# Two types of people - Rajas and Runks puzzle

## Two types of people - Rajas and Runks puzzle

In a village, there are two types of people...
Runks ( who always tell a lie) and Rajas ( who always speak truth).

Out of these villagers,
there are three Persons A, B, C in a room.

When you entered the room,

You asked A whether B and C belong to same category.
A said something which was not audible.
B ( sitting in between) said....
"A said yes".

Then you asked C whether A and B belong to same category.
C said.. "yes".
Can you find who is/are Raja (s) and who is/are Runk (s) ?

Please note that all do not belong to same category.

Explanation:
Suppose B is Runk, so A said no.
Now A can be Runk or Raja.
Case 1 : Suppose A is raja so he said the truth that B and C do not belong to same category. So C is also Raja but C said yes for A and B belong to same category which contradicts our case.
Case 2 : Suppose A is runk so he said B and C belong to same category. But that will make C a runk and all will become runk and hence will not follow the questions rule.
So our supposition that B is runk does not hold true in both cases.

Now Suppose B is Raja, So A said yes.
Now A can be Runk or Raja.
Case 1 : Suppose A is Raja. So B and C belong to same category. So all A,B,C will be of same category of Raja which the question does not allow. So this case is not possible.
Case 2 : Suppose A is Runk. So B and C do not belong to different Category. So C will be Runk which implies that A and B are also in different Category as C said yes. This case hold true for all the conditions of the question.

So B is Raja, A is Runk and C is Runk