36 men can build a wall 140 m long in 21 days , in how many days would 15 men be able to construct a similar wall 50 m long ?

Options

A. 20 days
B. 22 days
C. 22. 5 days
D. 18 days

Answer

To solve the problem, we will use the formula that relates the number of men (M), the number of days (D), and the amount of work done (W). The formula is:

\[ \frac{M_1 \times D_1}{W_1} = \frac{M_2 \times D_2}{W_2} \]

Where:
- \( M_1 \) = number of men in the first scenario
- \( D_1 \) = number of days in the first scenario
- \( W_1 \) = amount of work in the first scenario
- \( M_2 \) = number of men in the second scenario
- \( D_2 \) = number of days in the second scenario (which we need to find)
- \( W_2 \) = amount of work in the second scenario

### Step 1: Identify the values from the question
From the question:
- \( M_1 = 36 \) men
- \( D_1 = 21 \) days
- \( W_1 = 140 \) meters (length of the wall)
- \( M_2 = 15 \) men
- \( W_2 = 50 \) meters (length of the wall we want to build)

### Step 2: Substitute the values into the formula
Substituting the known values into the formula gives:

\[ \frac{36 \times 21}{140} = \frac{15 \times D_2}{50} \]

### Step 3: Simplify the left side
Calculating the left side:

\[ 36 \times 21 = 756 \]
So,

\[ \frac{756}{140} = \frac{15 \times D_2}{50} \]

### Step 4: Simplify \(\frac{756}{140}\)
Now we simplify \(\frac{756}{140}\):

\[ \frac{756 \div 28}{140 \div 28} = \frac{27}{5} \]

So we have:

\[ \frac{27}{5} = \frac{15 \times D_2}{50} \]

### Step 5: Cross-multiply to solve for \(D_2\)
Cross-multiplying gives:

\[ 27 \times 50 = 15 \times D_2 \times 5 \]

Calculating \(27 \times 50\):

\[ 1350 = 75 \times D_2 \]

### Step 6: Solve for \(D_2\)
Now, divide both sides by 75 to find \(D_2\):

\[ D_2 = \frac{1350}{75} = 18 \]

### Conclusion
Thus, 15 men would be able to construct a similar wall of 50 meters long in **18 days**.

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