What always comes into a house through the keyhole?

Find the value of "a" by solving the maths equation in the picture below:

He runs but never walks. Murmurs, but never talks. Has a bed, but never sleeps. And has a mouth, but never eats?

A murder has been committed in a house. You are a detective and have to find out the murderer.

You investigate by asking three questions to each of the six suspects. Out of those six suspects, four are liars. It is not necessary that they speak everything a lie. But in their answers, there must be at least one lie. One of the six is the murderer.

There are eight rooms in the house in which the murder has been committed: Kitchen, Living Room, Bathroom, Garage, Basement, 3 Bedrooms.

At the time of the murder, only the murderer was present in the killing room. Any number of people can be present in any of the other rooms at the same time.

Can you identify the murderer and the four liars? Also, can you find out who was in which room?

The responses of all the suspects are mentioned below.

Joseph:
Peter was in the 2nd bedroom.
So was I.
David was in the bathroom.

Mandy:
I agree with Joseph that David was in the bathroom and Peter was in the 2nd bedroom.
But I think that Joseph was in the living room, OH MY GOD!

Peter:
Mandy was in the kitchen with Christopher.
But I was in the bathroom.

David:
I still say Peter was in the 2nd bedroom and Jennifer was in the bathroom.
Joseph was in the 1st bedroom.

Jennifer:
Peter was in the bathroom with Christopher.
And Mandy was in the kitchen.

Christopher:
David was in the kitchen.
And I was in the 2nd bedroom with Peter.

PS: The corpse was found in the Living Room.

Krish is 45 years old and his mother Crishtina is 73 years old.

Can you find out how many years ago, his mother was three times his age?

Count the number of balls in picture below:

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?

If a boy blows 18 bubbles,
Then pops 6 eats 7 and then
He pops 5 and blows 1.
How many are left?

A boy purchased a book from a bookkeeper and gave him $100.
The cost of the book is $50 but the bookkeeper has no change, so he gets the change from the next shop and returns the boy his $50.

After some time the next shopkeeper came with the $100 note and told the bookkeeper that the note was a fraud, so he took the money back.

How much loss did the bookkeeper face?

If your uncle’s sister is not your aunt, what relation is she to you?