A farmer can plough a field working 6 hours per day in 18 days. The worker has to work how many hours per day to finish the same work in 12 days ?

Options

A. 7 hrs
B. 9 hrs
C. 11 hrs
D. 13 hrs

Answer

To solve the problem step by step, we need to determine how many hours the farmer must work each day to complete the same amount of work in 12 days instead of 18 days.

### Step 1: Calculate the total amount of work done in hours
The farmer works for 6 hours each day for 18 days. Thus, the total work done can be calculated as:
\[ \text{Total Work} = \text{Days} \times \text{Hours per Day} = 18 \, \text{days} \times 6 \, \text{hours/day} = 108 \, \text{hours} \]

### Step 2: Set up the equation for the new scenario
Now, we want to find out how many hours per day (let's call this \( x \)) the farmer needs to work to complete the same amount of work (108 hours) in 12 days. The equation will be:
\[ \text{Total Work} = \text{New Days} \times \text{New Hours per Day} \]
Substituting the values we have:
\[ 108 \, \text{hours} = 12 \, \text{days} \times x \, \text{hours/day} \]

### Step 3: Solve for \( x \)
To find \( x \), we can rearrange the equation:
\[ x = \frac{108 \, \text{hours}}{12 \, \text{days}} = 9 \, \text{hours/day} \]

### Conclusion
Thus, the farmer needs to work **9 hours per day** to finish the work in 12 days.

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