Certain number of men can complete a job in 30 days. If there were 5 more men, it could be completed in 10 days less. How many men were there in the beginning?a)10b)15c)25d)20e)None of theseCorrect answer is option 'A'. Can you explain this answer?

Question

Answer

Answer

Given:

- Number of men required to complete the job in 30 days = x
- Number of men required to complete the job in 20 days = x+5

To find: Number of men in the beginning

Solution:

Let the total work be 1 unit.

- Number of men required to complete the job in 30 days = x
- Work done by x men in 1 day = 1/(30x)
- Number of men required to complete the job in 20 days = x+5
- Work done by x+5 men in 1 day = 1/(20(x+5))

Equating the work done:

(1/(30x)) = (1/(20(x+5)))

Solving the above equation, we get:

x = 10

Therefore, the number of men in the beginning = x = 10

Hence, option A is the correct answer.

Answer

To solve this problem, we can use the concept of work and time. Let's assume that the number of men required to complete the job in 30 days is 'x'.

Let's break down the problem into two scenarios:

Scenario 1:
- Number of men = x
- Time taken = 30 days

Scenario 2:
- Number of men = x + 5 (5 more men)
- Time taken = 30 - 10 = 20 days (10 days less)

We can use the formula: Work = Number of Men x Time

In both scenarios, the work done is the same. Therefore, we can equate the two scenarios:

Number of Men (Scenario 1) x Time (Scenario 1) = Number of Men (Scenario 2) x Time (Scenario 2)

x * 30 = (x + 5) * 20

Now, let's solve this equation to find the value of 'x'.

30x = 20x + 100

30x - 20x = 100

10x = 100

x = 100 / 10

x = 10

Therefore, the initial number of men required to complete the job in 30 days is 10.

Hence, the correct answer is option A) 10 men.

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