21 men can complete a piece of work in `42/7` days. In how many days can 18 men complete the same piece of work?

Options

A. 6days
B. 5days
C. 4days
D. 7days

Answer

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

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

Where:
- \( M_1 \) = number of men working initially (21 men)
- \( D_1 \) = number of days taken by \( M_1 \) (42/7 days)
- \( M_2 \) = number of men working later (18 men)
- \( D_2 \) = number of days taken by \( M_2 \) (unknown)

### Step 1: Calculate \( D_1 \)

First, we need to calculate \( D_1 \):

\[ D_1 = \frac{42}{7} = 6 \text{ days} \]

### Step 2: Set up the equation

Now we can set up our equation using the values we have:

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

Substituting the known values:

\[ 21 \times 6 = 18 \times D_2 \]

### Step 3: Calculate the left side

Now, calculate the left side of the equation:

\[ 21 \times 6 = 126 \]

So, we have:

\[ 126 = 18 \times D_2 \]

### Step 4: Solve for \( D_2 \)

Now, we can solve for \( D_2 \):

\[ D_2 = \frac{126}{18} \]

Calculating \( D_2 \):

\[ D_2 = 7 \]

### Conclusion

Therefore, 18 men can complete the same piece of work in **7 days**.

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