$2 \mathrm{kg}$ of ice at $-\mathrm{20°C}$ is mixed with $5 \mathrm{kg}$ of water at $\mathrm{20°C}$. The water content of the final mixture is (Latent heat of ice $=80\mathrm{ }\mathrm{kcal} {\mathrm{kg}}^{-1}$, the specific heat of water $=1 \mathrm{kcal}{\mathrm{kg}}^{-1}°{\mathrm{C}}^{-1}$ and specific heat of ice $=\text{0.5}\mathrm{ }\mathrm{kcal}\mathrm{ }{\mathrm{kg}}^{–1}°{\mathrm{C}}^{–1}$ )

Here, $\mathrm{m}$, $\mathrm{s}$ and ${\mathrm{\theta }}_1$ are the mass, specific heat and temperature difference for water respectively. Similarly, $\mathrm{M}$, $\mathrm{S}$ and ${\mathrm{\theta }}_2$ are the corresponding quantities for ice. Here, $\mathrm{L}$ is the latent heat of fusion.

We have, the heat lost by water $=\mathrm{ms\theta }$, heat gained by ice $=\mathrm{MS\theta }+\mathrm{ML}$.

From the principle of calorimetry, we have, the heat lost by water=heat gained by ice.

Hence, ${\mathrm{ms\theta }}_1={\mathrm{MS\theta }}_2+\mathrm{ML}$.