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.

Solution:

The teacher will use a simple trick to form a perfect impression. He will ask all his students to raise their hands on each of the question that is asked. But the only catch will be that those who knows the answer correctly will raise their right hand and others will raise their left hand.

In this way, the principal will see all the hands being raised for each question even though all won't be knowing the correct answer. The teacher will ask only those who know the answer and they will always be correct. So the principal will be impressed to full extent.

Solution:

The only possible way to do it is to form an equilateral triangle pyramid and then place the balls at the corners of the figure. Yes, you will have to use 3 dimensional figure.

Solution:

First fill the 8 liters jug complete - 4, 8, 0
Fill the 5 liters jug with 8 liters jug - 4, 3, 5
Pour back the beer from 5 liters jug to 12 liters jug - 9, 3, 0
Pour the 3 liters from 8 liters jug to 5 liters jug - 9, 0, 3
Fill the 8 liters jug completely from 12 liters jug - 1, 8, 3
Fill the 5 liters jug from the 8 liters jug - 1, 6, 5
Pour the entire 5 liters jug back in 12 liters jug - 6, 6, 0

You have successfully split the beer into two equal parts.

Solution:

There is only one way to do it. The old man must ask one of his son to divide the land in two parts and then ask the other one to pick up any land he want from the two. In this way, the first son will try to be fair and the second one won't mind as he will get to choose one first.

Solution:

The image that we have attached here is self-explanatory. You just have to move four matches and you can obtain this figure.

Solution:

Since every bacterium divides into two in two minutes and we know the fact that the dish was half filled with bacteria at 3 pm, after exactly 2 minutes, all will divide into two and will fill the petri dish. Thus, the petri dish will become full at 3:02 pm.

Solution:

First climb the first rope and carry the end of the second one with you. Now cut the first rope and flush with the ceiling, then swing down on the second. This time, climb up the second and cut that flush with the ceiling as well but only part way till it can withstand your weight. Now slowly climb down till you're just short of the bottom. Now tie a tiny loop at this portion and climb up some two feet. Then secure the loop about your feet and jump to the ground. With a three feet fall, you won't be hurt but the force will snap off the rope at top and you will have the whole rope with you.

Solution:

Since you can't identify which tablets are meant for which purpose, what you can do is take half of each tablet. In this manner, you will be able to get 1 of each tablet no matter what.

Solution:

100

Series of number that do not contain albhabet 'T'