Solution:

Teapot B contains 20 cups of tea as its outlet is placed in the middle of teapot A. Rest of the
tea just starts overflowing.

Solution:

The old man gave the clerk four quarters so it's obvious that he needed two tickets, Otherwise, he would have only given 2 quarters.

Solution:

In a clock.

Explanation:
1300 + 20 = 1:00PM + 20 minutes = 1:20 PM

1400 - 40 = 2:00PM - 40 minutes = 1:20 PM

Solution:

No glass will ever fill.

Explanation:
Outlet to Glass-1 & 5 is blocked at the initial point, so they won't fill.
Outlet to Glass-2 is blocked at the endpoint, so it won't fill.
Outlet to Glass-3, 4 & 7 is also blocked in the middle, so they won't fill.
Nothing is connected to Glass-6.

Solution:

The Bomb will explode in just 5 minutes and he can use that exit afterward.

Solution:

Coffee.

The person with two a's drink coffee.
The person with two e's drink coke.
By the same logic, Armando drinks coffee.

Solution:

The Waiter

Holding a tray is a static job while serving dishes and drinks is their main work and hence the waiter is most likely the left-handed person.

Solution:

It can be done as shown below.

Solution:

Sunday

Explanation:
Since each day of the week is repeated after 7 days.
So, after 77 days, it will be Tuesday.
Therefore, After 75 days, it will be Sunday.

Solution:

Pizza

Explanation:
Pizza is served to people with 2 E's and rest are served Burgers.