If 78 men can do a work in 140 days, in how many days will 42 men do the same work ?

Answer

To solve the problem, we need to understand the relationship between the number of men and the number of days required to complete the work. Since more men can complete the work in fewer days, we have an inverse variation situation.

### Step-by-Step Solution:

1. **Identify the given values**:
- Number of men (M1) = 78
- Number of days (D1) = 140
- Number of men (M2) = 42
- Number of days (D2) = x (unknown)

2. **Set up the relationship**:
Since the number of men and the number of days are inversely proportional, we can write the equation:
\[ M1 \times D1 = M2 \times D2 \]
Substituting the known values into the equation:
\[ 78 \times 140 = 42 \times x \]

3. **Calculate the product of the known values**:
First, calculate \(78 \times 140\):
\[ 78 \times 140 = 10920 \]
So, we have:
\[ 10920 = 42 \times x \]

4. **Solve for x**:
To find x, divide both sides of the equation by 42:
\[ x = \frac{10920}{42} \]

5. **Perform the division**:
Now, calculate \( \frac{10920}{42} \):
\[ x = 260 \]

6. **Conclusion**:
Therefore, 42 men will take 260 days to complete the same work.

### Final Answer:
42 men will do the same work in **260 days**.

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