Can you find a number that lies one third of the distance between 1/3 and 2/3?

Find the mistake in the below maths equations

A = 2
A(A-1) = 2(A-1)
A2-A = 2A-2
A2-2A = A-2
A(A-2) = A-2
A = 1

I never stop running even when I standstill. If I am formed by joining two identical bodies together, can you guess who I am?

Find the 8 in the below-given Image.

There are 20 people in an empty, square room. Each person has full sight of the entire room and everyone in it without turning his head or body, or moving in any way (other than the eyes). Where can you place an apple so that all but one person can see it?

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?

A girl was standing near the window thinking something. All of a sudden she decides something and throws something out of the window. She dies very soon after throwing it. She was perfectly healthy and had no disease or allergy. No one killed her and she did not commit suicide.

Can you think of any possible explanation that is logical as well for what happened there?

John is looking at Jenifer, but Jenifer is looking at Jacob. John is married, but Jacob is not.

Is a married person looking at an unmarried person ?

Who is that with a neck and no head, two arms and no hands? What is it?

There are forty elephants and they have forty-fore heads. How can this be possible?