How many times do a clock's hands overlap in a day ?

Intelligence Agency need to break the vault but the problem is that they are not able to break the vault.

On the vault, a text is written as:

31 11 33 33 43 45
21 25
31 24 11 31 51 41

To Break the code Intelligence Agency brings a mathematician named Joseph.
Minutes later he deciphers the code.

Whats the code?

A man is found dead with a knife in his back When the investigation is done. A chair lays beside him and the forensic team finds moisture around the body.

If he committed suicide, how did he do it?

The following alphametic has only one solution. Can you find it?
ENLIST + SILENT + LISTEN = ANAGRAM

PS: You may start the number from 0.

Luis Garavito killed Density x Volume.

Who is Luis Garavito ?

Joseph buys three kinds of chocolates for 100 rupees. The first one is priced at 5 rupees, second one at 3 rupees and third one at 0.5 rupees.

If he bought 100 chocolates in total, how many pieces do you think he bought each chocolate?

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?

What has hands, but can’t clap?

In order to complete the racing competition, the Mexico racetrack has to submit its top and the most famous three horses to win the competition. Due to an electrical storm, all the records are cleared and no one knows which horse holds the record. They all look identical and it becomes even more difficult to differentiate the horses. There are 25 horses in the Mexico racetrack. But there can be only five horses at a time on the track. What will the least number of races that can be conducted to find out the three fastest horses?

I have a clock(12-hour format) and both the needles of the clock overlap at 12:00.
After how much time, they will overlap again?