I have teeth but i don't bite. Who Am I ?

I am taken from a mine and shut up in a wooden case, from which I am never released, and yet I am used by almost every person. What am I?

If,

20 % 5 = 24

21 % 7 = 33

42 % 6 = 67

Then;

66 % 6 = ?

A girl is twice as old as her brother and half as old as her father. In 50 years, her brother will be half as old as his father. How old is the daughter now?

If a wheel has 54 spokes, how many spaces are there between the spokes?

The following alphametic has only one solution. Can you find it?
ENLIST + SILENT + LISTEN = ANAGRAM

PS: You may start the number from 0.

If you go to the movies and you're paying, is it cheaper to take one friend to the movies twice, or two friends to the movies at the same time?

Mr Black, Mr Gray, and Mr White are fighting in a truel. They each get a gun and take turns shooting at each other until only one person is left. Mr Black, who hits his shot 1/3 of the time, gets to shoot first. Mr Gray, who hits his shot 2/3 of the time, gets to shoot next, assuming he is still alive. Mr White, who hits his shot all the time, shoots next, assuming he is also alive. The cycle repeats. If you are Mr Black, where should you shoot first for the highest chance of survival?

Can you fill the blank with the correct number?

6 30 870 756030 _____

Today is a very icy and cold morning in Newcastle. Mr Shearer, an office bus driver arrived to pick up the employees from the last stop. Shearer suddenly remembers that he needs to pick a newly joined 4miles to the north. Mr Shearer lost his direction compass, a few minutes later Shearer is able to figure that he is moving in the correct direction i.e. north. How did Shearer know that he is moving in the correct direction?