Take away the whole and some still remain. What is it?

If,
29 - 1 = 30
9 - 1 = 10
14 - 1 = 15

Based on similar logic, Can you prove that the below algebraic equation is true?
11 - 1 = 10 ?

A boy and a girl are sitting on the porch.
"I'm a boy," says the child with black hair.
"I'm a girl," says the child with red hair.
If at least one of them is lying, who is which?

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 ?

Manish and Manoj play 5 games of chess.
Both Manish and Manoj win the exact same number of games. There is no tie at all.

How?

In a supermarket, there is an intelligent glass pane before a refrigerating unit. This glass pane allows cherries and apples through it but does not allow grapes and Orange to pass through it.

Can you identify the rule that the glass pane is following?

"That Restaurant always remains crowded. This is the reason why nobody goes there".

Can you find a flaw in this statement?

You have a basket containing ten apples. You have ten friends, who each desire an apple. You give each of your friends one apple.
Now all your friends have one apple each, yet there is an apple remaining in the basket.
How?

What occurs twice in a week, once in a year but never in a day?

I was speeding and ran through a stop sign, yet two traffic officers who were there do nothing about it.

why?