Multiple choice

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. The 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. 3 20

  2. 3 10

  3. 1 5

  4. 1 20
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Sam rate = 1/20. Mohit rate = 2/20 = 1/10. Ayna rate = (1/10)/3 = 1/30. In 3 days: (S+M) + (S+A) + (M+A) = 2(S+M+A) = 2(1/20 + 1/10 + 1/30) = 2(6/60 + 3/60 + 2/60) = 2(11/60) = 11/30. Sam works on day 1 and 2, total 2/20 = 1/10. The pattern repeats. Total work = 1. The fraction is 3/10.

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