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 handed them a list of 10 dates and said, "My birthday is one of these dates".
July 14th, July 16th
May 15, May 16, and May 19
June 18 and June 17
Aug. 14, Aug. 15, Aug. 17
Then she told Ramu's ear only the month of her birthday. Likewise, Raju's ears were told only on the day of birth. 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. It 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 .. ???
Answers
Answer:Jul 16
Explanation:Let's break it into different cases
Consider if the day was either of 18 or 19 raju would have guessed immediately as it doesnt repeat. So both those numbers could be eliminated
Now consider the case of Ramu. If he was given the month of may or june he cannot say for sure that raju doesnt know the answer as 19 would be present in may and 18 in june so ramu cant be given either may or june.
Now 2 mnths remain aug or jul
Lets consider august first.
If ramu was given august he can certainly say raju doesnt knw the day as all the dates repeat. And when ramu says this, raju can find that ramu was not given the month of may or june as this would have confused ramu. But still, he cant figure out whether it is from july, so 14 can be avoided.
If 15 was given to raju, he could say that he has found the answer but ramu could never find the answer as 15 and 17 repeat in may and june so he would be confused and both these could be avoided.
So lets take july now.
14 was arleady considered and avoided so only one left is july 16
Lets check it.
If Ramu was given july and raju was given 16, initially ramu could say for certain that raju can never find it as it repeats. As he says this, raju finds out it is july 16. As 16 repeats in may only,
when raju says he found the answer, ramu can pick july 16
July 16 is Radha's birthday.
Explanation:
The choice of dates are:
July 14th, July 16th
May 15, May 16, and May 19
June 18 and June 17
Aug. 14, Aug. 15, Aug. 17
We first eliminate unique dates because that would have made Raju and Ramu guess easily. So June 18 and May 19 is removed. This helps us to further eliminate the months containing these two dates which brings us to remove May and June dates. We are now left with either July (2 days) or August (3 days).
Now we have to eliminate the common date between July and August, which makes us remove July 14 and August 14.
We are now left with July 16, and two dates in August.
The date has to be unique for Raju to guess. So August will be eliminated as it has two dates which will make it difficult for Raju to guess.
So the only unique date we are left with is July 16.
Hence July 16 is Radha's birthday.