A tank is fitted with pipes, some filling it and the rest draining it. All filling pipes fill at the same rate, and all draining pipes drain at the same rate. The empty tank gets completely filled in $6$ hours when $6$ filling and $5$ draining pipes are on, but this time becomes $60$ hours when $5$ filling and $6$ draining pipes are on. In how many hours will the empty tank get completely filled when one draining and two filling pipes are on?

Arun, Varun and Tarun, if working alone, can complete a task in 24, 21, and 15 days, respectively. They charge Rs 2160, Rs 2400, and Rs 2160 per day, respectively, even if they are employed for a partial day. On any given day, any of the workers may or may not be employed to work. If the task needs to be completed in 10 days or less, then the minimum possible amount, in rupees, required to be paid for the entire task is

A tank has an inlet pipe and an outlet pipe. If the outlet pipe is closed then the inlet pipe fills the empty tank in $8$ hours. If the outlet pipe is open then the inlet pipe fills the empty tank in $10$ hours. If only the outlet pipe is open then in how many hours the full tank becomes half-full?

Anil can paint a house in $60$ days while Bimal can paint it in $84$ days. Anil starts painting and after $10$ days, Bimal and Charu join him. Together, they complete the painting in $14$ more days. If they are paid a total of Rs. $21000$ for the job, then the share of Charu, in INR, proportionate to the work done by him, is

Amal and Vimal together can complete a task in 150 days, while Vimal and Sunil together can complete the same task in 100 days. Amal starts working on the task and works for 75 days, then Vimal takes over and works for 135 days. Finally, Sunil takes over and completes the remaining task in 45 days. If Amal had started the task alone and worked on all days, Vimal had worked on every second day, and Sunil had worked on every third day, then the number of days required to complete the task would have been

Humans and robots can both perform a job but at different efficiencies. Fifteen humans and five robots working together take thirty days to finish the job, whereas five humans and fifteen robots working together take sixty days to finish it. How many days will fifteen humans working together (without any robot) take to finish it?

Two pipes $A$ and $B$ are attached to an empty water tank. Pipe $A$ fills the tank while pipe $B$ drains it. If pipe $A$ is opened at $2$ pm and pipe $B$ is opened at $3$ pm , then the tank becomes full at $10 \mathrm{pm}$. Instead, if pipe $A$ is opened at $2 \mathrm{pm}$ and pipe $B$ is opened at $4 \mathrm{pm}$, then the tank becomes full at $6 \mathrm{pm}$. If pipe $B$ is not opened at all, then the time, in minutes, taken to fill the tank is