What is harder to catch the faster you run?

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?

Why is the Hole below a Lock?

You Throw The Outside, Cook The Inside
Eat The Outside, Throw The Inside.

What Is It?

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?

Which three-digit number, made of consecutive digits, like 567, is 2 less than a cube and 2 more than a square?

There was a greenhouse.
Inside the greenhouse, there is a white house.
Inside the white house, there is a red house.
Inside the red house, there are lots of babies.

What is It?

In a basket of apples,
when counted in twos, there was one extra
when counted in threes, there were two extra when counted in fours, there were three extra
when counted in fives, there were four extra
when counted in sixes, there was five extra.

However, if the apples were counted in sevens, no extra apple was left. Can you calculate the minimum number of apples that were present in the basket?

Before the start of the car race, John and Jacob have the same amount of fuel in their car. With this fuel, John can drive for 4 hours while Jacob can drive five hours.
After a time they realize that the amount of fuel left in John's car is 1/4th of the fuel in Jacob's.

For how long they are racing?

Rectify the following equality 101 - 102 = 1 by moving just one digit.