A certain number of men complete a work in 45 days. If there were 5 men more, the work could be fin- ished in 9 days less How many men were originally there?

Options

A. 30
B. 15
C. 25
D. 20

Answer

To solve the problem step by step, we will let the original number of men be \( x \).

**Step 1: Define the work done.**
- The original number of men \( x \) can complete the work in 45 days.

**Step 2: Calculate the total work in terms of men and days.**
- The total work can be expressed as:
\[ \text{Total Work} = \text{Number of Men} \times \text{Days} = x \times 45 \]

**Step 3: Set up the equation for the scenario with more men.**
- If there are 5 more men, the number of men becomes \( x + 5 \), and the work can be finished in 9 days less, which is \( 45 - 9 = 36 \) days.
- The total work in this scenario can be expressed as:
\[ \text{Total Work} = (x + 5) \times 36 \]

**Step 4: Equate the two expressions for total work.**
- Since both expressions represent the same total work, we can set them equal to each other:
\[ x \times 45 = (x + 5) \times 36 \]

**Step 5: Expand and simplify the equation.**
- Expanding the right side gives:
\[ 45x = 36x + 180 \]
- Now, subtract \( 36x \) from both sides:
\[ 45x - 36x = 180 \]
\[ 9x = 180 \]

**Step 6: Solve for \( x \).**
- Divide both sides by 9:
\[ x = \frac{180}{9} = 20 \]

**Conclusion:**
- The original number of men was \( 20 \).