Solution:

Let us solve this problem with variables to find the general nature. Let us assume that there are x black chocolates and y white chocolates. Three things can happen when you take out two chocolates.
1) You take out two black chocolates.
Then, you will be replacing one black chocolate and so the jar will have x+1 black chocolates and y-2 white chocolates.
2) You take out two white chocolates.
Then, you will be replacing 1 black chocolate and so the jar will have x-1 black chocolates and y white chocolates.
3) You take out 1 black chocolate and 1 white chocolate. Then, you will be replacing a white chocolate and so the jar will have x-1 black chocolates and y white chocolates.
Thus at every step, you are wither removing a black chocolate or replacing two white chocolates by one black chocolate irreversibly till there is just one chocolate left. Therefore each white chocolate is equivalent to two black chocolates.

This, if the number of white chocolates are odd in number, the last one remaining will be white chocolate and if the number of white chocolates are even in number, the last one remaining will be black chocolate.

Solution:

4 6 5 3 (from magician perspective)
3 5 6 4 (viewer perspective)

Detail:

From user perspective:
3 5 6 4 => 5 6 4 3 => 6 5 4 3

For magician perspective
3 4 5 6 (ascending order as)

Solution:

The Lady sitting in the chair has the detector attached to the back of her blouse.

Solution:

It is not possible to guess only three fruits correctly: the fourth fruit is then correct too! So nobody has guessed three fruits correctly and 123-43-39-31 = 10 people have guessed four fruits correctly.

Solution:

I will be thrown at lions. Now if Akbar threw him at lions, Birbal’s statement will stand true and he will have to bury him alive. But if he bury him, the statement will emerge as false. Thus he had no choice left

Solution:

Align the toothpicks to form TEN. Use one toothpick for each of the lines.

Solution:

25 Fruits

Remember we told you that Birbal is a witty trader. So his sole motive is to get rid of the sacks as fast as he can.

For the first sack:
He must be able to fill fruits from one sack to other two sacks. Assume that he is able to do that after M check points. Now to find M,

(Space in first sack) M + (Space in second sack) M = (Remaining fruits in Third Sack) 30 – M
M = 10

Thus after 10 checkpoints, Birbal will be left with only 2 sacks containing 30 fruits each.

Now he must get rid of the second sack.
For that, he must fill the fruits from second sack to the first sack. Assume that he manages to do that after N checkpoints.

(Space in First Sack) N = (Remaining fruits in second sack) 30 – N
N = 15

Thus after he has crossed 25 checkpoints, he will be left be one sack with 30 fruits in it. He has to pass five more checkpoints where he will have to give five fruits and he will be left with twenty five fruits once he has crossed all thirty check points.

Solution:

If you see the picture, they formed a pentagonal shape and achieved the required.

Solution:

The answer is very simple. All she had to do is take the fifteen cards from the top and reverse them. This would make another pile out of that and there will be two piles - one of 15 cards and one of 37 cards. Also both of them will have the same number of inverted cards.

Just think about it and if the mathematical explanation will help you understand better, here it is.
Assume that there were p inverted cards initially in the top 15 cards. Then the remaining 37 cards will hold 15-p inverted cards.
Now when she reverses the 15 cards on the top, the number of inverted cards will become 15-p and thus the number of inverted cards in both of the piles will become same.

Solution:

The driver is actually the wife and mother.

Solution:

step 3 is wrong