Question

Brain Challenge or Brain Challenge:
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  Radha is the new child of Ramu and Raju. One day, they both asked Radha for her birthday. After consulting one, Radha said, I'm not going to say, but give you a clue. Radha then gave them a list of 10 dates and said, "My birthday is one of these dates".
  July 14, 16 July
  May 15, May 16, and May 19
  June 17th, June 18th
  Aug. 14, Aug. 15, Aug. 17
  Then she told Ramu's ear only the month of her birthday. Likewise, Raju's ears were the only birth of the day. Then he asked Ramu "Did you get the grip?"
  Ramu: "I don't know, but I'm sure Raju doesn't know either."
  Raju: "I didn't know until Ramu said this, but now I know."
  Ramu: "Now I Got It"
  Q: What date is Radha's birthday given above?
  PS: 1. This is not a cunning question. This is a clear-cut question that needs to be solved logically. If someone answers their own brain talk, let's discuss.
  Any one can answer the Q .. ???

Answer 1

Radha's birthday is on July 16th.

This can be solved as follows:

1. Ramu knows the month whereas Raju knows the date.

Now when Ramu says that he doesn't know and also is sure that Raju isn't aware of the correct date, it means that it is not on an unique date, i.e. 18th and 19th.

Therefore, we eradicate the possibility of her birthday being in May and June.

2. Now considering July, we see that if the date is 16th, then it matches all the statements of Ramu and Raju.

Firstly, since July has two dates, Ramu says that he doesn't know and also sure that Raju doesn't know. From here, Raju gets to know that it must be either July/August and it must be 16th as it is an unique date between July and August.