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

Two trains start at the same time, one from Bangalore to Mysore and the other from Mysore to Bangalore. if they arrive at their destinations one hour and four hours respectively after passing one another, how much faster is one train running than the other?

How can you write nineteen in a manner that if we take out one, it becomes twenty?

I am white when I am dirty, and black when I am clean. What am I?

In the picture, you can see a chess board. On the top left position, the K marks a knight. Now, can you move the knight in a manner that after 63 moves, the knight has been placed at all the squares exactly once excluding the starting square?

There was a blind beggar living on the footpath of a street. Suddenly one day, the beggar's brother died. What was the relation of the blind beggar with the person who died?

PS: Brother is not the answer.

Christina, Allison and Lena are 3 daughters of John a well-known Mathematician, When I asked John the age of their daughters. He replied "The current age of her daughters is prime. Also, the difference between their ages is also prime."

How old are the daughters?

Can you think of any three-dimensional shape that comprises of exactly two surfaces?

What Time Should the last watch show in the below figure?

A woman lives in a Tall building thirty-six floors high and served by several elevators which stop at each floor going up and down. Each morning she leaves her apartment and goes to one of the elevators. Whichever one she takes is three times more likely to be going up than down. Why?