Ice at 20°C is added to 50g of water at 40°C. When the temperature of the mixture reaches 0°C, it is found that 20g of ice is still unmelted. The amount of ice added to the water was close to (specific heat of water = 4.2J/g/°C, specific heat of ice = 2.1J/g/°C, heat of fusion of water at 0°C = 334J/g)

Let the amount of ice added be m grams.

Heat gained by ice in rising from -20°C to 0°C = m × 2.1 × 20 = 42m J
Heat gained by ice in melting at 0°C = (m - 20) × 334 J
Heat lost by water in cooling from 40°C to 0°C = 50 × 4.2 × 40 = 8400 J

Heat gained by ice = Heat lost by water
42m + (m - 20) × 334 = 8400
42m + 334m - 6680 = 8400
376m = 15080
m = 15080 / 376
m ≈ 40 g

Therefore, the amount of ice added to the water was close to 40g.