If 5 cats catch 5 mice in 5 minutes, how long will it take one cat to catch a mouse?

I am the largest in my family of fifty.
The youngest of our family lives separately from the rest of the family and so do I.
I am regarded as harsh and tough.
I am so large, you cut me in two equal halves,
each half would still be larger than the second largest member of the family.
Who am I?

I am under you when I am whole.
I shift above you if you remove the first letter.
I come all around you if you remove the second as well.

Can you tell me who I am?

You’re out on the water and see a boat filled with people. You look away for a second and look back again, but this time you don’t see a single person on the boat. Why? Hint: The boat did not sink.

Manish and Manoj play 5 games of chess.
Both Manish and Manoj win the exact same number of games. There is no tie at all.

How?

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?

A sea diver is a real show-off. He showed everyone that he can hold his breath underwater for 15 minutes.

I went to the diver and told him that I can be underwater for double the time i.e 30 minutes.
He responded that he will give me 100$ if I would be able to do it. I won 100$.

What did I do?

How many points are there on the globe where, by walking one mile south, then one mile east and then one mile north, you would reach the place where you started?

We have four gears with below features=> Both Gear A and D has 60 teeth=> Gear B has 40 teeth=> Gear C has 20 teeth=> Every two minutes, Gear B makes 25 full turns.What is the relative speed of Gear A and Gear B?

I am a word that begins with the letter “i.” If you add the letter “a” to me, I become a new word with a different meaning, but that sounds exactly the same. What word am I?