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Twenty men can finish a piece of work in 30 days.When should 5 men leave the work so that it may be finished in 35 days?
- a)10 days
- b)12 days
- c)15 days
- d)20 days
Correct answer is option 'C'. Can you explain this answer?
Verified Answer
Twenty men can finish a piece of work in 30 days.When should 5 men lea...
The work requires 20 × 30 = 600 worker days.
Let x be the number of days before the 5 men leave.
You will then have x days with 20 workers and (35 - x) days with 15 workers.
Hence, 20× x + 15 × (35 - x) = 600
20x + 525 - 15x = 600
5x = 75
x = 15
So The five men should leave work after 15 days.
Let x be the number of days before the 5 men leave.
You will then have x days with 20 workers and (35 - x) days with 15 workers.
Hence, 20× x + 15 × (35 - x) = 600
20x + 525 - 15x = 600
5x = 75
x = 15
So The five men should leave work after 15 days.
Most Upvoted Answer
Twenty men can finish a piece of work in 30 days.When should 5 men lea...
Understanding the Work Capacity
Twenty men can complete a piece of work in 30 days.
- Total work = 20 men * 30 days = 600 man-days.
This means the total work required is 600 man-days.
Work Rate of 5 Men
- 5 men would complete the work in 600 man-days at a rate of 5 men.
- Thus, the time taken by 5 men to finish the work without any changes would be 600 man-days / 5 men = 120 days.
Adjusting the Timeline
However, we want the work to be finished in 35 days.
- The total work that needs to be done in 35 days is 600 man-days.
- The required work rate for the 35 days is 600 man-days / 35 days ≈ 17.14 men.
Calculating the Departure Time
We start with 20 men, but to meet the requirement of approximately 17.14 men, we need to determine when 5 men should leave:
- If 5 men leave after x days, the remaining work must be completed by the remaining 15 men in the remaining (35 - x) days.
Work Done Before Departure
- Work done in x days by 20 men = 20 men * x days = 20x man-days.
Remaining Work Calculation
- Remaining work = 600 man-days - 20x man-days.
- This must be completed by 15 men in (35 - x) days.
Setting the equation:
- Remaining work = 15 men * (35 - x) days
- Therefore, 600 - 20x = 15(35 - x)
Solving the Equation
- 600 - 20x = 525 - 15x
- 75 = 5x
- x = 15 days.
Conclusion
Therefore, 5 men should leave after 15 days to ensure the work is completed in 35 days. Hence, option 'C' is correct.
Twenty men can complete a piece of work in 30 days.
- Total work = 20 men * 30 days = 600 man-days.
This means the total work required is 600 man-days.
Work Rate of 5 Men
- 5 men would complete the work in 600 man-days at a rate of 5 men.
- Thus, the time taken by 5 men to finish the work without any changes would be 600 man-days / 5 men = 120 days.
Adjusting the Timeline
However, we want the work to be finished in 35 days.
- The total work that needs to be done in 35 days is 600 man-days.
- The required work rate for the 35 days is 600 man-days / 35 days ≈ 17.14 men.
Calculating the Departure Time
We start with 20 men, but to meet the requirement of approximately 17.14 men, we need to determine when 5 men should leave:
- If 5 men leave after x days, the remaining work must be completed by the remaining 15 men in the remaining (35 - x) days.
Work Done Before Departure
- Work done in x days by 20 men = 20 men * x days = 20x man-days.
Remaining Work Calculation
- Remaining work = 600 man-days - 20x man-days.
- This must be completed by 15 men in (35 - x) days.
Setting the equation:
- Remaining work = 15 men * (35 - x) days
- Therefore, 600 - 20x = 15(35 - x)
Solving the Equation
- 600 - 20x = 525 - 15x
- 75 = 5x
- x = 15 days.
Conclusion
Therefore, 5 men should leave after 15 days to ensure the work is completed in 35 days. Hence, option 'C' is correct.
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Twenty men can finish a piece of work in 30 days.When should 5 men leave the work so that it may be finished in 35 days?a)10 daysb)12 daysc)15 daysd)20 daysCorrect answer is option 'C'. Can you explain this answer?
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