A chicken farmer has figured out that a hen and a half can lay an egg and a half in a day and a half. How many hens does the farmer need to produce one dozen eggs in six days?

I want to fill my bucket using both cold and hot water.
I have two taps for both cold and hot water. The hot water tap fills the bucket in exact 6 hours and the cold water tap fills the bucket in exact 4 hours.
I turn both of them simultaneously but I forgot to turn off another tap which removes the water out of the bucket. This tap can empty the bucket in 12 hours.

How Long will it take to fill the bucket?

Christina has four daughters, and each of her daughters has a brother. How many children does Christina have?

You are given a cube that is made with the help of 10x10x10 smaller cubes summing up to a total of 1000 smaller cubes. You are asked to take off one layer of the cubes.
How many remain now?

John can fit six large chocolate boxes or nine small chocolate boxes into a carton. How many cartons will he require to put sixty-six chocolate boxes into?

There is a number which when you multiply by 3 and subtract 2 from the result, then the resulting number is the reverse of the actual number.

What is the smallest number that stands true on the statement?

Replace the question mark with the correct number in below Picture:

A man is walking down a road with a basket of eggs. As he
is walking he meets someone who buys one-half of his eggs
plus one-half of an egg.
He walks a little further and meets another person who buys
one-half of his eggs plus one-half of an egg.
After proceeding further he meets another person who buys
one-half of his eggs plus one half an egg. At this point, he
has sold all of his eggs, and he never broke an egg.
How many eggs did the man have to start with?

What will be the best approach to finding all the prime numbers less than 75 that leave an odd reminder when we divide them with 5?

0 0 0 = 6
1 1 1 = 6
2 2 2 = 6
3 3 3 = 6
4 4 4 = 6
5 5 5 = 6
6 6 6 = 6
7 7 7 = 6
8 8 8 = 6
9 9 9 = 6

You can use any mathematical symbols in the space provided to make all above algebraic expressions true.