P, Q, and R can do a piece of work in 38 days. Q and R can do the work in 76 days. Find the number of days in which P can complete the same work.

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SSC GD Constable (2022) Official Paper (Held On : 07 Feb 2023 Shift 4)
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  1. 81 days 
  2. 76 days
  3. 84 days
  4. 90 days

Answer (Detailed Solution Below)

Option 2 : 76 days
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Detailed Solution

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Given

P, Q, R can complete the work in 38 days.

Q and R can complete the work in 76 days.

Concept:

If A and B together can complete a job in 'd' days and B alone can complete the same job in 'f' days, then A alone can complete the job in (d × f) / (f - d) days.

Calculation:

Time taken by P alone to complete the work = (38 × 76)/(76 - 38)

Hence, P alone can complete the work in 76 days.

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