What is the centre of gravity?

A few friends are enjoying their sea voyage in a boat full of apples. On the way, they felt hungry and thus decided to eat the apples. Together, they ate two dozen of apples. When they have eaten the apples, will there be any change in the water level?

There is a box in which distinct numbered balls have been kept. You have to pick two balls randomly from the lot.

If someone is offering you a 2 to 1 odds that the numbers will be relatively prime, for example
If the balls you picked had the numbers 6 and 13, you lose $1.
If the balls you picked had the numbers 5 and 25, you win $2.

Will you accept that bet?

What number does the below three word/phrase identify and why?
1. Deck
2. Year
3. Singing in the Rain

Which fur should we be getting from the Lion?

What does the below rebus puzzle mean?

When my father was 31 I was 8. Now he is twice as old as me. How old am I?

10 people came into a hotel with 9 rooms and each guest wanted his own room. The bellboy solved this problem.
He asked the tenth guest to wait for a little with the first guest in room number 1. So in the first room, there were two people. The bellboy took the third guest to room number 2, the fourth to number 3, ..., and the ninth guest to room number 8. Then he returned to room number 1 and took the tenth guest to room number 9, still vacant.
How can everybody have his own room?

Transform the word THINK into BRAIN while changing only one letter at a time in a manner that each of the word in the process is a real word!!!

What 5-letter word typed in all capital letters can be read the same upside down?