NinetynineCAT 2022 Slot 3 QA Q3 Time & Work
Question 3 of the Quantitative Ability (QA) section, CAT 2022 Slot 3, with CAT's official answer and a worked solution.
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
TITA: type in the answer. There are no options and no negative marking.
Answer: 11 Time & Work TITA
Solution
- Take the job as 120 units. Bob does 3/day, Alex (twice Bob) 6/day, Cole (Alex/3) 2/day.
- Roster: A+B = 9, B+C = 5, C+A = 8, so each 3-day cycle does 22 units.
- 5 cycles (15 days) do 110 units; day 16 (A+B) brings it to 119; day 17 (B+C) finishes the job.
- Alex works 2 days per cycle: \(5\times2=10\), plus day 16, total 11 days.