Take away my first letter, then take away my second letter. Then take away the rest of my letters, yet I remain the same. What am I?

John is found dead in his office at his desk. The police have narrowed the suspects down to three people: Mrs. Jacob, John’s wife Hena and his business partner Jason . All three visited John on the day of his murder, but all three provide the police with stories of explanation as to the reason for their visit.
Police found John with his wrist watch still on his right arm, a torn up picture of his wife laying on the floor beside the trash can, and an ink pen in his right hand. On the desk, the police found a name plate, a telephone that was off the hook, and a personal calendar turned to the July 5th page with 7B91011 written on it. After examining this evidence, the police knew their suspect. Who was it ?

A girl is twice as old as her brother and half as old as her father. In 50 years, her brother will be half as old as his father. How old is the daughter now?

What number comes next in this sequence:
7 8 5 5 3 4 4 _

It is a six-letter word.
The first four letters are me.
The second and last letters are the same.
The fourth second and last letter is payment.

Who is it?

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?

While preparing the table for dinner, wife came up with an idea to tease his mathematician husband. She asked her husband to pick nine toothpicks and make ten without breaking any toothpick.

The husband was also smart and did it within seconds. How ?

At my favorite fruit stand,
an orange costs 18,
a pineapple costs 27,
and a grape costs 15.
Using the same logic, can you tell how much a mango costs?

There are a hundred statements.

First person says: At least one of the statements is false.

Second person says: At least two of the statements is false.

Third person says: At least three of the statements are false.

Fourth person says: At least four of the statements are false.

..

..

..

Hundredth person says: At least a hundred of the statements are false.

Analysing it, how many statements do you think are false and how many are true?

Three men in a cafe order a meal the total cost of which is $15. They each contribute $5. The waiter takes the money to the chef who recognises the three as friends and asks the waiter to return $5 to the men.

The waiter is not only poor at mathematics but dishonest and instead of going to the trouble of splitting the $5 between the three he simply gives them $1 each and pockets the remaining $2 for himself.

Now, each of the men effectively paid $4, the total paid is therefore $12. Add the $2 in the waiters pocket and this comes to $14. Where has the other $1 gone from the original $15?