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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 taken to complete the remaining work = 3 × 50 = 150 days
[∵ 3/4 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
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Most Upvoted Answer
A man undertakes to do a work in 150 days. He employs 200 men. He find...
Given information:
- 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?

Let's solve the problem step by step:

Step 1: Calculate the work done by 200 men in 50 days.
- It is given that only a quarter of the work is done in 50 days.
- Therefore, the total work can be represented as 4 times the work done in 50 days.
- Let the total work be W.
- So, the work done in 50 days by 200 men is W/4.

Step 2: Calculate the remaining work.
- The remaining work after 50 days can be represented as (3/4)W.

Step 3: Calculate the work done by 200 men in 1 day.
- The work done in 50 days by 200 men is W/4.
- Therefore, the work done by 200 men in 1 day is (W/4) / 50 = W/200.

Step 4: Calculate the work done by 1 man in 1 day.
- Since 200 men are employed, the work done by 1 man in 1 day is (W/200) / 200 = W/40,000.

Step 5: Calculate the number of days required to complete the remaining work.
- Let the number of days required to complete the remaining work be D.
- Therefore, the work done by 1 man in D days is (W/40,000) * D = (3/4)W.
- Solving this equation, we get D = 30,000.

Step 6: Calculate the number of additional men required.
- Since 200 men are already employed, the number of additional men required is (W/40,000) * D / (W/40,000) = D.
- Substituting the value of D, we get the number of additional men required as 30,000.

Therefore, the correct answer is option 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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