When I get multiplied by any number, the sum of the figures in the product is always me. What am I?

I am under you when I am whole.
I shift above you if you remove the first letter.
I come all around you if you remove the second as well.

Can you tell me who I am?

A family is trapped in a jungle. There is a bridge which can lead them to safety. But at one time, the bridge can only allow two people to pass through. Also, all of them are afraid of the dark and thus, they can't go alone.

Father takes 1 minute to cross, the mother takes 2 minutes, the son takes 4 and the daughter takes 5 minutes. While crossing the time taken will be according to the slower one. How can they all reach the other side in the minimum possible time?

In which direction should the missing arrow point?

You are presented with three boxes. One of them has a red ball inside and the other two have a black ball inside each of them. You are asked to pick up the one with red ball and you pick one. Now, one of the other boxes is opened and it is found to have a black ball.

You are presented with a chance to change your box with the one that is left closed. Will you change your box? Why or why not?

I have no life, but I can die. What am I?

You are on a Boat in the mid of a river. You have two cigarettes with you. One of these two you have to light, how will you light the cigarette?

An office is divided into 8 cubicles. How many of the cubicles are painted if only 1/8 of the cubicles are painted?

It's a 7-letter word.
If we remove 1 letter from it, it remains the same.
If we remove 2 letters from it, it remains the same.
If we remove 3 letters from it, it remains the same.
If we remove all the letters from it, still it remains the same.
What is it?

An ant is travelling on a 1-meter-long rope at 1 cm/second but also the entire rope is being stretched by an extra 1 meter/second. Is it possible for the ant to reach at the end of the rope?