Take away my first letter, then take away my second letter. Then take away the rest of my letters, yet I remain the same. What am I?

Alpha is Beta's sister.

Gamma is a Beta mother.

Delta is Gamma's father.

Tango is Delta's mother.

Then,

How is Alpha related to Delta?

It is a six-letter word.
The first four letters are me.
The second and last letters are the same.
The fourth second and last letter is payment.

Who is it?

Chocolate costs 6 rupees and a Toy costs 5 rupees. If you have 32 rupees in total, how many chocolates and how many Toys can be purchased with that amount?

Use only one mathematical symbol and all numbers (0-9) to get a sum of 99

A father's child, a mother's child, yet no one's son.

Who am I?

Take one out and scratch my head, I am now black but once was red. What am I?

A number with an interesting property:

When I divide it by 2, the remainder is 1.
When I divide it by 3, the remainder is 2.
When I divide it by 4, the remainder is 3.
When I divide it by 5, the remainder is 4.
When I divide it by 6, the remainder is 5.
When I divide it by 7, the remainder is 6.
When I divide it by 8, the remainder is 7.
When I divide it by 9, the remainder is 8.
When I divide it by 10, the remainder is 9.

It's not a small number, but it's not really big, either.
When I looked for a smaller number with this property I couldn't find one.

Can you find it?

If you read clockwise, you can form a word by inserting three missing letters in the picture given below. Can you do it?

A B C D E F G H

These are the letters given to you. Now you have to find out the letter that comes two to the right of the letter which is immediately to the left of the letter that comes three to the right of the letter that comes midway between the letter two to the left of the letter C and the letter immediately to the right of the letter F.