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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. $\frac{1}{5}$
  2. $\frac{3}{10}$
  3. $\frac{3}{20}$
  4. $\frac{1}{20}$

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