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M is twice as efficient as N and thrice as efficient as O. If N finishes a piece of work in 6 days, in how many days M, N and O complete the same piece of work together? 
1. 15/11 days
2. 4 days
3. 3 days
4. 18/11 days

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Correct Answer - Option 4 : 18/11 days

Given:

M is twice as efficient as N and thrice as efficient as O.

N finishes a piece of work in 6 days.

Concepts used:

Time = Work/Efficiency

Calculation:

Time ratio of M, N and O = 1 ∶ 2 ∶ 3

Let M, N and O finish a piece of work in x, 2x and 3x days respectively.

As N finishes piece of work in 6 days,

⇒ 2x = 6 days

⇒ x = 3 days.

Time taken by M to complete the piece of work = x = 3 days

Time taken by O to complete the piece of work = 3x = 3 × 3 days = 9 days

1 day work of M, N and O =  (1/3) + (1/6) + (1/9) = 11/18 days 

Time taken by M, N and O to complete the work together = 18/11 days

∴ M, N and O took 18/11 days to complete a piece of work together.

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