow \frac{P_2}{P_1}=\frac{4}{1}$