Solution:

43

Explanation:
Here is the thing. You can buy any number of wings that can be divided evenly by three except for three by using the combinations of boxes of 6 and boxes of 9. (You must use at most the box of 9 and then multiple boxes of 6). Now, if there is a number that can't be divided by 3, use a box of 20. After purchasing the box of 20, if the number that remains is divisible by 3, then you are good to go. On the other hand if it is not, you will have to use a second box of 20. And the remaining number will definitely be divisible by 3.

Thus if we calculate the largest number that can't be bought is the one that requires two 20 pieces boxes before the remainder can be thinned down to a number divisible by 3. We know that 3 is the number that can't be purchased and can evenly be divisible, the largest possible number of wings that can't be bought are:
3 + 20 + 20 = 43.

Solution:

They can say this line only on Thursday.

Explanation:
Let us analyze the statement. If the person who is speaking this line is speaking truth, then the person will have to speak a lie on the next day. But if the person is lying, the next day, that person must speak truth on the next day.

If you notice here, the behavior is changing on the next day no matter what the person speaks. If we create a response table for both Jack and Rose, it will look like this:

Jack Rose
Monday Truth Truth
Tuesday Truth Lie
Wednesday Truth Lie
Thursday Truth Lie
Friday Lie Truth
Saturday Lie Truth
Sunday Lie Truth

Now as you can clearly see, Jack can say this statement on Thursdays and Sundays while Rose can say this statement on Mondays and Thursdays.

Since they are saying on the same day, the required day is Thursday.

Solution:

AMAN

Explanation:
The numbers actually corresponds to the months of the year.

4 - April
5 - May
8 - August
11 - November

Now when you combine the initials of these months, you will get the killer's name i.e. AMAN

Solution:

No one can take out any money from the taxi meter because it simply does not contain any money. It just has a timer installed that is used to decide the fare as per the distance covered.

Solution:

40 minutes

Explanation:
The total number of players = 8 + 6 = 14
According to the question, only eight players can be present on the field. Thus calculating the total time:
70 * 8 = 560
We know that there are 14 players in total so dividing the total time by 14 will give us the time spent by each player.
560/14 = 40 minutes

Solution:

The only possible way to do it is to form an equilateral triangle pyramid and then place the balls at the corners of the figure. Yes, you will have to use 3 dimensional figure.

Solution:

There is only one way to do it. The old man must ask one of his son to divide the land in two parts and then ask the other one to pick up any land he want from the two. In this way, the first son will try to be fair and the second one won't mind as he will get to choose one first.

Solution:

The image that we have attached here is self-explanatory. You just have to move four matches and you can obtain this figure.

Solution:

Since you can't identify which tablets are meant for which purpose, what you can do is take half of each tablet. In this manner, you will be able to get 1 of each tablet no matter what.

Solution:

101

Assuming '?' is no. of runs needed by Ajit in 51st inning.
(50 * 50 + ?)/51 = 51
=>2500 + ? = 51 * 51
=> ? = 2601 - 2500
=> ? = 101 (Answer)