Heat is lost by steam in two stages: 

(i) for change of state from steam at 100^oC to water at 100^oC is m x 540
(ii) to change water at 100^oC to water at 80^oC is m $\times$ 1 $\times$ (100 - 80), where m is the mass of steam condensed.
Total heat lost by steam is m $\times$ 540 + m $\times$ 20 = 560m (cals) Heat
gained by calorimeter and its contents is

$=(1.1+0.02)\times (80-15)=1.12\times 65\text{ cals }$

using Principle of calorimetery, Heat gained = heat lost

$$\begin{gathered} \therefore 560\mathrm{m}=1.12\times 65 \\ \Rightarrow \mathrm{m}=0.130\mathrm{gm} \end{gathered}$$