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M is thrice as efficient as N and N is twice as efficient as O. If O alone can complete a piece of work in 25 days, find the time taken by the three of them to complete the piece of work together. 


1. 20/7 days
2. 25/9 days
3. 50/6 days
4. 20/9 days

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Best answer
Correct Answer - Option 2 : 25/9 days

Given:                                 

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

O alone can complete a piece of work in 25 days.

Concepts used:

Time = Work/Efficiency

1 day work of individual = Work/Time

Calculation:

O alone can complete a piece of work in 25 days.

1 day work of O = 1/25

⇒ The efficiency of O = 1/25

⇒ The efficiency of N = 2 × 1/25 

⇒ Efficiency of M = 3 × 2/25 = 6/25

⇒ 1 day work or combined efficiency of M, N and O = (1/25) + (2/25) + (6/25) = 9/25

⇒ Time taken by M, N and O in completing a full piece of work = 25/9 days

∴ M, N and O took 25/9 days to complete the full piece of work.

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