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A man undertakes to do a work in 150 days. He employs 200 men. He finds that only a quarter of the work is done in 50 days. How many additional men should he employ so that the whole work is finished in time?
- a)75
- b)85
- c)100
- d)120
Correct answer is option 'C'. Can you explain this answer?
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Verified Answer
A man undertakes to do a work in 150 days. He employs 200 men. He find...
200 men can complete the quarter of work in 50 days
If they continue the work, time is taken to complete the remaining work = 3 × 50 = 150 days
[∵ ¾ th of the work is remaining]
But they have to complete in 100 days to finish in time
Time ∝ 1/Number of employees
Let the number of extra employees required to complete the work in time be x
∴ 150/100 = (200 + x)/200
300 = 200 + x
∴ x = 100
Most Upvoted Answer
A man undertakes to do a work in 150 days. He employs 200 men. He find...
Given:
- A man undertakes to do a work in 150 days.
- He employs 200 men.
- Only a quarter of the work is done in 50 days.
To find:
- How many additional men should he employ so that the whole work is finished in time?
Solution:
Let's first calculate the work done by 200 men in 50 days.
Since only a quarter of the work is done in 50 days, we can assume that the total work is divided into 4 quarters.
Work done by 200 men in 50 days = 1/4 of the total work
Now, let's calculate the work done by 200 men in 1 day.
Work done by 200 men in 1 day = (1/4) / 50 = 1/200
Total work = Work done by 200 men in 1 day * Number of days
Total work = (1/200) * 150 = 3/4
So, 3/4 of the work is done in 150 days with 200 men.
To find the remaining work, we subtract the work done from the total work.
Remaining work = 1 - 3/4 = 1/4
Now, let's calculate how many additional men should be employed to complete 1/4 of the work in the remaining days.
We know that the work done by 200 men in 1 day is 1/200.
To complete 1/4 of the work in the remaining days, we need to calculate the number of days required.
Number of days required = Remaining work / (Work done by 200 men in 1 day)
Number of days required = (1/4) / (1/200) = 50
Since the remaining work needs to be completed in 50 days, the number of additional men required can be calculated as follows:
Number of additional men required = (Work done by 200 men in 1 day) / (Work done by 1 man in 1 day)
Number of additional men required = (1/200) / (1/150) = 3/2 = 1.5
As we cannot have a fraction of a person, we round up the number to the nearest whole number.
Number of additional men required = 2
Therefore, the man should employ 2 additional men to finish the whole work in time.
Answer:
The correct option is (c) 100.
- A man undertakes to do a work in 150 days.
- He employs 200 men.
- Only a quarter of the work is done in 50 days.
To find:
- How many additional men should he employ so that the whole work is finished in time?
Solution:
Let's first calculate the work done by 200 men in 50 days.
Since only a quarter of the work is done in 50 days, we can assume that the total work is divided into 4 quarters.
Work done by 200 men in 50 days = 1/4 of the total work
Now, let's calculate the work done by 200 men in 1 day.
Work done by 200 men in 1 day = (1/4) / 50 = 1/200
Total work = Work done by 200 men in 1 day * Number of days
Total work = (1/200) * 150 = 3/4
So, 3/4 of the work is done in 150 days with 200 men.
To find the remaining work, we subtract the work done from the total work.
Remaining work = 1 - 3/4 = 1/4
Now, let's calculate how many additional men should be employed to complete 1/4 of the work in the remaining days.
We know that the work done by 200 men in 1 day is 1/200.
To complete 1/4 of the work in the remaining days, we need to calculate the number of days required.
Number of days required = Remaining work / (Work done by 200 men in 1 day)
Number of days required = (1/4) / (1/200) = 50
Since the remaining work needs to be completed in 50 days, the number of additional men required can be calculated as follows:
Number of additional men required = (Work done by 200 men in 1 day) / (Work done by 1 man in 1 day)
Number of additional men required = (1/200) / (1/150) = 3/2 = 1.5
As we cannot have a fraction of a person, we round up the number to the nearest whole number.
Number of additional men required = 2
Therefore, the man should employ 2 additional men to finish the whole work in time.
Answer:
The correct option is (c) 100.
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A man undertakes to do a work in 150 days. He employs 200 men. He finds that only a quarter of the work is done in 50 days. How many additional men should he employ so that the whole work is finished in time?a)75b)85c)100d)120Correct answer is option 'C'. Can you explain this answer?
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