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100 men were to complete a piece of work in 20 days. After they worked for 10 days, 60 more men were employed to complete the work on time. If additional men were not employed, then how many days behind schedule the work would be finished?
- a)12
- b)8
- c)10
- d)6
- e)None of these
Correct answer is option 'D'. Can you explain this answer?
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Verified Answer
100 men were to complete a piece of work in 20 days. After they worked...
D) 6
Explanation: Let 100 men complete x work in 10 days after which (100+60) = 160 men complete the remaining (1-x) work in remaining 10 days [Total work to be completed in 20 days] So, M1*D1*W2 = M2*D2*W1 100*10*(1-x) = 160*10*x Solve, x= 5/13 This means that initially employed 100 men can finish 5/13th of work in 10 days, so let they will complete 1 whole work in x days.
M1*D1*W2 = M2*D2*W1
100*10*1 = 100*x*(5/13) Solve, x = 26 This means extra (26-20) = 6 days will be required if additional men are not employed after 10 days.
Explanation: Let 100 men complete x work in 10 days after which (100+60) = 160 men complete the remaining (1-x) work in remaining 10 days [Total work to be completed in 20 days] So, M1*D1*W2 = M2*D2*W1 100*10*(1-x) = 160*10*x Solve, x= 5/13 This means that initially employed 100 men can finish 5/13th of work in 10 days, so let they will complete 1 whole work in x days.
M1*D1*W2 = M2*D2*W1
100*10*1 = 100*x*(5/13) Solve, x = 26 This means extra (26-20) = 6 days will be required if additional men are not employed after 10 days.
Most Upvoted Answer
100 men were to complete a piece of work in 20 days. After they worked...
Given:
100 men complete a piece of work in 20 days
Work started with 100 men and after 10 days 60 more men were employed
To find:
How many days behind schedule the work would be finished if additional men were not employed
Solution:
Let's assume the total work is equal to 100 units (this is just an assumption for ease of calculation)
Total work = 100 units
100 men complete 100 units of work in 20 days
So, 1 man will complete 1 unit of work in 20 * 100 = 2000 days
100 men will complete 100 units of work in 2000/100 = 20 days
Now, after 10 days, 100 men have completed 10 * 100 = 1000 units of work
Remaining work = 100 - 1000 = -900 units (negative value indicates that the work is already completed)
So, to complete the work on time, 60 more men were employed
Total men now = 100 + 60 = 160
Work remaining = -900 units (as previously calculated)
Now, 160 men will complete 900 units of work in 900/(160*10) = 0.5625 days
So, the work will be completed in a total of 10 + 0.5625 = 10.5625 days
If additional men were not employed, then the work would have been completed in 20 - 10 = 10 days
So, the work will be finished behind schedule by 10.5625 - 10 = 0.5625 days = 6/11 days ≈ 0.5 days
Therefore, the correct option is (D) 6 days.
100 men complete a piece of work in 20 days
Work started with 100 men and after 10 days 60 more men were employed
To find:
How many days behind schedule the work would be finished if additional men were not employed
Solution:
Let's assume the total work is equal to 100 units (this is just an assumption for ease of calculation)
Total work = 100 units
100 men complete 100 units of work in 20 days
So, 1 man will complete 1 unit of work in 20 * 100 = 2000 days
100 men will complete 100 units of work in 2000/100 = 20 days
Now, after 10 days, 100 men have completed 10 * 100 = 1000 units of work
Remaining work = 100 - 1000 = -900 units (negative value indicates that the work is already completed)
So, to complete the work on time, 60 more men were employed
Total men now = 100 + 60 = 160
Work remaining = -900 units (as previously calculated)
Now, 160 men will complete 900 units of work in 900/(160*10) = 0.5625 days
So, the work will be completed in a total of 10 + 0.5625 = 10.5625 days
If additional men were not employed, then the work would have been completed in 20 - 10 = 10 days
So, the work will be finished behind schedule by 10.5625 - 10 = 0.5625 days = 6/11 days ≈ 0.5 days
Therefore, the correct option is (D) 6 days.
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Community Answer
100 men were to complete a piece of work in 20 days. After they worked...
D) 6
Explanation: Let 100 men complete x work in 10 days after which (100+60) = 160 men complete the remaining (1-x) work in remaining 10 days [Total work to be completed in 20 days] So, M1*D1*W2 = M2*D2*W1 100*10*(1-x) = 160*10*x Solve, x= 5/13 This means that initially employed 100 men can finish 5/13th of work in 10 days, so let they will complete 1 whole work in x days.
M1*D1*W2 = M2*D2*W1
100*10*1 = 100*x*(5/13) Solve, x = 26 This means extra (26-20) = 6 days will be required if additional men are not employed after 10 days.
Explanation: Let 100 men complete x work in 10 days after which (100+60) = 160 men complete the remaining (1-x) work in remaining 10 days [Total work to be completed in 20 days] So, M1*D1*W2 = M2*D2*W1 100*10*(1-x) = 160*10*x Solve, x= 5/13 This means that initially employed 100 men can finish 5/13th of work in 10 days, so let they will complete 1 whole work in x days.
M1*D1*W2 = M2*D2*W1
100*10*1 = 100*x*(5/13) Solve, x = 26 This means extra (26-20) = 6 days will be required if additional men are not employed after 10 days.
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