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A certain number of men can finish a piece of work in 100 days. However, if there were 10 men less, then it would take 10 days more for the work to be finished How many men were there originally?
- a)110
- b)75
- c)50
- d)100
Correct answer is option 'A'. Can you explain this answer?
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Most Upvoted Answer
A certain number of men can finish a piece of work in 100 days. Howeve...
Given:
- Number of men required to finish the work in 100 days = x
- If there were 10 men less, then it would take 10 days more to finish the work
To Find:
- Number of men originally
Assumption:
- The amount of work is the same throughout the process
Explanation:
Let's assume that the total work is represented by W.
1. Work completed per day by x men = W/100
2. Work completed per day by (x-10) men = W/(100+10) = W/110
Since the amount of work is the same, we can equate these two expressions:
W/100 = W/110
Solving the equation:
Cross-multiplying the equation, we get:
110W = 100W
Simplifying the equation, we get:
10W = 0
Since the equation is not possible, it means that our assumption was wrong.
Conclusion:
We cannot determine the number of men originally based on the given information. The information provided is contradictory and does not lead to a valid solution.
Therefore, the correct answer is none of the given options.
- Number of men required to finish the work in 100 days = x
- If there were 10 men less, then it would take 10 days more to finish the work
To Find:
- Number of men originally
Assumption:
- The amount of work is the same throughout the process
Explanation:
Let's assume that the total work is represented by W.
1. Work completed per day by x men = W/100
2. Work completed per day by (x-10) men = W/(100+10) = W/110
Since the amount of work is the same, we can equate these two expressions:
W/100 = W/110
Solving the equation:
Cross-multiplying the equation, we get:
110W = 100W
Simplifying the equation, we get:
10W = 0
Since the equation is not possible, it means that our assumption was wrong.
Conclusion:
We cannot determine the number of men originally based on the given information. The information provided is contradictory and does not lead to a valid solution.
Therefore, the correct answer is none of the given options.
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