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Time and Work Statement Analysis

CMAT 2021 · Quantitative Techniques & Data Interpretation · Medium · Time and Work

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Given: Anuj takes 1 day to complete a job. Bharat takes twice the time as Anuj to complete the same job. Chetan takes twice the time as Bharat to complete that job. Dhiraj takes twice the time as Chetan to complete that job.

(A) Chetan and Dhiraj will take 8/3 days to complete the work (B) The second fastest pair to complete the work is Anuj and Dhiraj (C) The second slowest pair to complete the work is Bharat and Dhiraj (D) Bharat and Dhiraj will take 4/3 days to complete the work

  1. A.

    (A), (B) and (C) only

  2. B.

    (A) and (D) only

  3. C.

    (A) and (C) only

  4. D.

    (A) only

Answer

C

Explanation

Anuj takes 1 day, Bharat takes 2 days, Chetan takes 4 days, and Dhiraj takes 8 days. Chetan and Dhiraj together take 4×84+8=3212=83\frac{4 \times 8}{4 + 8} = \frac{32}{12} = \frac{8}{3} days, so statement (A) is correct. Calculating time taken by pairs: AB = 2/3 days, AC = 4/5 days, AD = 8/9 days, BC = 8/6 = 4/3 days, BD = 16/10 = 8/5 days, CD = 8/3 days. Slowest pair is CD (8/3 days), second slowest is BD (8/5 days), so statement (C) is correct. Hence, (A) and (C) only are correct.

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