Our product and our sum always give the same answer. Who are we?

Solve The below Equation:

ALFA + BETA + GAMA = DELTA

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 ?

What number divided by 4 is the same as that number minus 4?

I want to fill my bucket using both cold and hot water.
I have two taps for both cold and hot water. The hot water tap fills the bucket in exact 6 hours and the cold water tap fills the bucket in exact 4 hours.
I turn both of them simultaneously but I forgot to turn off another tap which removes the water out of the bucket. This tap can empty the bucket in 12 hours.

How Long will it take to fill the bucket?

John needs to purchase 100 chocolates from three different shops and he has exactly 100 rupees to do that which he must spend entirely. He must buy at least 1 Chocolate from each shop.

The first shop is selling each chocolate at 5 paise, the second is selling at 1 rupee and the third is selling at 5 rupees.

How many chocolates should he buy from each shop?

John went to buy some expensive, foreign chocolates. He only had Rs 100 with him. When he reached the shop, he got out and know that on those chocolates, there was a 15% import duty and 5% VAT.

How much worth chocolate should he buy so that he can accommodate it in Rs 100?

The centre of the third figure is empty. What digit should fit inside?

Prove that twice of ten is the same as twice of eleven.

You are in a land where thirty men and two women were dressed in classic black and white dresses.
They begin to fight as soon as any of them move.

Where are you?