CAT (QA) PYQs

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?

A group of $N$ people worked on a project. They finished $35 \%$ of the project by working $7$ hours a day for $10$ days. Thereafter, $10$ people left the group and the remaining people finished the rest of the project in $14$ days by working $10$ hours a day. Then the value of $N$ is

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