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 ?

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 ?

Three cars are driving on a track that forms a perfect circle and is wide enough that multiple cars can pass anytime. The car that is leading in the race right now is driving at 55 MPH and the car that is trailing at the last is going at 45 MPH. The car that is in the middle is somewhere between these two speeds.
Right now, you can assume that there is a distance of x miles between the leading car and the middle car and x miles between the middle car and the last car and also, x is not equal to 0 or 1.
The cars maintain their speed till the leading car catches up with the last car and then every car stops. In this scenario, do you think of any point when the distance between any two pairs will again be x miles i.e. the pairs will be x distance apart at the same time ?

Can you fill the blank with the correct number?

6 30 870 756030 _____

Three people are in a room. Ronni looks at the Nile. The Nile looks at Senthil. Ronni is married but Senthil is not married. At any point, is a married person looking at an unmarried person? Yes, No or Cannot be determined.

Why do we preferably have round manhole covers and not square ones?

Can you divide the below-given shape into four equal and identical pieces?

Which statement is true out of the following?
One statement here is false.
Two statements here are false.
Three statements here are false.

Six glasses are in a row. The first three are filled with milk and the last three are empty. By moving only one glass, can you arrange them so that the full and the empty glasses alternate?

Can you identify the hidden rebus in the image below?