'THIS' is The Color of His Hat!

What was the challenge?

Since there are only 2 black hats if Tom had saw 2 black hats (on heads of Tim & Jim) then he would have realized that he must be wearing white hat. Since, he says he doesn't know color of his hat that mean he can see either 2 white  hats or 1 black & 1 white hat on heads of other 2.

Now when Tim is saying he doesn't know color of his hat that means Jim must not be wearing black hat. If Jim had black hat then Tim would know that his color of hat is white but can't be black again as in that case Tom would have identified color of his hat in first attempt.

Hence, Jim must be wearing white hat!