Heat required to melt m kg of ice = $m \times L = m \times 80$ cal/g. Heat available from water cooling to 0°C = $m \times s \times \Delta T = m \times 1 \times 10$ cal/g. Since the heat available (10m) is less than the heat required to melt all the ice (80m), not all the ice will melt, and the final temperature of the mixture will be 0°C.