In order to complete a work in 28 days, 60 men are required. How Mny men will be required if the same work is to be completed in 40 days ?

Answer

To solve the problem step by step, we can use the concept of direct variation. The number of men required to complete a work is inversely proportional to the number of days taken to complete it.

### Step 1: Understand the relationship
We know that if more days are taken to complete the same work, fewer men will be required. This is an inverse variation.

### Step 2: Calculate the total work in man-days
To find out how many men are needed for different durations, we first calculate the total work in man-days required to complete the task in 28 days with 60 men.

\[ \text{Total work} = \text{Number of men} \times \text{Number of days} = 60 \text{ men} \times 28 \text{ days} = 1680 \text{ man-days} \]

### Step 3: Calculate the number of men needed for 40 days
Now, we need to find out how many men are required to complete the same amount of work (1680 man-days) in 40 days.

Let \( x \) be the number of men required.

Using the formula for total work:

\[ \text{Total work} = \text{Number of men} \times \text{Number of days} \]

We can set up the equation:

\[ 1680 \text{ man-days} = x \text{ men} \times 40 \text{ days} \]

### Step 4: Solve for \( x \)
Now, we can solve for \( x \):

\[ x = \frac{1680 \text{ man-days}}{40 \text{ days}} = 42 \text{ men} \]

### Final Answer
Therefore, 42 men will be required to complete the work in 40 days.

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