Work done in repeating three-day pattern

CAT 2024 Slot 3 · QA · Medium · Arithmetic

All CAT 2024 Slot 3 questionsMore Arithmetic questionsAll CAT QA

Sam can complete a job in 20 days when working alone. Mohit is twice as fast as Sam and thrice as fast as Ayna in the same job. They undertake a job with an arrangement where Sam and Mohit work together on the first day, Sam and Ayna on the second day, Mohit and Ayna on the third day, and this three-day pattern is repeated till the work gets completed. Then, the fraction of total work done by Sam is

  1. A.

    3/20

  2. B.

    3/10

  3. C.

    1/20

  4. D.

    1/5

Answer

B

Explanation

Let total work = 60 units.

  • Sam's rate: S=6020=3S = \frac{60}{20} = 3 units/day.
  • Mohit's rate: M=2×3=6M = 2 \times 3 = 6 units/day.
  • Ayna's rate: A=63=2A = \frac{6}{3} = 2 units/day.

3-day cycle:

  • Day 1: Sam + Mohit = 3+6=93 + 6 = 9 units.
  • Day 2: Sam + Ayna = 3+2=53 + 2 = 5 units.
  • Day 3: Mohit + Ayna = 6+2=86 + 2 = 8 units. Total work in one 3-day cycle = 9+5+8=229 + 5 + 8 = 22 units.

In 2 complete cycles (6 days), work done = 22×2=4422 \times 2 = 44 units. Remaining work = 60−44=1660 - 44 = 16 units.

  • Day 7 (Sam + Mohit): 9 units done. Remaining = 7 units.
  • Day 8 (Sam + Ayna): 5 units done. Remaining = 2 units.
  • Day 9 (Mohit + Ayna): remaining 2 units completed.

Sam worked on Days 1, 2, 4, 5, 7, and 8 (6 full days). Work done by Sam = 6×3=186 \times 3 = 18 units.

Fraction of total work done by Sam = 1860=310\frac{18}{60} = \frac{3}{10}.

Practise this under exam conditions

Sign in to solve it with a live timer, the on-screen CAT calculator, and streak and accuracy tracking across every question you attempt.

Solve in the workspace