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A contractor employed 60 men to do a piece of work in 76 days. After 50 days, he employed 10 more men and the work was finished 2 day earlier. How many days he would have been behind, if he had not employed additional men?
- a)1 day
- b)2 days
- c)3 days
- d)4 days
- e)None of these
Correct answer is option 'B'. Can you explain this answer?
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A contractor employed 60 men to do a piece of work in 76 days. After 5...
Answer –b) 2 days Explanation : Total work = 60*50 + 70*24 Now days = D D*60 = 60*50 + 70*24
We get D = 78, so 2 more days
We get D = 78, so 2 more days
Most Upvoted Answer
A contractor employed 60 men to do a piece of work in 76 days. After 5...
Answer –b) 2 days Explanation : Total work = 60*50 + 70*24 Now days = D D*60 = 60*50 + 70*24
We get D = 78, so 2 more days
We get D = 78, so 2 more days
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A contractor employed 60 men to do a piece of work in 76 days. After 5...
Given information:
- Number of men initially employed: 60
- Number of days initially allocated for the work: 76
- Additional men employed after 50 days: 10
- Time taken to finish the work after employing additional men: 74 days
To solve this problem, we can use the concept of man-days. A man-day refers to the amount of work done by one person in one day.
Step 1: Calculate the total man-days required to complete the work before employing additional men.
- Total man-days = Number of men * Number of days
- Total man-days = 60 * 76 = 4560
Step 2: Calculate the total man-days available after 50 days.
- Total man-days available after 50 days = Number of men * Number of days
- Total man-days available after 50 days = 60 * 50 = 3000
Step 3: Calculate the additional man-days contributed by the 10 new workers.
- Additional man-days contributed by 10 new workers = Number of men * Number of days
- Additional man-days contributed by 10 new workers = 10 * 24 (since they worked for 24 days) = 240
Step 4: Calculate the remaining man-days required to complete the work after 50 days.
- Remaining man-days required = Total man-days - Total man-days available after 50 days
- Remaining man-days required = 4560 - 3000 = 1560
Step 5: Calculate the man-days contributed by each worker per day.
- Man-days contributed by each worker per day = Remaining man-days required / Number of additional workers
- Man-days contributed by each worker per day = 1560 / 10 = 156
Step 6: Calculate the number of days required to finish the work with the additional men.
- Number of days required to finish the work with additional men = Remaining man-days required / (Number of men + Number of additional workers)
- Number of days required to finish the work with additional men = 1560 / (60 + 10) = 24
Step 7: Calculate the number of days the contractor would have been behind if he had not employed additional men.
- Difference in days = Number of days initially allocated - Number of days required with additional men
- Difference in days = 76 - 24 = 52
Therefore, if the contractor had not employed additional men, he would have been behind by 52 days. However, since he employed additional men, he finished the work 2 days earlier. Thus, the answer is option 'B', 2 days.
- Number of men initially employed: 60
- Number of days initially allocated for the work: 76
- Additional men employed after 50 days: 10
- Time taken to finish the work after employing additional men: 74 days
To solve this problem, we can use the concept of man-days. A man-day refers to the amount of work done by one person in one day.
Step 1: Calculate the total man-days required to complete the work before employing additional men.
- Total man-days = Number of men * Number of days
- Total man-days = 60 * 76 = 4560
Step 2: Calculate the total man-days available after 50 days.
- Total man-days available after 50 days = Number of men * Number of days
- Total man-days available after 50 days = 60 * 50 = 3000
Step 3: Calculate the additional man-days contributed by the 10 new workers.
- Additional man-days contributed by 10 new workers = Number of men * Number of days
- Additional man-days contributed by 10 new workers = 10 * 24 (since they worked for 24 days) = 240
Step 4: Calculate the remaining man-days required to complete the work after 50 days.
- Remaining man-days required = Total man-days - Total man-days available after 50 days
- Remaining man-days required = 4560 - 3000 = 1560
Step 5: Calculate the man-days contributed by each worker per day.
- Man-days contributed by each worker per day = Remaining man-days required / Number of additional workers
- Man-days contributed by each worker per day = 1560 / 10 = 156
Step 6: Calculate the number of days required to finish the work with the additional men.
- Number of days required to finish the work with additional men = Remaining man-days required / (Number of men + Number of additional workers)
- Number of days required to finish the work with additional men = 1560 / (60 + 10) = 24
Step 7: Calculate the number of days the contractor would have been behind if he had not employed additional men.
- Difference in days = Number of days initially allocated - Number of days required with additional men
- Difference in days = 76 - 24 = 52
Therefore, if the contractor had not employed additional men, he would have been behind by 52 days. However, since he employed additional men, he finished the work 2 days earlier. Thus, the answer is option 'B', 2 days.
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