CAT (QA) PYQs

Gautam and Suhani, working together, can finish a job in $20$ days. If Gautam does only $60 \%$ of his usual work on a day, Suhani must do $150 \%$ of her usual work on that day to exactly make up for it. Then, the number of days required by the faster worker to complete the job working alone is

At their usual efficiency levels, $A$ and $B$ together finish a task in $12$ days. If $A$ had worked half as efficiently as she usually does, and $B$ had worked thrice as efficiently as he usually does, the task would have been completed in $9$ days. How many days would $A$ take to finish the task if she works alone at her usual efficiency?

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