How many words can a pen with half refill write?

Can you place three balls such that the equation shown in the picture holds true?

The sum of a mother, her baby and her dog's weight is 170 Kg. How much does the baby weigh if the mother weighs 100 kg more than the combined weight of the baby and the dog, and the dog weighs 60 per cent less than the baby?

A boy was at a carnival and went to a booth where a man said to the boy, "If I write your exact weight on this piece of paper then you have to give me $50, but if I cannot, I will pay you $50." The boy looked around and saw no scale so he agrees, thinking no matter what the carny writes he'll just say he weighs more or less. In the end the boy ended up paying the man $50. How did the man win the bet?

I am sure no one can have two things for dinner. what are they?

Three ants are going up a hill, one behind the other. The last ant then says to the other ants, 'There is an ant behind me!'' How come?

By moving just one matchstick, you need to make the below statement true. Can you do it?

Find out a multi-digit number that if multiplied by the number 9 or any of its multiplications products (i.e. 18, 27, 36, 45,..) will result in the multiplication factor repeated (n) number of times.

A girl was sitting in her hotel room when she heard a knock on the door. She opened the door and found that a man was standing outside. The man said, "Oh! I am really sorry, I thought this was my room." He then walked through the corridor to the elevator. The girl did not know the man. She closed her door and called security asking them to apprehend the man. What made her suspicious of that man? He might have been genuinely mistaken.

It is a six-letter word.
The first four letters are me.
The second and last letters are the same.
The fourth second and last letter is payment.

Who is it?