Below, you will find the mathematical proof that 10 equals 9.99999?. But is that possible or there is something wrong about it? Can you find the error?

x = 9.999999...
10x = 99.999999...
10x - x = 90
9x = 90
x = 10

I am a five-letter word under you,
Remove the first letter and I am above you,
Remove the second as well and I am around you.

Who am I?

A mile-long train is moving at sixty miles an hour when it reaches a mile-long tunnel. How long does it take the entire train to pass through the tunnel?

If you were to put a coin into an empty bottle and then insert a cork into the neck, how could you remove the coin without taking out the cork or breaking the bottle?

Which word does the below Plexor means ?

An exterior architect is asked by a builder to plant seven trees in a manner that there are exactly six rows of trees in a straight line and each row has three trees in particular.

How will he do it?

A charming young lady was approached by a kind looking old woman in a restaurant. The old woman said to her, 'You look exactly like my younger daughter. Sadly she passed away a couple of months back. Could you do me a favor and say 'Goodbye, mother' with a kind smile on your face when I leave?

The young lady agreed for the same and said, 'Goodbye, mother' when the old woman left. Soon after, she got the most disengaging shock of her life.

Can you guess what the shock was?

I am beautiful, up in the sky. I am magical, yet I cannot fly. To people I bring luck, and to some people, riches. The boy at my end does whatever he wishes. What am I?

What can go up a chimney down, but can’t go down a chimney up?

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