If 10 men can complete a work in 12 days . In how many days can 18 men complete the same work ?

Answer

To solve the problem step by step, we can use the concept of work done, which relates the number of men, the number of days, and the total work.

### Step-by-Step Solution:

1. **Identify the given values**:
- Number of men (M1) = 10
- Number of days (D1) = 12
- Number of men in the second scenario (M2) = 18
- We need to find the number of days (D2) for 18 men to complete the same work.

2. **Use the work formula**:
The relationship between men, days, and work can be expressed as:
\[ M1 \times D1 = M2 \times D2 \]

3. **Substitute the known values into the equation**:
\[ 10 \times 12 = 18 \times D2 \]

4. **Calculate the left side**:
\[ 120 = 18 \times D2 \]

5. **Solve for D2**:
To find D2, divide both sides by 18:
\[ D2 = \frac{120}{18} \]

6. **Simplify the fraction**:
\[ D2 = \frac{120 \div 6}{18 \div 6} = \frac{20}{3} \]

7. **Convert to a mixed number**:
\[ D2 = 6 \frac{2}{3} \text{ days} \]

### Final Answer:
18 men can complete the work in \( 6 \frac{2}{3} \) days or approximately 6.67 days.