Solution:

In such questions, the best thing is to assume each one of them as his sister till you can find all the conditions fulfilled. According to our assumptions, Megan is Alex's sister. We will discuss only this case therefore.

Assuming that Megan is Alex's sister, she has told a lie. This also means that Maggie is not Alex's girlfriend.
If Katie is the truth speaking girl, Megan is lying and it proves our assumption.
Now, if Charlize is Alex's girlfriend, she has also told a lie. This further tells that Katie is speaking the truth which also supports our assumption.
Maggie stated that Charlize is not his sister and that is also true because according to our assumption, Charlize is his girlfriend.

Taking that into account, we can conclude that Megan is Alex's sister and Charlize is his girlfriend.

In any other assumption, you will find the data conflicting with the conditions.

Solution:

Mythology is the word that can be formed using all the 9 letters. Can you think of any other word? Do comment if you can.

Solution:

This picture comprises of 31 hands and 155 fingers.

Solution:

The movie name is - Limitless. If you have studies mathematics and are fond of movies, it was quite easy.

Solution:

The four vegetables that can be formed by adding vowels to the given random letters are the following:

TURNIP
LETTUCE
CUCUMBER
POTATO

Solution:

Look at her hand. She has five fingers besides the obvious thumb that is not visible. This is not possible and that is what is wrong with the picture.

Solution:

Now there can be two solutions to the given situation because there can be two situations:
Suppose if B and C have same colors, A will know that his color is the other one and he will be able to speak up the first.
Now if B and C do not have same colors, A will stay silent. This will tell B that his and C's colors are different. Thus he will speak up first.

So either A or B will speak up first depending on the situation.

Solution:

Diwali was celebrated as a mark of Lord Krishna win over the Narakasuna by killing him. Now Krishnavathaar comes after Raamavathaar in the Dasavataar. Therefore, Lord Rama could not have celebrated Diwali.

Solution:

Look at the eyes of all the three images. The second one has eyes positioned at different places. This is why the second image is the odd one out.

Solution:

Rohan kept his finger in the center of the table (not the exact center). The interviewer asked him how he was so sure that this was the exact center. He told the interviewer that according to the interviewer, his last question had already been asked.

The interviewer was impressed by his quick witted brain and he was offered the job.

Solution:

The movie name is Divergent.

Its based on a popular fiction series by Veronica Roth. Easy to guess for book lovers.

Solution:

There are a total of 104 triangles in this picture.

Solution:

There is no mention if you can use sign or not and thus the only possible way to get this is as follows:

(15 - 9) + (13 - 7) + (7 - 1) + (9 - 1) + (13 - 9)

If you solve inside the brackets, you will get the following equation
6 + 6 + 6 + 8 + 4
Adding all these numbers, you will get 30 which is the required sum.

Solution:

Suppose that we have B buses at present and S refers to the space before we expanded. This implies that
S = B - 12 ----- [1]

When we expanded, we came up with more space. It can be equated as
S + 0.4 x S = B + 12 ------ [2]

Rewriting the equation we get
1.45 = B + 12
Also, B = 1.45 - 12 ----- [3]

The first equation can also be written as
B = S + 12 ----- [4]

If we equate the third and fourth equation, we will have
1.4 S - 12 = S + 12

Let us subtract S from both the sides
0.4 S - 12 = 12

Adding 12 to both sides
0.4 S = 24

Multiplying by ten and dividing by four on both sides
S = 60

If we insert this value in the fourth equation, we will have
B = 72

Thus there are 72 buses.

Initially we had room for 60 buses after expanding the garage space by 40 percent, we will be having enough room to have 84 buses out of which twelve is for future.

Solution:

We have moved the two matchsticks colored in purple and now the resultant figure contains five 1x1 squares, one 2x2 square and one 3x3 square.

Solution:

Rhea will open just one present.
Cindy|Y - Y is the 25th alphabet
Duk|E - E is the 5th alphabet
Joh|N - N is the fifteenth alphabet
Rhe|A - A is the first alphabet

Solution:

Need for Speed.

Explanation:
Clearly, ds/dt refers to speed. Concluding with whats written already, the movie name is Need for Speed.

Solution:

It was easy as it was daytime. They did not need headlights or the light on the number plate.

Solution:

It is called harmony. The reason is simple. The husband receives peace after giving that money to his wife.

Solution:

19|9|9

Explanation:
This is simple. All the months have been coded with a distinctive way.
Let's see about January:
January = 1071 = 10|7|1
10 is the position of J, the first letter of January in alphabetical order.
7 is the number of letters used in forming the word January.
1 is the position of January in the calendar.

For February:
February = 682 = 6|8|2
6 is the position of F, the first letter of February in the alphabetical order.
8 are the number of letters used in forming the word.
2 is the position of February in the calendar.

Similarly, September = 19|9|9
19 is the position of S, the first letter of September in the alphabetical order.
9 are the number of letters used in forming the word.
9 is the position of September in the calendar.