72 men do a piece of work in 25 days. In how many days will 30 men do the same work ?

Answer

To solve the problem step by step, we will use the concept of inverse variation.

### Step 1: Understand the relationship
We know that the amount of work done is constant. Therefore, if the number of men increases, the number of days required to complete the work decreases, and vice versa. This is an example of inverse variation.

### Step 2: Set up the equation
Let the number of days required by 30 men to complete the work be \( x \). We can set up the relationship as follows:
\[ \text{(Number of men)} \times \text{(Number of days)} = \text{constant} \]
From the problem, we know:
\[ 72 \text{ men} \times 25 \text{ days} = 30 \text{ men} \times x \text{ days} \]

### Step 3: Substitute the known values
Substituting the known values into the equation gives us:
\[ 72 \times 25 = 30 \times x \]

### Step 4: Calculate the left side
Now calculate \( 72 \times 25 \):
\[ 72 \times 25 = 1800 \]
So, we have:
\[ 1800 = 30 \times x \]

### Step 5: Solve for \( x \)
To find \( x \), divide both sides of the equation by 30:
\[ x = \frac{1800}{30} \]

### Step 6: Perform the division
Now, perform the division:
\[ x = 60 \]

### Conclusion
Thus, the number of days required by 30 men to complete the same work is **60 days**.

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