Calorimetry!

A Copper calorimeter of mass 100 gm contains 200 gm of a mixture of ice and water. Steam at 100 degree celsius under normal pressure is passed into the container and the temperature of the mixture is allowed to rise to 50 degree celsius. if the mass of the calorimeter and its contents now is 330 gm what was the ratio of ice and water in the beginning (by mass)?

Neglect heat losses.

If this ratio is $\dfrac ab$ , where $a$ and $b$ are coprime positive integers, find $a+b$ .

Details:

• All are in SI Units
• Specific heat of copper = 420
• Specific heat of water = 4200
• Specific heat of fusion of ice = 336000
• Latent heat of condensation of steam = 2250000