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A Contractor employed a certain number of workers to finish constructing a building in a certain scheduled time. Some time later, when a part of work had been completed, he realized that the work would get delayed by half of the scheduled time, so he at once doubled the no of workers and thus he managed to finish the building on the scheduled time. How much work he had been completed, before increasing the number of workers?
- a)200/3%
- b)100/3%
- c)300/3%
- d)Can’t be determined
- e)None of these
Correct answer is option 'B'. Can you explain this answer?
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Verified Answer
A Contractor employed a certain number of workers to finish constructi...
D * x +(100- D) * 2x= 150x
⇒ D = 50 days
work done in 50 days = 50x
Total work = 150x
50x/150x * 100 = 100/3
⇒ D = 50 days
work done in 50 days = 50x
Total work = 150x
50x/150x * 100 = 100/3
Most Upvoted Answer
A Contractor employed a certain number of workers to finish constructi...
Not be determined
Let's assume that the contractor initially employed x workers to finish the building in t time. Let's also assume that the total work required to finish the building is 1 unit. Therefore, each worker would complete 1/(xt) units of work in 1 unit of time.
After completing a part of the work, the contractor realized that the work would get delayed by half of the scheduled time, which means that he had completed only half of the work. Therefore, the amount of work completed before increasing the number of workers is 1/2 unit.
When the contractor doubled the number of workers, the rate of work completion also doubled. Therefore, each worker would now complete 2/(xt) units of work in 1 unit of time.
Let's assume that the contractor increased the number of workers to y. Therefore, we can write the following equation:
(1/2) = (1/x)t ----> equation 1 (since half of the work was completed initially)
1 = (2/y)t ----> equation 2 (since the work was completed on the scheduled time after doubling the workers)
From equation 1, we get:
t = (1/2)(x) ----> equation 3
Substituting equation 3 in equation 2, we get:
1 = (2/y)(1/2)(x)
y = 4x
Therefore, the contractor increased the number of workers to 4x.
Now, let's calculate the amount of work completed by the initial x workers before doubling the workers:
Amount of work completed by x workers = (work done by 1 worker in 1 unit of time) x (number of workers) x (time taken)
= (1/(xt)) x (x) x ((1/2)(x))
= (1/2) unit
Therefore, the amount of work completed before increasing the number of workers is 1/2 unit.
Now, let's calculate the percentage of work completed before increasing the number of workers:
Percentage of work completed = (amount of work completed / total work required) x 100
= (1/2 / 1) x 100
= 50%
Therefore, the answer is option (d) "Cannot be determined" since the percentage of work completed before increasing the number of workers is independent of the initial number of workers and the scheduled time.
Let's assume that the contractor initially employed x workers to finish the building in t time. Let's also assume that the total work required to finish the building is 1 unit. Therefore, each worker would complete 1/(xt) units of work in 1 unit of time.
After completing a part of the work, the contractor realized that the work would get delayed by half of the scheduled time, which means that he had completed only half of the work. Therefore, the amount of work completed before increasing the number of workers is 1/2 unit.
When the contractor doubled the number of workers, the rate of work completion also doubled. Therefore, each worker would now complete 2/(xt) units of work in 1 unit of time.
Let's assume that the contractor increased the number of workers to y. Therefore, we can write the following equation:
(1/2) = (1/x)t ----> equation 1 (since half of the work was completed initially)
1 = (2/y)t ----> equation 2 (since the work was completed on the scheduled time after doubling the workers)
From equation 1, we get:
t = (1/2)(x) ----> equation 3
Substituting equation 3 in equation 2, we get:
1 = (2/y)(1/2)(x)
y = 4x
Therefore, the contractor increased the number of workers to 4x.
Now, let's calculate the amount of work completed by the initial x workers before doubling the workers:
Amount of work completed by x workers = (work done by 1 worker in 1 unit of time) x (number of workers) x (time taken)
= (1/(xt)) x (x) x ((1/2)(x))
= (1/2) unit
Therefore, the amount of work completed before increasing the number of workers is 1/2 unit.
Now, let's calculate the percentage of work completed before increasing the number of workers:
Percentage of work completed = (amount of work completed / total work required) x 100
= (1/2 / 1) x 100
= 50%
Therefore, the answer is option (d) "Cannot be determined" since the percentage of work completed before increasing the number of workers is independent of the initial number of workers and the scheduled time.
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Community Answer
A Contractor employed a certain number of workers to finish constructi...
D * x +(100- D) * 2x= 150x
⇒ D = 50 days
work done in 50 days = 50x
Total work = 150x
50x/150x * 100 = 100/3
⇒ D = 50 days
work done in 50 days = 50x
Total work = 150x
50x/150x * 100 = 100/3
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A Contractor employed a certain number of workers to finish constructing a building in a certain scheduled time. Some time later, when a part of work had been completed, he realized that the work would get delayed by half of the scheduled time, so he at once doubled the no of workers and thus he managed to finish the building on the scheduled time. How much work he had been completed, before increasing the number of workers?a)200/3%b)100/3%c)300/3%d)Can’t be determinede)None of theseCorrect answer is option 'B'. Can you explain this answer?
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