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

In the below-given picture of a pretty girl, there is something wrong. Can you find out what it is?

What English word has three consecutive double letters?

In the addition below, all digits have been replaced by letters. Equal letters represent equal digits and different letters represent different digits.
ABCABA
BBDCAA
ABEABB
ABDBAA
------- +
AAFGBDH
What does the complete addition look like in digits?

You need to remove two matchsticks to make the below equation true. Can you do it ?

What begins with T, ends with T, and has T in it?

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 ?

You along with your friend are standing in front of two houses. Each of those houses inhabits a family with two children.

Your friend tells you the below two facts:
1) On your left is a family that has a boy who likes accounts but the other child loves science.
2) On the right is a family with a seven-year-old boy and a newborn baby.

You ask him, "Does either of the family have a girl?"

To this, he replies, "I am not quite sure. But can you guess that? If you are right, I will give you $500."

Which family do you think is likely to have a girl?

It is a nine-letter word.
The exact opposite of the phrase "friendly and outgoing"
It contains the word "over".
It starts will a vowel.

What is it?

One of the leprechaun is missing if you see the two pictures attached to this question. Where did he go? When he comes back, do you know where has he been?