A black body calorimeter filled with hot water cools from ${60}^{0}C$  to ${50}^{0}C$ in 4 min and ${40}^{0}C$   to ${30}^{0}C$  in 8 min. The approximate temperature of surrounding is 

$\frac{({\mathrm{\theta }}_1-{\mathrm{\theta }}_2)}{\mathrm{t}}=-\mathrm{K}[\frac{({\mathrm{\theta }}_1+{\mathrm{\theta }}_2)}{2}-{\mathrm{\theta }}_0]$

${\theta }_0$   is the  temperature of surroundings  substituting the values we have, 

$\frac{60-50}{4}=-\mathrm{K}\left[\left(\frac{60+50}{2}\right)-{\mathrm{\theta }}_0\right]$

$\frac{40-30}{8}=-\mathrm{K}\left[\frac{(40+30)}{2}-{\mathrm{\theta }}_0\right]$
Solving these two equations  we set   ${\theta }_0={15}^{0}C$