I start and end with 500 and carry a 5 in my heart. But I require the first letter and the first number to be complete. I am the name of a King.

Who am I ?

If,

6 / 7 = 2
3 / 9 = 7
8 / 2 = 6

Then

4 / 5 = ?

What can run but never walks, has a mouth but never talks, has a head but never weeps, has a bed but never sleeps?

Find a 9-digit number, which you will gradually round off starting with units, then tenth, hundred etc., until you get to the last numeral, which you do not round off. The rounding alternates (up, down, up ...). After rounding off 8 times, the final number is 500000000. The original number is commensurable by 6 and 7, all the numbers from 1 to 9 are used, and after rounding four times the sum of the not-rounded numerals equals 24.

What can you catch but never throw?

There is one thing that goes round the house and also inside the house but never even share a brief touch. What is it?

If we change the South-East direction into North and North-East into West and all others similarly.
Can you find out which direction will be in the place of South-West direction?

Two friends were betting. One said to the other, "The coin will be flipped twenty times and each time the coin lands on the head, I will give you $2 and each time it lands on the tale, you will give me $3." After flipping the coin twenty times not a single penny was exchanged among them.

How many times did the coin land on heads?

A large container is kept in open under the rain. Every passing hour, the water collected inside the container becomes double what it was.

In ten hours, the container is filled completely. Can you calculate how long would it have taken to be filled in half?

Which three-digit number, made of consecutive digits, like 567, is 2 less than a cube and 2 more than a square?