40 men build a well 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 will use the concept of direct variation, which can be represented in the form of a chain rule. The relationship between the number of men (m), the number of days (d), and the height of the wall (w) can be expressed as follows:

Given:
- \( m_1 = 40 \) men
- \( d_1 = 15 \) days
- \( w_1 = 20 \) m (height of the well)

We need to find the number of men (\( m_2 \)) required to build a wall of:
- \( d_2 = 6 \) days
- \( w_2 = 25 \) m (height of the wall)

Using the formula:
\[ \frac{m_1 \cdot d_1}{w_1} = \frac{m_2 \cdot d_2}{w_2} \]

Substituting the known values into the equation:
\[ \frac{40 \cdot 15}{20} = \frac{m_2 \cdot 6}{25} \]

Now, we can simplify the left side:
\[ \frac{40 \cdot 15}{20} = \frac{600}{20} = 30 \]

So, we have:
\[ 30 = \frac{m_2 \cdot 6}{25} \]

Next, we will cross-multiply to solve for \( m_2 \):
\[ 30 \cdot 25 = m_2 \cdot 6 \]
\[ 750 = m_2 \cdot 6 \]

Now, divide both sides by 6 to find \( m_2 \):
\[ m_2 = \frac{750}{6} = 125 \]

Thus, the number of men required to build a similar wall 25 m high in 6 days is **125 men**.