Let whole of the ice melts and let the final temperature of the mixture be T^oC. Amount of heat energy gained by 10g of ice at -10^oC to raise its temperature to 0^oC = 10 × 10 × 2.1 = 210J

Amount of heat energy gained by 10g of ice at 0^oC to convert into water at 0^oC = 10 × 336 = 3360 J Amount of heat energy gained by 10g of water (obtained from ice) at 0oC to raise its temperature to T^oC = 10 × 4.2 × (T − 0) = 42T.

Amount of heat energy released by 10g of water at 10^oC to lower its temperature to T^oC = 10 x 4.2 x (10 − T) = 420 − 42T

Heat energy gained = Heat energy lost

210 + 3360 + 42T = 420 − 42T

T = −37.5^oC

This cannot be true because water cannot exist at this temperature.

So whole of the ice does not melt. Let m gm of ice melts. The final temperature of the mixture becomes 0^oC.

So, amount of heat energy gained by 10g of ice at -10^oC to raise its temperature to 0^oC = 10 x 10 x 2.1 = 210J

Amount of heat energy gained by m gm of ice at 0^oC to convert into water at 0^oC = m x 336 = 336m J

Amount of heat energy released by 10g of water at 10^oC to lower its temperature to 0^oC = 10 x 4.2 x 10 − 0) = 420

Heat energy gained = Heat energy lost

210 + 336m = 420

m = 0.625 gm