CAT (QA) PYQs

Anu, Vinu and Manu can complete a work alone in 15 days, 12 days and 20 days, respectively. Vinu works everyday. Anu works only on alternate days starting from the first day while Manu works only on alternate days starting from the second day. Then, the number of days needed to complete the work is

Pipes $A$ and $C$ are fill pipes while Pipe $B$ is a drain pipe of a tank. Pipe $B$ empties the full tank in one hour less than the time taken by Pipe $A$ to fill the empty tank. When pipes $A$, $B$ and $C$ are turned on together, the empty tank is filled in two hours. If pipes $B$ and $C$ are turned on together when the tank is empty and Pipe $B$ is turned off after one hour, then Pipe $C$ takes another one hour and $15$ minutes to fill the remaining tank. If Pipe $A$ can fill the empty tank in less than five hours, then the time taken, in minutes, by Pipe $C$ to fill the empty tank is

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