A calorimeter of water equivalent 10g contains a liquid of mass 50g at 40°C. When $m$ gram of ice at -10°C is put into the calorimeter and the mixture is allowed to attain equilibrium, the final temperature was found to be 20°C . It is known that specific heat capacity of the liquid changes with temperature as $\mathrm{S}=(1+\frac{\mathrm{\theta }}{500})\mathrm{cal}{\mathrm{g}}^{-1}{}^0{\mathrm{C}}^{-1}$ where $\mathrm{\theta }$ is temperature in °C. The specific heat capacity of ice, water and the calorimeter remains constant and values are ${\mathrm{S}}_{\mathrm{ice}}=0.5$ $\mathrm{cal}{{\mathrm{g}}^{-1}}^0{\mathrm{C}}^{-1};$ ${\mathrm{S}}_{\mathrm{water}}=1.0 {\mathrm{calg}}^{-1}{}^0{\mathrm{C}}^{-1}$and latent heat of fusion of ice is ${\mathrm{L}}_{\mathrm{f}}=80$ ${\mathrm{calg}}^{-1}$. Assume no heat loss to the surrounding, the value of $m$ is: