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Work and Daily Wages Minimization

CAT 2025 Slot 1 · Quantitative Ability · Hard · Arithmetic

This is a hard Quantitative Ability question from the CAT 2025 Slot 1 paper. It tests Arithmetic. The full answer key and a step-by-step explanation are below — try it yourself first, then reveal the solution.

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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.

    47040

  2. B.

    38880

  3. C.

    34400

  4. D.

    38400

Answer

B

Explanation

Total work = LCM(24, 21, 15) = 840 units. Rates of work per day: Arun = 840/24=35840 / 24 = 35 units/day, cost = Rs 2160. Varun = 840/21=40840 / 21 = 40 units/day, cost = Rs 2400. Tarun = 840/15=56840 / 15 = 56 units/day, cost = Rs 2160.

Cost per unit of work: Arun: 2160/35=61.712160 / 35 = 61.71 Rs/unit. Varun: 2400/40=602400 / 40 = 60 Rs/unit. Tarun: 2160/56=38.572160 / 56 = 38.57 Rs/unit.

Tarun is the most cost-effective. Tarun works all 10 days, doing 10×56=56010 \times 56 = 560 units. Cost = 10×2160=2160010 \times 2160 = 21600. Remaining work = 840−560=280840 - 560 = 280 units. To minimize cost, hire Arun or Varun for full days within the 10 days. If Varun works 7 days: 7×40=2807 \times 40 = 280 units. Cost = 7×2400=168007 \times 2400 = 16800. Total cost = 21600+16800=3840021600 + 16800 = 38400. Wait, let's check if employing Arun or combination gives less. If Arun works 8 days: 8×35=2808 \times 35 = 280 units. Cost = 8×2160=172808 \times 2160 = 17280. If Arun works 8 days and Varun works 0 days, total = 38880. But 21600+16800=3840021600 + 16800 = 38400 is lower, which corresponds to option 4 (38400).

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