The water equivalent of a calorimeter is $10\, g$ and it contains $50 \,g$ of water at $15�C$. Some amount of ice, initially at $-10�C$ is dropped in it and half of the ice melts till equilibrium is reached. What was the initial amount of ice that was dropped (when specific heat of ice $= 0.5 \,cal\, gm^{-1}�C^{-1},$ specific heat of water $= 1.0 \,cal\, gm^{-1}�C^{-1}$ and latent heat of melting of ice $= 80 \,cal \,gm^{-1}$) ?