CAT (QA) PYQs

Bob can finish a job in $40$ days, if he works alone. Alex is twice as fast as Bob and thrice as fast as Cole in the same job. Suppose Alex and Bob work together on the first day, Bob and Cole work together on the second day, Cole and Alex work together on the third day, and then, they continue the work by repeating this three- day roster, with Alex and Bob working together on the fourth day, and so on. Then, the total number of days Alex would have worked when the job gets finished, 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?

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