CAT 2025 Slot 1 QA Q18 Time & Work

Question 18 of the Quantitative Ability (QA) section, CAT 2025 Slot 1, with CAT's official answer and a worked solution.

Arun, Varun and Tarun, if working alone, can complete a task in 24, 21, and 15 days, respectively. They charge Rs 2160, Rs 2400, and Rs 2160 per day, respectively, even if they are employed for a partial day. On any given day, any of the workers may or may not be employed to work. If the task needs to be completed in 10 days or less, then the minimum possible amount, in rupees, required to be paid for the entire task is
  1. A
    34400
  2. B
    38880
  3. C
    47040
  4. D
    38400

Answer: (D) 38400 Time & Work MCQ

Solution

  1. Cost to do the whole task alone: Arun \(2160 \times 24 = 51840\), Varun \(2400 \times 21 = 50400\), Tarun \(2160 \times 15 = 32400\).
  2. Tarun is cheapest, but in 10 days he can do only \(\frac{10}{15} = \frac23\) of the task, costing \(21600\).
  3. Give the remaining \(\frac13\) to the next cheapest, Varun: \(7\) full days, costing \(16800\).
  4. Minimum \(= 21600 + 16800 = 38400\).

Shortcut. Compare cost per whole task (daily rate times days), then fill with the cheapest worker first.

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