Sham knows that Ram's birthday falls between 14th and 21st October. According to Shalini, Ram's birthday falls between 15th and 20th October. Both of them also know that this year his (Ram's) birthday falls on Wednesday. If 2nd October is Monday, then when does Ram's birthday fall?

Sham: Ram's birthday is between 14th and 21st October (i.e., 15th to 20th inclusive).

Shalini: Ram's birthday is between 15th and 20th October (i.e., 15th to 19th inclusive).

Common Range: 15th to 20th October.

Now, Ram's birthday falls on a Wednesday and 2nd October is a Monday. 

If 2nd October is a Monday, 4th October will be a Wednesday. 

Then, 4+7 = 11th October will also be Wednesday. 

Similarly, 11 + 7 = 18th October will also be Wednesday.

Hence, the only Wednesday possible between the common range is 18th October. Hence, we can say Ram's birthday falls on 18th October.