a $100$g class container is at $10\mathrm{.}0$ C$.200$g of water at $90\mathrm{.}0$ C is added to the glass container. $($specific heat of water $=1\mathrm{.}00$ cal$/$gC$,$ specific heat of glass $=\mathrm{.}200$ cal$/$gC$,$ specific heat of ice $=\mathrm{.}500$cal$/$gC$).$ After sometime $10$g of ice at $-10$C is added to the system and final temperature of $50$C is reached.

d$)$ after the ice is added, calculate the latent heat of the ice