Can you solve the photo plexer logic ?

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 ?

Assume the given figure to be a delicious doughnut. Yes, now you can concentrate more on the puzzle. So you have this delicious doughnut in your refrigerator when your friends come knocking at the door. There are eight of them. Now you have to make three cuts in this doughnut so that each one of you nine people can enjoy a piece of it. Neither you nor your friends would mind the size of their piece as long as they are getting it. How will you do it?

The average age of 10 members of a committee is the same as it was 4 years ago, because an old member has been replaced by a young member. Find how much younger is the new member ?

Jessica is telling her friends this story and asks them to guess if it’s the truth or a lie: “There was a man sitting in a house at night that had no lights on at all. There was no lamp, no candle, and no other source of light. Yet, he sat in the house and read his book happily.” Her friends say she’s lying, but Jessica corrects them and says she’s telling the truth. Jessica’s story is true—but how?

How can one talk without saying a single word?

Two batsman each on 94 runs. Seven runs needed to win in last 3 balls. Both make 100*. How?

There is something which is always coming but never arrives?

At a party, there are five people and a whole round cake lying at the centre of the table. Only four people will make a cut and take their piece and the last one will get the remaining piece on the table. How can they make sure that everyone gets a 1/5th of the piece?

I have lakes with no water, mountains with no stone and cities with no buildings. What am I?