If 40 men can finish a piece of work in 26 days, how many men will be required to finish it in 20 days?

Options

A. 52
B. 31
C. 13
D. 65

Answer

To solve the problem step by step, we can use the concept of inverse proportionality between the number of men and the number of days required to complete the work.

### Step 1: Understand the relationship between men and days
We know that if more men are working, the number of days required to complete the work will decrease. Conversely, if fewer men are working, the number of days required will increase. This means that the number of men and the number of days are inversely proportional.

### Step 2: Calculate the total work in man-days
First, we need to calculate the total amount of work in terms of man-days. If 40 men can finish the work in 26 days, we can calculate the total work as follows:
\[ \text{Total Work} = \text{Number of Men} \times \text{Number of Days} = 40 \text{ men} \times 26 \text{ days} = 1040 \text{ man-days} \]

### Step 3: Determine the number of men required for 20 days
Now, we want to find out how many men are needed to complete the same amount of work (1040 man-days) in 20 days. Let \( x \) be the number of men required. We can set up the equation:
\[ x \text{ men} \times 20 \text{ days} = 1040 \text{ man-days} \]

### Step 4: Solve for \( x \)
To find \( x \), we rearrange the equation:
\[ x = \frac{1040 \text{ man-days}}{20 \text{ days}} = 52 \text{ men} \]

### Conclusion
Therefore, the number of men required to finish the work in 20 days is **52 men**.

---