22 men can dig a 27 m long trench in one day. How many men should be employed for digging 135 m long trench of the same type in one day ?

Answer

To solve the problem of how many men are required to dig a 135 m long trench in one day, we can use the concept of direct variation. Here’s a step-by-step solution:

### Step 1: Understand the relationship
We know that 22 men can dig a 27 m trench in one day. This means that the number of men required is directly proportional to the length of the trench.

### Step 2: Set up the proportion
Let \( M \) be the number of men required to dig a 135 m trench in one day. We can set up the proportion based on the information given:
\[ \frac{22 \text{ men}}{27 \text{ m}} = \frac{M \text{ men}}{135 \text{ m}} \]

### Step 3: Cross-multiply to solve for \( M \)
Cross-multiplying gives us:
\[ 22 \times 135 = 27 \times M \]
Now, calculate \( 22 \times 135 \):
\[ 22 \times 135 = 2970 \]
So, we have:
\[ 2970 = 27 \times M \]

### Step 4: Solve for \( M \)
Now, divide both sides by 27 to find \( M \):
\[ M = \frac{2970}{27} \]
Calculating this gives:
\[ M = 110 \]

### Conclusion
Therefore, the number of men required to dig a 135 m long trench in one day is **110 men**.

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