30 men can finish a piece of work in 28 days. How many days will be taken by 21 men to finish it?

Answer

To solve the problem step by step, we can use the concept of direct proportion. Here’s how we can approach it:

### Step 1: Calculate the Total Work
First, we need to determine the total amount of work done by 30 men in 28 days. The total work can be calculated using the formula:

\[ \text{Total Work} = \text{Number of Men} \times \text{Number of Days} \]

So, for 30 men working for 28 days, the total work is:

\[ \text{Total Work} = 30 \times 28 = 840 \text{ man-days} \]

### Step 2: Set Up the Equation for 21 Men
Next, we need to find out how many days (let's call it \( x \)) it will take for 21 men to complete the same amount of work (840 man-days). We can set up the equation as follows:

\[ \text{Total Work} = \text{Number of Men} \times \text{Number of Days} \]

For 21 men, the equation becomes:

\[ 840 = 21 \times x \]

### Step 3: Solve for \( x \)
Now, we can solve for \( x \):

\[ x = \frac{840}{21} \]

Calculating this gives:

\[ x = 40 \]

### Conclusion
Thus, it will take 21 men a total of 40 days to finish the work.