A certain number of men can complete a book in 10 days. If there were three more men, then book could be completed in 2 days less. How many men were there in the beginning?

Options

A. a. 8
B. b. 15
C. c. 12
D. d. 10

Answer

To solve the problem step by step, let's denote the number of men initially as \( x \).

### Step 1: Understand the total work done
The total work can be calculated as:
\[ \text{Total Work} = \text{Number of Men} \times \text{Number of Days} \]
In the first scenario, \( x \) men complete the book in 10 days. Therefore, the total work done can be expressed as:
\[ \text{Total Work} = x \times 10 \]

### Step 2: Set up the equation for the second scenario
In the second scenario, if there are 3 more men, the total number of men becomes \( x + 3 \), and they can complete the book in 8 days (since it is 2 days less than 10 days). Thus, the total work in this case can be expressed as:
\[ \text{Total Work} = (x + 3) \times 8 \]

### Step 3: Equate the total work from both scenarios
Since the total work remains the same in both scenarios, we can set the two expressions equal to each other:
\[ x \times 10 = (x + 3) \times 8 \]

### Step 4: Expand and simplify the equation
Expanding the right side of the equation:
\[ 10x = 8x + 24 \]

### Step 5: Rearrange the equation
Now, we can rearrange the equation to isolate \( x \):
\[ 10x - 8x = 24 \]
\[ 2x = 24 \]

### Step 6: Solve for \( x \)
Now, divide both sides by 2 to find \( x \):
\[ x = \frac{24}{2} = 12 \]

### Conclusion
Thus, the number of men in the beginning was \( 12 \).