IIMB 2001 (QA) PYQs

An overhead tank that is filled by two pumps - $X$ and $Y$. $X$ can fill the tank in $10$ hours while $Y$ can fill the tank in $12$ hours. There is a pipe $Z$ which can empty the tank in $8$ hours. Both the pumps are opened simultaneously. The supervisor of the tank, before going out on a work, asks his assistant to open $Z$ when the tank is exactly $55\%$ filled so that the tank is exactly filled up by the time he is back. If he starts $X$ and $Y$ at exactly $11:00$ am and he comes back at a time represented in hours and minute as $A:B$ . Then find the value of $A+B$.

A, B, and C can complete a piece of work in $10, 12,$ and $15$ days respectively. They start working together but after $2$ days, A leaves. B leaves $3$ days before the completion of the work, and C completes the remaining work alone. In how many days is the total work completed?

Aman, Baman and Chaman need a certain unique time to do a certain work. Chaman needs one hour less than Aman to complete the work. Working together, they require $60$ minutes to complete the job. The work also gets completed if Aman and Baman start working together and Aman leaves after one hour and Baman works for a further three hours. How much work does Charan do per hour?