CAT (QA) PYQs

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

John takes twice as much time as Jack to finish a job. Jack and Jim together take one-thirds of the time to finish the job than John takes working alone. Moreover, in order to finish the job, John takes three days more than that taken by three of them working together. In how many days will Jim finish the job working alone?

Amar, Akbar and Anthony are working on a project. Working together Amar and Akbar can complete the project in $1$ year, Akbar and Anthony can complete in $16$ months, Anthony and Amar can complete in $2$ years. If the person who is neither the fastest nor the slowest works alone, the time in months he will take to complete the project is