CAT 2025 Slot 3 QA Q10 Time & Work

Question 10 of the Quantitative Ability (QA) section, CAT 2025 Slot 3, with CAT's official answer and a worked solution.

Teams A, B, and C consist of five, eight, and ten members, respectively, such that every member within a team is equally productive. Working separately, teams A, B, and C can complete a certain job in 40 hours, 50 hours, and 4 hours, respectively. Two members from team A, three members from team B, and one member from team C together start the job, and the member from team C leaves after 23 hours. The number of additional member(s) from team B, that would be required to replace the member from team C, to finish the job in the next one hour, is
  1. A
    2
  2. B
    4
  3. C
    1
  4. D
    3

Answer: (A) 2 Time & Work MCQ

Solution

  1. Take the job as 400 units. Per member per hour: A \(= \frac{400}{5 \times 40} = 2\), B \(= \frac{400}{8 \times 50} = 1\), C \(= \frac{400}{10 \times 4} = 10\).
  2. 2A + 3B + 1C work at \(4 + 3 + 10 = 17\) units/h; in 23 hours they do 391 units, leaving 9.
  3. In the next hour 2A + 3B give 7 units, so \(n\) extra B members must add 2 units: \(n = 2\).

Same concept in other years

See every question on Person-days or person-hours are proportional to work done.

More Time & Work questions from CAT

All 34 Time & Work questions asked since 2017.