Solution:

Solution well explained in picture below.

Solution:

The series are prime numbers with one added to it.
The original prime numbers are as follows.
101, 103, 107, 109, 113, 127

Solution:

If two widows, each having a son married the son of the other widow, and then by the consummation of marriage, both the couples had a daughter, all the aforementioned relationships will turn to be true.

Solution:

{a +b +abs (a-b)}/2
It is shown that {a +b-abs (a-b)}/2 is < {a, b}

Solution:

Charlie will be able to buy 22 chocolates.

Explanation:
The cost of each chocolate is rs.3 and Charlie has rs.45. He buys 15 chocolates with them. Since there is an offer and the scheme, he returns 15 wrappers and he gets 5 chocolates in return for free. Again he returns 3 wrappers and gets another chocolate free. Again he uses that one wrapper with the other two and gets another chocolate. So all together it is 22 chocolates.

Solution:

You can ask this question to any one person, "if I ask the man who is next you: which is the correct way and the road to the village, what would the person next to you answer?"
If you happened to ask this question to the liar, he will show you the wrong way.
And if you happened to ask this question to the one who says truth, he will also show you the wrong way.
Once you are done with this, take the other way. This will lead you to the village

Solution:

The guard and the prisoner cross the river
The guard comes back
The guard and the girl cross the river.
The guard and the prisoner comes back.
The mother and the girl cross the river.
Mother comes back
The mother and the father cross the river
Father comes back
The guard and the prisoner cross the river
Mother comes back
The father and the mother cross the river
Father comes back
The father and the boy cross the river
The guard and the prisoner comes back
The guard and the boy cross the river
The guard comes back
The guard and the prisoner cross the river.

Solution:

Nice Personality.

Explanation:
N + ice + Purse on "ality" =>Nice Personality

Solution:

There are 24 squares in this picture.

Solution:

The best way to increase the probability of winning is to place one yellow ball in the first bowl and all the other balls in the second bowl.

Now, you have a 1/2 probability of choosing the bowl with just one yellow ball. If you choose that, you win.

If you choose the other bowl, it has 49 yellow balls and 50 white balls. You still have almost 1/2 probability of picking a yellow ball out of it and winning.