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A piece of work is done by a man in 6 days when he works 5 hours a day while the same piece of work is completed by a woman in 5 days when she worked 4 hours a day.  In how many days they can complete the same piece of work together if each works 6 hours a day?


1. 1 day
2. 3 days
3. 2 days
4. 5 days

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Correct Answer - Option 3 : 2 days

Given:

A man can complete a piece of work in 6 days, working 5 hours a day.

A woman can complete a piece of work in 5 days, working 4 hours a day.

Concepts used:

1-day work done by individual = Work/time

Time = Work/Efficiency

Calculation:

Total working hours of a man = 6 × 5 = 30 hours 

⇒ 1-hour work done by individual = Work/time

⇒ 1 hour work of 1 man = 1/(6 × 5) = 1/30

Total working hours of a woman = 4 × 5 = 20 hours 

⇒ 1 hour work of 1 woman = 1/(5 × 4) = 1/20

⇒ 1 day work of 1 man and 1 woman working 6 hours a day = 6 × [(1/30) + (1/20)] = 6 × 5/60 = 1/2

Time = Work/Efficiency

⇒ Time taken by 1 man and 1 woman to complete work, working 6 hours day = 1/(1/2) days = 2 days

∴ The work is completed in 2 days by one man and woman when they worked 6 hours day.

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