CAT 2023 Slot 3 QA Q8 Time & Work

Question 8 of the Quantitative Ability (QA) section, CAT 2023 Slot 3, with CAT's official answer and a worked solution.

Rahul, Rakshita and Gurmeet, working together, would have taken more than 7 days to finish a job. On the other hand, Rahul and Gurmeet, working together would have taken less than 15 days to finish the job. However, they all worked together for 6 days, followed by Rakshita, who worked alone for 3 more days to finish the job. If Rakshita had worked alone on the job then the number of days she would have taken to finish the job, cannot be
  1. A
    17
  2. B
    21
  3. C
    16
  4. D
    20

Answer: (B) 21 Time & Work MCQ

Solution

  1. Let rates be R, K (Rakshita), G per day. Job: \(6(R+K+G)+3K=1\), so \(R+G = \frac{1-9K}{6}\).
  2. \(R+G>\frac1{15}\): \(1-9K>0.4 \Rightarrow K<\frac1{15}\), so Rakshita alone takes more than 15 days.
  3. \(R+K+G<\frac17\): \(\frac{1-3K}{6}<\frac17 \Rightarrow K>\frac1{21}\), so she takes fewer than 21 days.
  4. Her time lies strictly between 15 and 21, so it cannot be 21.

More Time & Work questions from CAT

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