I know a country, If you remove the last alphabet of its name, it will become a part of your body. Do you name it?

In one of the popular batman series movie "Batman Forever", there was a riddle that goes like "Tear me off and then scratch my head and I was red then and now I am back. Who am I?

Detective John was investigating a murder in China.
It was a difficult case, and John was completely stumped until he noticed a message sent to him by the killer cunningly hidden in a newspaper advertisement selling Car Licence Plates.
Detective John thought about it for a while, and when he had solved the puzzle, immediately arrested the guilty man.

Q1) How did John know the advert was a clue for him?

Q2) Solve the code and tell me who John arrested.

This is the newspaper advert (Car licence plates for sale) that Detective John saw.

Plates For Sale;

[W 05 NWO]
[H 13 HSR]
[O 05 EBM]
[D 08 UNE]
[U 10 HTY]
[N 04 BRE]
[N 16 TTE]
[I 26 LHC]
[T 10 AEE]
[I 26 CNA]
[X 22 VDA]

In a school, there are four subjects. Seventy percent of students study English, seventy five percent of students study Science, eighty five percent of students study Mathematics and eighty percent of students study Spanish.

Can you calculate the percentage of students that study all four subjects?

You are in a room that has three switches and a closed door. The switches control three light bulbs on the other side of the door. Once you open the door, you may never touch the switches again. How can you definitively tell which switch is connected to each of the light bulbs?

In a kingdom, King George did not allow any citizen to visit the world outside. Also, only a person with proper paperwork was allowed to enter or he was sent back. A wooden bridge was what connected the kingdom to the world. The king had appointed a sharpshooter who would check the every five minutes on the bridge to check. After checking, he would go back to his hut and return exactly after five minutes again. The bridge took 9 minutes to cross.

A merchant was able to escape the kingdom without harming the shooter. How?

At a Society election for president, precisely 963 votes were cast.
There is a total of 4 candidates that participate in the election.

The winning candidate exceeds the opponents by 53, 79 and 105 votes.

How many votes do each candidate gets?

This is a famous paradox which has caused a great deal of argument and disbelief from many who cannot accept the correct answer. Four balls are placed in a hat. One is white, one is blue and the other two are red. The bag is shaken and someone draws two balls from the hat. He looks at the two balls and announces that at least one of them is red. What are the chances that the other ball he has drawn out is also red?

Can you find out the number that should replace the question mark with a valid reason?

I have a head like a cat and feet like a cat, but I am not a cat. What am I?