A certain number of men take 45 days to complete a work. If there are 10 men less then they will take 60 days to complete the work. Find the original number of men.a)30b)40c)50d)60e)None of theseCorrect answer is option 'B'. Can you explain this answer?

Question

Answer

Given:
Let the original number of men be x.
They take 45 days to complete the work.
If there are 10 men less, then they will take 60 days to complete the work.

Approach:
We can solve this problem using the concept of work done. The total work done is the same in both cases, so we can equate the work done by the two groups of men.

Solution:

Step 1: Determine the work done by the group of men who take 45 days to complete the work.
Let the work done be W.
We know that work done is equal to the product of the number of men, the number of days, and the efficiency of each man.
Efficiency is the reciprocal of the time taken by one man to complete the work.
So, the efficiency of each man is 1/45.

Therefore, the work done by the group of men who take 45 days to complete the work is:
W = x * 45 * (1/45) = x

Step 2: Determine the work done by the group of men who take 60 days to complete the work.
If there are 10 men less, the new number of men will be (x - 10).
The efficiency of each man in this case is 1/60.

Therefore, the work done by the group of men who take 60 days to complete the work is:
W = (x - 10) * 60 * (1/60) = (x - 10)

Step 3: Equate the work done by the two groups of men.
Since the total work done is the same, we have:
x = (x - 10)

Step 4: Solve the equation to find the value of x.
x - x + 10 = 0
10 = 0

Therefore, the original number of men is 10.

Step 5: Check the options.
None of the given options match the solution obtained above.

Conclusion:
The given options do not match the solution obtained. Therefore, the original number of men cannot be determined from the given information.

Answer

Let initially there are X men. Then x*45 = (x-10)*60. So we get x = 40

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