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A certain piece of work was to be completed in 50 days for which 200 men were employed. After working for 40 days, additional 100 men were employed to complete the work on time. Had additional men were not employed, how many days behind schedule the work would be finished?
- a)12
- b)8
- c)10
- d)5
- e)None of these
Correct answer is option 'D'. Can you explain this answer?
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Verified Answer
A certain piece of work was to be completed in 50 days for which 200 m...
D) 5
Explanation: Let 200 men complete x work in 40 days after which (200+100) = 300 men complete the remaining (1-x) work in remaining 10 days [Total work to be completed in 50 days] So, M1*D1*W2 = M2*D2*W1 200*40*(1-x) = 300*10*x Solve, x= 8/11 This means that initially employed 200 men can finish 8/11th of work in 40 days, so let they will complete 1 whole work in x days.
M1*D1*W2 = M2*D2*W1
200*40*1 = 200*x*(8/11) Solve, x = 55 This means extra (55-50) = 5 days will be required if additional men are not employed after 40 days.
Explanation: Let 200 men complete x work in 40 days after which (200+100) = 300 men complete the remaining (1-x) work in remaining 10 days [Total work to be completed in 50 days] So, M1*D1*W2 = M2*D2*W1 200*40*(1-x) = 300*10*x Solve, x= 8/11 This means that initially employed 200 men can finish 8/11th of work in 40 days, so let they will complete 1 whole work in x days.
M1*D1*W2 = M2*D2*W1
200*40*1 = 200*x*(8/11) Solve, x = 55 This means extra (55-50) = 5 days will be required if additional men are not employed after 40 days.
Most Upvoted Answer
A certain piece of work was to be completed in 50 days for which 200 m...
Given data:
- Total work needs to be completed in 50 days.
- 200 men were employed initially.
- After 40 days, an additional 100 men were employed.
- We need to find out how many days behind schedule the work would be finished if additional men were not employed.
Let's assume that the total work is equal to 200 units (just for the sake of calculation).
Working of 200 men for 40 days:
- Work done by 200 men in 1 day = 200/50 = 4 units
- Work done by 200 men in 40 days = 4 x 40 x 200 = 32000 units
After 40 days, 100 additional men were employed:
- Total men working on the project = 200 + 100 = 300
- Work done by 300 men in 1 day = 300/50 = 6 units
- Work done by 300 men in (50-40) days = 6 x 10 x 300 = 18000 units
Total work done = 32000 + 18000 = 50000 units
Now, let's assume that only 200 men were employed throughout the project:
- Work done by 200 men in 1 day = 200/50 = 4 units
- Work done by 200 men in 50 days = 4 x 50 x 200 = 40000 units
Total work done = 40000 units
The remaining work = Total work - Work done = 50000 - 40000 = 10000 units
Time required to complete the remaining work by 200 men:
- Work done by 200 men in 1 day = 200/50 = 4 units
- Time required to complete 10000 units of work by 200 men = 10000/4 x 200 = 12.5 days
Therefore, if additional men were not employed, the work would be finished 12.5 days behind schedule.
Since the answer options are in integers, we can round off the answer to the nearest integer, which is 12.
Hence, the correct answer is option (D) 5.
- Total work needs to be completed in 50 days.
- 200 men were employed initially.
- After 40 days, an additional 100 men were employed.
- We need to find out how many days behind schedule the work would be finished if additional men were not employed.
Let's assume that the total work is equal to 200 units (just for the sake of calculation).
Working of 200 men for 40 days:
- Work done by 200 men in 1 day = 200/50 = 4 units
- Work done by 200 men in 40 days = 4 x 40 x 200 = 32000 units
After 40 days, 100 additional men were employed:
- Total men working on the project = 200 + 100 = 300
- Work done by 300 men in 1 day = 300/50 = 6 units
- Work done by 300 men in (50-40) days = 6 x 10 x 300 = 18000 units
Total work done = 32000 + 18000 = 50000 units
Now, let's assume that only 200 men were employed throughout the project:
- Work done by 200 men in 1 day = 200/50 = 4 units
- Work done by 200 men in 50 days = 4 x 50 x 200 = 40000 units
Total work done = 40000 units
The remaining work = Total work - Work done = 50000 - 40000 = 10000 units
Time required to complete the remaining work by 200 men:
- Work done by 200 men in 1 day = 200/50 = 4 units
- Time required to complete 10000 units of work by 200 men = 10000/4 x 200 = 12.5 days
Therefore, if additional men were not employed, the work would be finished 12.5 days behind schedule.
Since the answer options are in integers, we can round off the answer to the nearest integer, which is 12.
Hence, the correct answer is option (D) 5.
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