Solution:

9862

Sum of digits of all other numbers is 21 , but sum of digits of 9862 is 25

Solution:

2 minutes (duration between 9:59 and 10:01)

Solution:

step 3 is wrong

Solution:

Isaac Newton picks up a piece of wood and lights it from the fire on the west end of the island.

He then quickly carries it near the east end of he island and starts a new fire. The wind will cause that fire to burn out the eastern end and he can then shelter in the burnt area.

(Funny Part : Isaac Newton survives the fire, but dies of starvation, with all the food in the forest burnt )

Solution:

The two numbers are 4 and 13 whose product is 52 and sum is 17.

Solution:

13 + 11 + 6 = 30

Explanation
The trick is that you just need to rotate '9' to form '6'.

Solution:

16-days

In 15-days, he will climb 15-inch and when he climbs 5 inch more, he will be out of the well :-)

Solution:

Rhea will open just one present.
Cindy|Y - Y is the 25th alphabet
Duk|E - E is the 5th alphabet
Joh|N - N is the fifteenth alphabet
Rhe|A - A is the first alphabet

Solution:

41312432

Solution:

The Stars

Solution:

The Lady sitting in the chair has the detector attached to the back of her blouse.