If 27 men take 15 days to mow 225 hectares of grass, how long will 33 men take to mow 165 hectare ?
A)9 days
B)18 days
C)6 days
D)12 days

Options

A. 9 days
B. 18 days
C. 6 days
D. 12 days

Answer

To solve the problem, we can use the concept of work done, which can be expressed using the formula:

\[ \text{Work} = \text{Men} \times \text{Days} \times \text{Time} \]

Given:
- 27 men take 15 days to mow 225 hectares of grass.

We need to find out how long it will take for 33 men to mow 165 hectares.

### Step 1: Calculate the total work done in man-days for the first scenario.

The total work done (in man-days) can be calculated as follows:

\[ \text{Total Work} = \text{Men} \times \text{Days} = 27 \text{ men} \times 15 \text{ days} = 405 \text{ man-days} \]

### Step 2: Calculate the work done per hectare.

Now, we can find out how much work is done per hectare:

\[ \text{Work per hectare} = \frac{\text{Total Work}}{\text{Total hectares}} = \frac{405 \text{ man-days}}{225 \text{ hectares}} = 1.8 \text{ man-days per hectare} \]

### Step 3: Calculate the total work needed for 165 hectares.

Now, we need to find out how much work is required to mow 165 hectares:

\[ \text{Work for 165 hectares} = 165 \text{ hectares} \times 1.8 \text{ man-days per hectare} = 297 \text{ man-days} \]

### Step 4: Calculate the number of days required for 33 men to complete the work.

Now we can find out how many days it will take for 33 men to do 297 man-days of work:

\[ \text{Days} = \frac{\text{Total Work}}{\text{Men}} = \frac{297 \text{ man-days}}{33 \text{ men}} = 9 \text{ days} \]

### Conclusion

Thus, it will take 33 men 9 days to mow 165 hectares of grass.

**Final Answer: A) 9 days**

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