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If 4 people can do a piece of work in 16 days working 5 hours each day. In how many the same work will be completed by 20 people working 4 hours each day?
- a)10
- b)8
- c)4
- d)6
- e)7
Correct answer is option 'C'. Can you explain this answer?
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Verified Answer
If 4 people can do a piece of work in 16 days working 5 hours each day...
C) 4
Explanation: M1*H1*D1 = M2*H2*D2
4*5*16 = 20*4*D2
Solve D2 = 4
Explanation: M1*H1*D1 = M2*H2*D2
4*5*16 = 20*4*D2
Solve D2 = 4
Most Upvoted Answer
If 4 people can do a piece of work in 16 days working 5 hours each day...
Understanding the Problem
To solve this problem, we first need to determine the total amount of work done in terms of person-hours.
Calculating Total Work
- Number of People: 4
- Days Taken: 16
- Hours per Day: 5
The total work is calculated as:
- Total Work = Number of People x Days x Hours per Day
- Total Work = 4 people x 16 days x 5 hours/day = 320 person-hours
New Scenario with More People
Now we need to find out how long it will take for 20 people to complete the same amount of work, but they will be working for 4 hours each day.
Calculating Work Done by 20 People
- Number of People: 20
- Hours per Day: 4
Let the number of days required be 'D'. The total work done by 20 people in D days is:
- Total Work = Number of People x Days x Hours per Day
- Total Work = 20 people x D days x 4 hours/day = 80D person-hours
Equating the Total Work
Since both scenarios complete the same work:
- 80D = 320
Solving for D
Dividing both sides by 80 gives:
- D = 320 / 80 = 4 days
Conclusion
Thus, it will take 20 people working 4 hours each day a total of 4 days to complete the work.
The correct answer is option 'C' (4 days).
To solve this problem, we first need to determine the total amount of work done in terms of person-hours.
Calculating Total Work
- Number of People: 4
- Days Taken: 16
- Hours per Day: 5
The total work is calculated as:
- Total Work = Number of People x Days x Hours per Day
- Total Work = 4 people x 16 days x 5 hours/day = 320 person-hours
New Scenario with More People
Now we need to find out how long it will take for 20 people to complete the same amount of work, but they will be working for 4 hours each day.
Calculating Work Done by 20 People
- Number of People: 20
- Hours per Day: 4
Let the number of days required be 'D'. The total work done by 20 people in D days is:
- Total Work = Number of People x Days x Hours per Day
- Total Work = 20 people x D days x 4 hours/day = 80D person-hours
Equating the Total Work
Since both scenarios complete the same work:
- 80D = 320
Solving for D
Dividing both sides by 80 gives:
- D = 320 / 80 = 4 days
Conclusion
Thus, it will take 20 people working 4 hours each day a total of 4 days to complete the work.
The correct answer is option 'C' (4 days).
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