What is both possible and impossible at the same time?

Replace the letters of words with a number so that the below equation holds true

BASE +
BALL
---------
GAMES
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A man has a barrel filled with oil that weighs 100 pounds, and then he puts something into it. Now the barrel weighs less than 100 pounds. What did he put in the barrel?

A man stands on one side of a river, his dog on the other. The man calls his dog, who immediately crosses the river without getting wet and without using a bridge or a boat. How did the dog do it?

Can you find the ages of a son, father and grandfather based on the following facts?
The sum of the ages of grandfather, father and son is 140 years.
The age of the son in months is the same as the grandfather in years.
The age of the son in days is the same as the father in weeks.

I am a type of vehicle that has two wheels and is powered by humans. What am I?
Hint 1: You can ride me for exercise.
Hint 2: I am environment-friendly.

John was born on March 5, 1970, in Delhi, India. Jacob was born 25 days before John. The year when they took birth, Republic Day fell on Monday.

Can you find out on what day was Jacob born?

A boy and a girl are sitting on the porch.
"I'm a boy," says the child with black hair.
"I'm a girl," says the child with red hair.
If at least one of them is lying, who is which?

If eleven plus two equals one, what does nine plus five equal?

In a basket of apples,
when counted in twos, there was one extra
when counted in threes, there were two extra when counted in fours, there were three extra
when counted in fives, there were four extra
when counted in sixes, there was five extra.

However, if the apples were counted in sevens, no extra apple was left. Can you calculate the minimum number of apples that were present in the basket?