CAT (QA) PYQs

A tank is emptied everyday at a fixed time point. Immediately thereafter, either pump $A$ or pump $B$ or both start working until the tank is full. On Monday, $A$ alone completed filling the tank at $8 \mathrm{pm}$. On Tuesday, B alone completed filling the tank at $6 \mathrm{pm}$. On Wednesday, $A$ alone worked till $5 \mathrm{pm}$, and then B worked alone from $5 \mathrm{pm}$ to $7 \mathrm{pm}$, to fill the tank. At what time was the tank filled on Thursday if both pumps were used simultaneously all along?

One day, Rahul started a work at $9$ AM and Gautam joined him two hours later. They then worked together and completed the work at $5$ PM the same day. If both had started at $9$ AM and worked together, the work would have been completed $30$ minutes earlier. Working alone, the time Rahul would have taken, in hours, to complete the work is

A water tank has inlets of two types $A$ and $B$. All inlets of type $A$ when open, bring in water at the same rate. All inlets of type $B$, when open, bring in water at the same rate. The empty tank is completely filled in $30$ minutes if $10$ inlets of type $A$ and $45$ inlets of type $B$ are open, and in $1$ hour if $8$ inlets of type $A$ and $18$ inlets of type $B$ are open. In how many minutes will the empty tank get completely filled if $7$ inlets of type $A$ and $27$ inlets of type $B$ are open?