Find the least number

Find the least number which when divided by 35, leaves remainder 25;
when divided by 45, leaves remainder 35 and
when divided by 55, leaves remainder 45 ?

Bet

I bet you for Rs. 100 that if you give me Rs. 200, I will give you
Rs. 300 in return.

Would you bet with me? Why?

Secret agents

There are N secret agents each know a different piece of secret
information. They can telephone each other and exchange all the
information they know. After the telephone call, they both
know anything that either of them knew before the call. What are
the minimum number of telephone calls needed so that all of
them know everything?

1 1 2 1 2 2 3 1 2 2 3 2 3 3 4 1 2 2 3 2 3 3 4 2 3 3 ?

What are the next three numbers in the given series?

1 1 2 1 2 2 3 1 2 2 3 2 3 3 4 1 2 2 3 2 3 3 4 2 3 3 _ _ _ ?

Phone number permutation

If you were to dial any 7 digits on a telephone in random order,
what is the probability that you will dial your own phone number?

Assume that your telephone number is of 7-digits.