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Work and time with three workers

CAT 2019 Slot 2 · Quantitative Ability · Medium · Work & time

This is a medium Quantitative Ability question from the CAT 2019 Slot 2 paper. It tests Work & time. The full answer key and a step-by-step explanation are below — try it yourself first, then reveal the solution.

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Anil alone can do a job in 20 days while Sunil alone can do it in 40 days. Anil starts the job, and after 3 days, Sunil joins him. Again, after a few more days, Bimal joins them and they together finish the job. If Bimal has done 10% of the job, then in how many days was the job done?

  1. A.

    13

  2. B.

    12

  3. C.

    15

  4. D.

    14

Answer

A

Explanation

Bimal does 10% of the total work, which means Anil and Sunil together do 90% (or 0.9) of the total work.

Let DD be the total number of days taken to finish the job.

  • Anil works for all DD days.
  • Sunil works for (D−3)(D - 3) days.

Anil's rate =1/20= 1/20 per day, Sunil's rate =1/40= 1/40 per day. D20+D−340=0.9\frac{D}{20} + \frac{D - 3}{40} = 0.9

Multiply by 40: 2D+D−3=362D + D - 3 = 36 3D=39  ⟹  D=13 days3D = 39 \implies D = 13\text{ days}

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