A certain number of men can do a work in 60 days. If there were 8 men more it could be finished in 10 days less. How many men are there?

Options

A. 50
B. 40
C. 56
D. 58

Answer

To solve the problem step by step, we will follow these steps:

### Step 1: Define the Variables
Let the number of men be \( X \).

### Step 2: Set Up the Work Equation
According to the problem, \( X \) men can complete the work in 60 days. Therefore, the total work can be expressed as:
\[ \text{Total Work} = X \times 60 \]

### Step 3: Consider the New Scenario
If there are 8 more men, the new number of men becomes \( X + 8 \). The work can then be completed in 10 days less, which means it can be done in \( 60 - 10 = 50 \) days. Thus, the total work can also be expressed as:
\[ \text{Total Work} = (X + 8) \times 50 \]

### Step 4: Set the Two Expressions for Total Work Equal
Since both expressions represent the same total work, we can set them equal to each other:
\[ X \times 60 = (X + 8) \times 50 \]

### Step 5: Expand the Equation
Expanding the right side gives:
\[ 60X = 50X + 400 \]

### Step 6: Solve for \( X \)
Now, we will isolate \( X \):
\[ 60X - 50X = 400 \]
\[ 10X = 400 \]
\[ X = 40 \]

### Step 7: Conclusion
Therefore, the number of men is \( 40 \).