A certain number of men can do a piece of work in 80 days. If there were 10 men less, It could be finished in 20 days more. How many men are there in the starting?

Options

A. 45
B. 50
C. 40
D. 40

Answer

To solve the problem, we will follow these steps:

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

### Step 2: Calculate the Total Work
The total work done by \( x \) men in 80 days can be expressed as:
\[ \text{Total Work} = x \times 80 \]

### Step 3: Set Up the New Scenario
If there are 10 men less, the number of men becomes \( x - 10 \). According to the problem, with these men, the work will take 20 days more, which means it will take 100 days to complete the work.

### Step 4: Calculate Work with Fewer Men
The total work done by \( x - 10 \) men in 100 days can be expressed as:
\[ \text{Total Work} = (x - 10) \times 100 \]

### Step 5: Set Up the Equation
Since the total work remains the same in both scenarios, we can equate the two expressions for total work:
\[ x \times 80 = (x - 10) \times 100 \]

### Step 6: Expand and Rearrange the Equation
Expanding the right side:
\[ 80x = 100x - 1000 \]
Now, rearranging the equation to isolate \( x \):
\[ 80x - 100x = -1000 \]
\[ -20x = -1000 \]
Dividing both sides by -20:
\[ x = \frac{1000}{20} \]
\[ x = 50 \]

### Step 7: Conclusion
The initial number of men is \( 50 \).