If 45 men can do a piece of work in 49 days, in how many days will 35 men do it?

Options

A. `63`
B. `53`
C. `43`
D. `33`

Answer

To solve the problem, we will use the concept of inverse proportions. The amount of work done is constant, so if the number of men decreases, the number of days required to complete the work will increase.

### Step-by-Step Solution:

1. **Identify the given information**:
- Number of men (M1) = 45
- Number of days (D1) = 49
- Number of men (M2) = 35
- Number of days (D2) = ? (This is what we need to find)

2. **Understand the relationship**:
The relationship between the number of men and the number of days is inversely proportional. This means:
\[ M1 \times D1 = M2 \times D2 \]

3. **Substitute the known values into the equation**:
\[ 45 \times 49 = 35 \times D2 \]

4. **Calculate the left side of the equation**:
\[ 45 \times 49 = 2205 \]
So, we have:
\[ 2205 = 35 \times D2 \]

5. **Solve for D2**:
To find D2, divide both sides of the equation by 35:
\[ D2 = \frac{2205}{35} \]

6. **Calculate D2**:
\[ D2 = 63 \]

7. **Conclusion**:
Therefore, 35 men will take **63 days** to complete the work.

### Final Answer:
35 men will do the work in **63 days**.

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