If 4 men can reap a field in 5 days working 9 hours a day. in how many days can 10 men reap the same field working 6 hours a day?

Options

A. 5
B. 4
C. 3
D. 2

Answer

To solve the problem, we can follow these steps:

### Step 1: Calculate the total man-hours required to reap the field.
Given that 4 men can reap the field in 5 days working 9 hours a day, we can calculate the total man-hours as follows:

\[ \text{Total man-hours} = \text{Number of men} \times \text{Number of days} \times \text{Hours per day} \]
\[ \text{Total man-hours} = 4 \text{ men} \times 5 \text{ days} \times 9 \text{ hours/day} = 180 \text{ man-hours} \]

### Step 2: Determine the daily work capacity of 10 men working 6 hours a day.
Next, we need to find out how many man-hours 10 men can work in one day:

\[ \text{Daily work capacity} = \text{Number of men} \times \text{Hours per day} \]
\[ \text{Daily work capacity} = 10 \text{ men} \times 6 \text{ hours/day} = 60 \text{ man-hours/day} \]

### Step 3: Calculate the number of days required for 10 men to reap the field.
Now, we can find out how many days it will take for 10 men to complete the same amount of work (180 man-hours) at their daily work capacity:

\[ \text{Number of days} = \frac{\text{Total man-hours}}{\text{Daily work capacity}} \]
\[ \text{Number of days} = \frac{180 \text{ man-hours}}{60 \text{ man-hours/day}} = 3 \text{ days} \]

### Final Answer:
Thus, 10 men can reap the same field in **3 days** working 6 hours a day.

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