Solution:

Chair is the required five letter word.

Solution:

This statement is true but only in a specific case i.e. if both of the siblings continue to live till the day the younger is as old as the elder one was during the time of their birth.

Solution:

Yes it is possible in Roman Numerals. In Roman Numerals,
9 = IX
10 = X
11 = XI

Thus by removing one from 9, you are getting 10 and by removing one from 11, you are getting 10 again.

Solution:

The figure tells that B is located to the North-East of E.

Solution:

The man asked the king that he wanted to die of old age.

Solution:

Karate Kid (car + at + tea + kid)

Solution:

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

Solution:

She is near the trunk of the tree as shown below.

Solution:

Lucky days are here again.

Explanation:
Lucky + Day + s + R + H + Ear + Again (Flower represent lucky symbol)

Solution:

41312432

Solution:

Never

Explanation:
In the question, the distance of x miles is given at a particular moment. The middle car is running at that time at 50 MPH. The distance will keep increasing with time as three are running at different speeds. It will increase by x miles every hour till a certain point of time and then it will start decreasing till the fastest car meets the slowest again.

As per question, all the cars stop then. Thus, the distance will never be x miles again.