24 men can complete a job in 20 days. The number of men required to complete the job in 16 days is :

Options

A. 30
B. 40
C. 25
D. 50

Answer

To solve the problem step by step, we will use the relationship between the number of men (M), the number of days (D), and the amount of work (W). The formula we will use is:

\[ M_1 \times D_1 = M_2 \times D_2 \]

Where:
- \(M_1\) = initial number of men
- \(D_1\) = initial number of days
- \(M_2\) = required number of men
- \(D_2\) = required number of days

### Step 1: Identify the given values
From the problem, we have:
- \(M_1 = 24\) (the number of men)
- \(D_1 = 20\) (the number of days)
- \(D_2 = 16\) (the new number of days)

### Step 2: Set up the equation
We want to find \(M_2\). According to the formula:
\[ M_1 \times D_1 = M_2 \times D_2 \]
Substituting the known values into the equation gives us:
\[ 24 \times 20 = M_2 \times 16 \]

### Step 3: Calculate the left side of the equation
Calculating \(24 \times 20\):
\[ 24 \times 20 = 480 \]
So, we have:
\[ 480 = M_2 \times 16 \]

### Step 4: Solve for \(M_2\)
To find \(M_2\), we can rearrange the equation:
\[ M_2 = \frac{480}{16} \]

### Step 5: Perform the division
Calculating \(480 \div 16\):
\[ M_2 = 30 \]

### Conclusion
The number of men required to complete the job in 16 days is \(30\).