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.