Five persons paint a house in 3 days when they work 8 hours everyday. Then if one person works 4 hours everyday, how much time (day) will he take to complete the same work?

Question

Accepted Answer

To determine how much time one person will take to complete the same work when working 4 hours a day, we need to analyze the given scenario and calculate accordingly.

### Explanation:

1. **Initial Scenario:**
   - Five persons paint a house in 3 days, working 8 hours each day.
   - Total work done by five persons = 5 persons × 3 days × 8 hours/day = 120 person-hours.

2. **Work Done by One Person:**
   - Since the total work is 120 person-hours, the work done by one person would be the same amount of work, i.e., 120 person-hours.

3. **New Scenario:**
   - One person works 4 hours each day.
   - We need to find out how many days it will take for this one person to complete 120 person-hours of work.

4. **Calculation:**
   - If one person works 4 hours a day, the number of days required to complete 120 person-hours of work is calculated as follows:
   $$
   \text{Number of days} = \frac{\text{Total work (person-hours)}}{\text{Work per day (person-hours)}} = \frac{120}{4} = 30 \text{ days}
   $$

### Justification for Option 1:

- **Option 1 (30 days):** This is the correct answer because, as calculated, one person working 4 hours a day will indeed take 30 days to complete the work of 120 person-hours.

### Explanation for Incorrect Options:

- **Option 2 ($\frac{15}{2}$ days):** This option suggests that the work would be completed in 7.5 days, which is incorrect because it underestimates the time required for one person working only 4 hours a day to complete 120 person-hours of work.

- **Option 3 ($\frac{6}{5}$ days):** This option suggests that the work would be completed in 1.2 days, which is not feasible given the work requirement and the reduced daily working hours.

- **Option 4 ($\frac{3}{10}$ days):** This option suggests that the work would be completed in 0.3 days, which is clearly incorrect as it grossly underestimates the time needed for the task.

In conclusion, Option 1 is the correct answer because it accurately reflects the time required for one person working 4 hours a day to complete the work, based on the calculations provided.