A certain number of men can complete a job in 30 days. If there were 5 men more, it could be completed in 10 days less. How many men were in the beginning?

Options

A. 10
B. 15
C. 20
D. 25

Answer

To solve the problem step by step, we will denote the number of men initially as \( x \).

### Step 1: Define the total work
The total work can be calculated based on the number of men and the number of days they take to complete the job. If \( x \) men can complete the job in 30 days, the total work \( W \) can be expressed as:
\[ W = x \times 30 \]

### Step 2: Define the scenario with more men
If there are 5 more men, the number of men becomes \( x + 5 \). According to the problem, with these additional men, the job can be completed in 10 days less, which means it will take 20 days (30 - 10 = 20 days). The total work can also be expressed as:
\[ W = (x + 5) \times 20 \]

### Step 3: Set up the equation
Since both expressions represent the same total work \( W \), we can set them equal to each other:
\[ x \times 30 = (x + 5) \times 20 \]

### Step 4: Expand and simplify the equation
Expanding the right side of the equation gives:
\[ 30x = 20x + 100 \]

### Step 5: Solve for \( x \)
Now, we will isolate \( x \):
\[ 30x - 20x = 100 \]
\[ 10x = 100 \]
\[ x = 10 \]

### Conclusion
Thus, the number of men in the beginning is \( \boxed{10} \).

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