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\( 2 \mathrm{~kg} \) of ice at \( -20^{\circ} \mathrm{C} \) is mixed with \( 5 \mathrm{~kg} \) of water at \( 20^{\circ} \mathrm{C} \) in an insulating vessel having a negligible heat capacity. Calculate the final mass of water remaining in the container. It is given that the specific heats of water and ice are 1 \( \mathrm{kcal} / \mathrm{kg} \) per \( { }^{\circ} \mathrm{C} \) and \( 0.5 \mathrm{kcal} / \mathrm{kg} /{ }^{\circ} \mathrm{C} \) while the latent heat of fusion of ice is \( 80 \mathrm{kcal} / \mathrm{kg} \quad \) [IIT-JEE (Screening) 2003]
(a) \( 7 \mathrm{~kg} \)
(b) \( 6 \mathrm{~kg} \)
(c) \( 4 \mathrm{~kg} \)
(d) \( 2 \mathrm{~kg} \)
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