Solution:

An Echo

An echo is a reflection of sound waves. It "speaks" because it repeats the sound it hears without having an actual mouth to produce sounds. It "hears" because it listens to the original sound and then reflects it back. It has no physical body because it is just a sound wave traveling through the air. When the wind carries sound waves, the echo is "brought to life" as it reflects and repeats the sound, making it seem as though it has come alive with the wind.

Solution:

I + IX = X

The equation read from the other side becomes X = XI + I which is false.

Solution:

XIX is the answer which refers to nineteen in roman numeric system. On taking out one i.e. I, we will get XX that is equal to twenty.

Solution:

In the corners of the square, tighten two ropes. Tighten another rope between them by putting rings on each rope. That rope should be tightened on the sheep's neck on the other end.

Solution:

he was genius.

Officials must have thought he was jumping with a hostage, they would never risk giving him a faulty parachute.

Solution:

None

The sum of numbers from 0-9(0,1,2,3,4,5,6,7,8,9) is 45 and therefore can be divisible by 3 and 9.

Solution:

One Minute building

building 62 => Sixty second building => One minute building

Solution:

The person on 73rd number will survive.

Explanation:
Till the number is the power of 2, the last person to survive will be the one who started it. But since the number here is not the power of 2, we will take the greatest power of 2 that is less than the number which is 64.
100 - 64 = 36
36 people are killed as 2, 4, 6, ..., 72. Thus the sword will now be given to the 73rd person. Now he is the first person to start in the remaining 64 people. Thus he will be the one to survive.

Solution:

Anybody will prefer the shop in the eastern market for sure. There are two reasons for it:
Firstly, since there are only two barbers in the town, the one running the shop in eastern market must have gotten his hair done by the one running the shop in the northern market and vice versa. Thus, if the barber in the eastern market has a shabby haircut, it must be due to the incompatibility.
Secondly, the neat and clean shop can be due to the scarcity of customers as well. While the untidy place refers to the fact that so many customers get their hair done in that shop.

Thus any one will opt for the barber shop in the eastern market.

Solution:

The guard and the prisoner cross the river
The guard comes back
The guard and the girl cross the river.
The guard and the prisoner comes back.
The mother and the girl cross the river.
Mother comes back
The mother and the father cross the river
Father comes back
The guard and the prisoner cross the river
Mother comes back
The father and the mother cross the river
Father comes back
The father and the boy cross the river
The guard and the prisoner comes back
The guard and the boy cross the river
The guard comes back
The guard and the prisoner cross the river.

Solution:

The wise man told them to switch the horses and then race. In this manner, both of them will be willing to race as fast as they can to prove that the other horse (his own horse) is slow.