The work done by a woman in 8 h is equal to the work done by a man in 6 h and…
2023
The work done by a woman in 8 h is equal to the work done by a man in 6 h and by a boy in 12 h. If working 6h/day 9 men can complete a work in 6 days, then in how many days 12 women and 12 boys together finish the same work working 8 h/day?
- A.
9/4 days
- B.
5/2 days
- C.
13/7 days
- D.
8/3 days
Attempted by 2 students.
Show answer & explanation
Correct answer: D
Explanation:
Let one woman's 8-hour work be 1 unit of work. Then:
Woman's rate = 1/8 unit per hour.
Man's rate = 1/6 unit per hour.
Boy's rate = 1/12 unit per hour.
Compute total work from the given: 9 men working 6 hours/day for 6 days.
Total hours = 6 hours/day × 6 days = 36 hours.
Each man does 36 × 1/6 = 6 units, so 9 men do 9 × 6 = 54 units.
Now find daily output of 12 women and 12 boys working 8 hours/day.
Hourly rate = 12×(1/8) + 12×(1/12) = 1.5 + 1 = 2.5 units/hour.
Daily output (8 hours) = 2.5 × 8 = 20 units/day.
Days required = total work / daily output = 54 / 20 = 27/10 = 2.7 days.
Answer: 27/10 days (2.7 days).