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?

Using mathematical symbols like +, -, and x in order to make the equations correct. Replace # with the above-given symbols.

9 # 8 # 7 # 6 # 5 # 4 = 91

A car meter reading shows 72927 miles a palindromic number.
what is the minimum number of miles you would need to travel to see another palindromic number on the car meter reading?

At a Society election for president, precisely 963 votes were cast.
There is a total of 4 candidates that participate in the election.

The winning candidate exceeds the opponents by 53, 79 and 105 votes.

How many votes do each candidate gets?

Can you think of a smallest +ve number such that if we shuffle the digits of the number, the new number becomes double the original number?

By using all numbers, i.e. 123456789 and subtraction/addition, operators number 100 can be formed in many ways.
Example: 98 + 7 + 6 - 5 - 4 - 3 + 2 - 1 = 100

But if we add a condition use of the number 32 is a must. Then there are limited solutions.
One of such solution is: 9 - 8 + 76 + 54 - 32 + 1 = 100

Can you tell me any other solution?

Three friends decide to distribute the soda cans they had among them. When all of them had drunk four cans each, the total number of cans that remained was equal to the cans each one of them had after they had divided the cans.

Can you calculate the total number of cans before distribution?

John was running from 40 thieves. John has got 3 gold boxes which weigh as 4kg, 2kg, and 1kg respectively. A witty man asked John to stay with him for seven days in exchange for 1kg gold per day. John needs to stay there for seven days and also do not want to give the witty man any advance. How can John pay for his seven days stay?

Can you find a number that lies one third of the distance between 1/3 and 2/3?

A large water tank has two inlet pipes (a large one and a small one) and one outlet pipe. It takes 3 hours to fill the tank with the large inlet pipe. On the other hand, it takes 6 hours to fill the tank with the small inlet pipe. The outlet pipe allows the full tank to be emptied in 9 hours.

What fraction of the tank (initially empty) will be filled in 0.64 hours if all three pipes are in operation? Give your answer to two decimal places (e.g., 0.25, 0.5, or 0.75).