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39 persons can repair a road in 12 days, working 5 hours a day. In how many days will 30 persons, working 6 hours a day, complete the work?
- a)10
- b)13
- c)18
- d)136
Correct answer is option 'B'. Can you explain this answer?
Verified Answer
39 persons can repair a road in 12 days, working 5 hours a day. In how...
Since 39 persons can repair a road by working 5 hours in a day in 12 days.
∴ 1 persons can repair a road by working 5 hours in a day in 39 x 12 days.
∴ 1 persons can repair a road by working 1 hours in a day in 39 x 12 x 5 days.
∴ 30 persons can repair a road by working 1 hours in a day in 39 x 12 x 5 / 30 days.
∴ 30 persons can repair a road by working 6 hours in a day in 39 x 12 x 5 / 30 x 6 days.
∴ 30 persons can repair a road by working 6 hours in a day in 39 x 2 x 1 / 6 days.
∴ 30 persons can repair a road by working 6 hours in a day in 39 x 1 x 1 / 3 days.
∴ 30 persons can repair a road by working 6 hours in a day in 13 days.
∴ 1 persons can repair a road by working 5 hours in a day in 39 x 12 days.
∴ 1 persons can repair a road by working 1 hours in a day in 39 x 12 x 5 days.
∴ 30 persons can repair a road by working 1 hours in a day in 39 x 12 x 5 / 30 days.
∴ 30 persons can repair a road by working 6 hours in a day in 39 x 12 x 5 / 30 x 6 days.
∴ 30 persons can repair a road by working 6 hours in a day in 39 x 2 x 1 / 6 days.
∴ 30 persons can repair a road by working 6 hours in a day in 39 x 1 x 1 / 3 days.
∴ 30 persons can repair a road by working 6 hours in a day in 13 days.
Most Upvoted Answer
39 persons can repair a road in 12 days, working 5 hours a day. In how...
Understanding the Work Done
To find out how many days 30 persons, working 6 hours a day, will take to complete the same work, we first need to determine the total work done in terms of person-hours.
Total Work Calculation
- The total work done by 39 persons in 12 days, working 5 hours a day:
- Total Person-Hours = 39 persons × 12 days × 5 hours/day
- Total Person-Hours = 39 × 12 × 5 = 2340 person-hours
Work Done by 30 Persons
- Now, let's find out how many person-hours 30 persons can contribute in one day while working 6 hours:
- Daily Work = 30 persons × 6 hours/day = 180 person-hours/day
Finding the Number of Days
- To find out how many days (D) it will take for 30 persons to complete 2340 person-hours of work:
- Total Work = Daily Work × Number of Days
- 2340 person-hours = 180 person-hours/day × D
- Rearranging the equation to solve for D:
- D = 2340 person-hours / 180 person-hours/day
- D = 13 days
Conclusion
Thus, 30 persons working 6 hours per day will complete the work in 13 days. Therefore, the correct answer is option B.
To find out how many days 30 persons, working 6 hours a day, will take to complete the same work, we first need to determine the total work done in terms of person-hours.
Total Work Calculation
- The total work done by 39 persons in 12 days, working 5 hours a day:
- Total Person-Hours = 39 persons × 12 days × 5 hours/day
- Total Person-Hours = 39 × 12 × 5 = 2340 person-hours
Work Done by 30 Persons
- Now, let's find out how many person-hours 30 persons can contribute in one day while working 6 hours:
- Daily Work = 30 persons × 6 hours/day = 180 person-hours/day
Finding the Number of Days
- To find out how many days (D) it will take for 30 persons to complete 2340 person-hours of work:
- Total Work = Daily Work × Number of Days
- 2340 person-hours = 180 person-hours/day × D
- Rearranging the equation to solve for D:
- D = 2340 person-hours / 180 person-hours/day
- D = 13 days
Conclusion
Thus, 30 persons working 6 hours per day will complete the work in 13 days. Therefore, the correct answer is option B.
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Question Description
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