40 men can build a wall 20 m high in 15 days. The number of men required to build a similar wall 25 m high in 6 days will be:

Options

A. 100
B. 125
C. 150
D. 200

Answer

To solve the problem, we need to determine the number of men required to build a wall that is 25 meters high in 6 days, given that 40 men can build a wall that is 20 meters high in 15 days. We will use the concept of work done, which is proportional to the number of men, the number of days, and the height of the wall.

### Step-by-Step Solution:

1. **Identify the given values**:
- Let \( M_1 = 40 \) (number of men)
- Let \( D_1 = 15 \) (number of days)
- Let \( W_1 = 20 \) (height of the wall in meters)

2. **Determine the work done by the first group**:
- The work done can be represented as \( \text{Work} = \text{Men} \times \text{Days} \times \text{Height} \).
- Therefore, for the first scenario, the work done is:
\[ \text{Work}_1 = M_1 \times D_1 \times W_1 = 40 \times 15 \times 20 \]

3. **Calculate the total work done**:
- Calculate \( 40 \times 15 = 600 \).
- Then, \( 600 \times 20 = 12000 \).
- Thus, \( \text{Work}_1 = 12000 \) (in terms of man-days per meter).

4. **Identify the new scenario**:
- Let \( M_2 \) be the number of men required.
- Let \( D_2 = 6 \) (number of days for the new wall).
- Let \( W_2 = 25 \) (height of the new wall).

5. **Set up the equation for the new scenario**:
- The work done in the new scenario can be represented as:
\[ \text{Work}_2 = M_2 \times D_2 \times W_2 \]
- We know that \( \text{Work}_1 = \text{Work}_2 \), so:
\[ 12000 = M_2 \times 6 \times 25 \]

6. **Calculate \( M_2 \)**:
- First, calculate \( 6 \times 25 = 150 \).
- Now, substitute this into the equation:
\[ 12000 = M_2 \times 150 \]
- To find \( M_2 \), divide both sides by 150:
\[ M_2 = \frac{12000}{150} \]

7. **Perform the division**:
- Calculate \( \frac{12000}{150} = 80 \).
- Thus, \( M_2 = 80 \).

### Conclusion:
The number of men required to build a wall that is 25 meters high in 6 days is **80 men**.