Why did the Girl throw the butter out of the window?

I am a type of vehicle that has two wheels and is powered by humans. What am I?
Hint 1: You can ride me for exercise.
Hint 2: I am environment-friendly.

Make eight squares by moving only two matchsticks.
Note- Square can be of different sizes.

Queen Elizabeth organised a royal party.

To Avoid uninvited guest royal family set a password.
Jack (an uninvited person) plan to enter the party. He stand nearby the door.

First guest comes, the security person said 'twelve' and guest replied with six.
Second guest comes , the security person said 'six' and guest replied with 'three'.

Jack thought is enough and he walked to the entry point. The security person said 'eight' , Jack replied smilingly 'four'.
He was immediately thrown out of the party. why ?

Below is the sum of symbols in each row and column in the figure. Analyzing the figure, can you find out the value of the symbols?

There is a square of a particular number which when doubled, becomes 7 more than its quarter.

Can you find the number?

A man always keeps a spare tyre in his car. To make full use of all the five tyres, he changes the tyres in a manner that for a distance of 1, 00,000 km, each of them runs the same distance.

Can you calculate the distance travelled by each tyre on that journey?

I am a five-letter word under you,
Remove the first letter and I am above you,
Remove the second as well and I am around you.

Who am I?

Two old friends, Jack and Jill, meet after a long time, and discussing as:

Jack: Hey, how are you, man?

Bill: Not bad, got married and I have three kids now.

Jack: That's awesome. How old are they?

Bill: The product of their ages is 72 and the sum of their ages is the same as your birth date.

Jack: Cool..But I still don't know.

Bill: My eldest kid just started taking piano lessons.

Jack: Oh, now I get it.

How old are Bill's kids?

How can a man go eight days without sleep?