Solution:

Mahrez Pick 4 marbles.

Explanation:
How many marbles Vardy picks, Mahrez needs to make sure that only 1 marble is left after his move, So Vardy needs to pick the last marble.

Example:
If Vardy picks 1, Mahrez picks 5
If Vardy picks 2, Mahrez picks 4
....
...
If Vardy picks 5, Mahrez picks 1

Solution:

The girl was born on 29 February. Thus her birthday came once in four years only while her sister was born on a normal day and celebrated her birthday every year. Thus the girl had a chance of depositing money only 10 times in 4 years through which she collected $2500 while her sister took $50 from the piggy bank every year making the total amount to be $2000. Thus when the piggy bank was opened, it had just $500.

Solution:

The receptionist was pretty clever she played with the mute button of the phone while talking with her mother. She muted everything except the word emergency, call and help. So while talking, she sounded like 'Emergency… Call… Help' to her mother and thus she called the police.

Solution:

Put one black rock in one sack and put all the rest in the other one. In such manner you will get about 3/4 probability of surviving.

Solution:

Blue could only be wearing white or red and we know that there is already someone else wearing the white shirt so Mr. Blue could only be wearing the red shirt.

Mr. White could have only been wearing a blue or a red shirt, and red is already taken, so Mr. White is wearing a blue shirt.

Mr. Red now has to be wearing a white shirt.

Solution:

See the figure for the answer. Wasn't it a bit tricky?

Solution:

'five'

Its the count of alphabet

Solution:

Solution is shown in image below

Solution:

They use the bricks and dirt from the tunnel to stand on it.

Solution:

7 Races.

Solution:

Both will rotate at Same speed.

Explanation:
Gears of the same size will always rotate at constant speeds despite any smaller or larger gears in between them.