What is more useful when it is broken?

Replace the question mark with the correct number, given the pair of numbers exhibits a similar relationship?

? : 3839 :: 11 : 1209

A Scientist was fifty years old in the year 2000 but he was forty years old in the year 2010. How can this be possible?

PS: It has a logical answer.

Two natural numbers have a sum of less than 100 and are greater than one.

John knows the product of the numbers and Jacob knows the sum of numbers.

The following conversation takes place between them:
John: 'I am not aware of those numbers.'
Jacob: 'I knew you wouldn't be. I am not aware myself.'
John: 'Now I know them!'
Jacob: 'Now I know them, too!'

What are the two numbers?

What Deficiency does the below rebus represent?

VIT_MIN

Begin with a word, five letters to my name,
Remove the first and last but I am the same
Take out my middle and still, I remain.
What word am I?

You bought me for dinner but never eat me. What am I?

Manish and Manoj play 5 games of chess.
Both Manish and Manoj win the exact same number of games. There is no tie at all.

How?

If 24H in a D => 24 hours in a day.
What does "64S on CB" stand for?

If a shopkeeper can only place the weights on one side of the common balance. For example, if he has weights 1 and 3 then he can measure 1, 3 and 4 only. Now the question is how many minimum weights and names of the weights you will need to measure all weights from 1 to 1000? This is a fairly simple problem and very easy to prove also.