If 70 men dig 15,00 sq. m of a field in 5 days. Find how many men will dig 22,500 sq. m field in 25 days ?

Answer

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

### Step 1: Understand the given information
We know that:
- 70 men can dig 15,000 sq. m in 5 days.

### Step 2: Set up the relationship
We can express the work done in terms of men, days, and work:
\[ \text{Men} \times \text{Days} = \text{Work} \]
From the first condition:
\[ 70 \text{ men} \times 5 \text{ days} = 15,000 \text{ sq. m} \]

### Step 3: Set up the equation for the second condition
We need to find out how many men (let's call it \( x \)) are required to dig 22,500 sq. m in 25 days:
\[ x \text{ men} \times 25 \text{ days} = 22,500 \text{ sq. m} \]

### Step 4: Write the equation using the relationship
From the first and second conditions, we can set up the equation:
\[ 70 \text{ men} \times 5 \text{ days} = 15,000 \text{ sq. m} \]
\[ x \text{ men} \times 25 \text{ days} = 22,500 \text{ sq. m} \]

Using the relationship:
\[ 70 \times 5 = x \times 25 \]

### Step 5: Substitute the values into the equation
Substituting the values we have:
\[ 70 \times 5 = x \times 25 \]
\[ 350 = x \times 25 \]

### Step 6: Solve for \( x \)
Now, we can solve for \( x \):
\[ x = \frac{350}{25} \]
\[ x = 14 \]

### Step 7: Calculate the number of men needed
To find the number of men needed to dig 22,500 sq. m in 25 days, we need to adjust the equation:
Since we are looking for the number of men to dig 22,500 sq. m:
\[ 70 \times 5 \div 15,000 = x \times 25 \div 22,500 \]

### Step 8: Final calculation
Using the ratio:
\[ \frac{70 \times 5}{15,000} = \frac{x \times 25}{22,500} \]
Cross-multiplying gives:
\[ 70 \times 5 \times 22,500 = x \times 25 \times 15,000 \]

Now simplifying:
\[ 350 \times 22.5 = x \times 375 \]
\[ 7875 = x \times 375 \]
\[ x = \frac{7875}{375} \]
\[ x = 21 \]

### Conclusion
Thus, the number of men required to dig 22,500 sq. m in 25 days is **21 men**.