If I mix ice at -10 C to water at 60 C having the same amount, the final temperature of mixture comes out to be 0 C, but Can we calculate the time it takes?

Dear student,

In this case, with just this information given? No. Infact one could use the concept of thermal conductivity of water to find it, but in this problem it would be very complex since we will have to assume that temperature gets changed layer by layer.