People make me, save me, change me, raise me. What am I?

Some friends went on a vacation to a resort. It was raining heavily and it kept raining for thirteen days.

When it rained in the morning, the afternoon was beautiful and when it rained in the afternoon, the day was blessed with a clear morning.

Overall, the friends experienced eleven nice mornings and twelve nice afternoons. Can you find out the number of days they spent on vacation?

You are mixing a mixture of cement and Sand with five gallons of water. You have a garden hose giving you all the water you need. The problem is that you only have a four-gallon bucket and a seven-gallon bucket and neither has graduation marks. Find a method to measure five gallons.

In the picture given below, can you find out which digit will take place of the question mark?

There is a five-letter word which has 3 consonants(all are same) and 2 different vowels.
Also, something wrong is associated with the word.

Can you name it?

What is the centre of gravity?

What is the longest word in the dictionary?

Below, you will find the mathematical proof that 10 equals 9.99999?. But is that possible or there is something wrong about it? Can you find the error?

x = 9.999999...
10x = 99.999999...
10x - x = 90
9x = 90
x = 10

A man who was outside in the rain without an umbrella or hat didn’t get a single hair on his head wet. Why?

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