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Twenty workers can finish a piece of work in 30 days. After how many days should 5 workersleave the job so that the work is completed in 35 days?
- a)5 days
- b)10 days
- c)15 days
- d)20 days
Correct answer is option 'C'. Can you explain this answer?
Verified Answer
Twenty workers can finish a piece of work in 30 days. After how many d...
rate of 1 man per day=1/(20*30)=1/600
let d=number of days with 20 workers
20d/600+[15(35-d)]/600=1
d=15 days
Most Upvoted Answer
Twenty workers can finish a piece of work in 30 days. After how many d...
First of all we convert it in unit like this
20 workers � 30 days = 600 units work
After leave the 5 workers , we have 35 days for complete the work.
In 35 days only 15 workers will do the work.
So the work completed in 35 days by 15 workers = 35 �15 =525 units
Remaining unit = 600 -525 =75 units
This units would done by 5 workers in ( 75/5) = 15 days .
So after 15 days 5 workers should leave the job.
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Community Answer
Twenty workers can finish a piece of work in 30 days. After how many d...
Given:
Number of workers = 20
Time taken to complete work = 30 days
Number of workers to leave the job = 5
Time taken to complete work after 5 workers leave = 35 days
To find:
After how many days should 5 workers leave the job?
Solution:
Let's assume that the work requires X units of effort to complete.
From the given information, we can say that:
20 workers can complete X units of work in 30 days
1 worker can complete X units of work in 20*30 = 600 days (since he will take 20 times longer than 20 workers)
5 workers can complete X units of work in 600/5 = 120 days (since they will take 1/5th of the time taken by 1 worker)
Let's assume that the 20 workers start the work on day 0.
If all 20 workers work for 35 days, they will complete the work in 35/30 = 7/6 times the time required to complete the work.
So, the amount of work completed by them in 35 days = (7/6)*X units.
Now, 5 workers leave the job after 'n' days.
So, the remaining 15 workers have to complete the remaining work in (35-n) days.
Let's say that they complete 'Y' units of work in 'n' days.
So, the amount of work remaining after 'n' days = X - Y units.
The remaining 15 workers have to complete this work in (35-n) days.
From the given information, we know that:
5 workers can complete X units of work in 120 days
5 workers can complete Y units of work in n*5 days
Using the above information, we can form an equation:
5*(35-n) = (X-Y)
(35-n) = (X-Y)/5
Substituting the value of Y from the second equation in the first equation, we get:
5*(35-n) = X - 5*n*Y/5
5*(35-n) = X - n*Y
Y = X - (5*(35-n))/n
Now, we can substitute the value of Y in the equation (35-n) = (X-Y)/5 and simplify:
(35-n) = (X - (X - (5*(35-n))/n))/5
(35-n) = (5*(35-n))/n*5
n = 15
Therefore, 5 workers should leave the job after 15 days so that the work is completed in 35 days.
Number of workers = 20
Time taken to complete work = 30 days
Number of workers to leave the job = 5
Time taken to complete work after 5 workers leave = 35 days
To find:
After how many days should 5 workers leave the job?
Solution:
Let's assume that the work requires X units of effort to complete.
From the given information, we can say that:
20 workers can complete X units of work in 30 days
1 worker can complete X units of work in 20*30 = 600 days (since he will take 20 times longer than 20 workers)
5 workers can complete X units of work in 600/5 = 120 days (since they will take 1/5th of the time taken by 1 worker)
Let's assume that the 20 workers start the work on day 0.
If all 20 workers work for 35 days, they will complete the work in 35/30 = 7/6 times the time required to complete the work.
So, the amount of work completed by them in 35 days = (7/6)*X units.
Now, 5 workers leave the job after 'n' days.
So, the remaining 15 workers have to complete the remaining work in (35-n) days.
Let's say that they complete 'Y' units of work in 'n' days.
So, the amount of work remaining after 'n' days = X - Y units.
The remaining 15 workers have to complete this work in (35-n) days.
From the given information, we know that:
5 workers can complete X units of work in 120 days
5 workers can complete Y units of work in n*5 days
Using the above information, we can form an equation:
5*(35-n) = (X-Y)
(35-n) = (X-Y)/5
Substituting the value of Y from the second equation in the first equation, we get:
5*(35-n) = X - 5*n*Y/5
5*(35-n) = X - n*Y
Y = X - (5*(35-n))/n
Now, we can substitute the value of Y in the equation (35-n) = (X-Y)/5 and simplify:
(35-n) = (X - (X - (5*(35-n))/n))/5
(35-n) = (5*(35-n))/n*5
n = 15
Therefore, 5 workers should leave the job after 15 days so that the work is completed in 35 days.
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Twenty workers can finish a piece of work in 30 days. After how many days should 5 workersleave the job so that the work is completed in 35 days?a)5 daysb)10 daysc)15 daysd)20 daysCorrect answer is option 'C'. Can you explain this answer?
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