18 persons working 8 hours a day can complete 3 units of works in 10 days. How many persons are required to complete 5 units of that work in 16 days working 6 hours a day?

Options

A. 25
B. 15
C. 20
D. 9

Answer

To solve the problem step by step, we will first determine the total work done in terms of person-hours and then use that information to find out how many persons are required to complete the new task.

### Step 1: Calculate the total work done in person-hours for the first scenario.

Given:
- 18 persons
- 8 hours a day
- 10 days
- 3 units of work

Total work done in person-hours can be calculated as:
\[ \text{Total Work} = \text{Number of Persons} \times \text{Hours per Day} \times \text{Number of Days} \]
\[ \text{Total Work} = 18 \times 8 \times 10 = 1440 \text{ person-hours} \]

This means that 1440 person-hours are required to complete 3 units of work.

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

To find the work done per unit, we divide the total work by the number of units:
\[ \text{Work per Unit} = \frac{\text{Total Work}}{\text{Units of Work}} = \frac{1440}{3} = 480 \text{ person-hours per unit} \]

### Step 3: Calculate the total work required for the new scenario.

Now, we need to find out how much work is required to complete 5 units of work:
\[ \text{Total Work for 5 Units} = 5 \times 480 = 2400 \text{ person-hours} \]

### Step 4: Calculate the total available work hours in the new scenario.

In the new scenario, we have:
- Working hours per day = 6 hours
- Number of days = 16 days

The total available work hours can be calculated as:
\[ \text{Total Available Work Hours} = \text{Hours per Day} \times \text{Number of Days} = 6 \times 16 = 96 \text{ hours} \]

### Step 5: Calculate the number of persons required.

Let \( x \) be the number of persons required. The total work done by \( x \) persons in 96 hours should equal the total work required for 5 units:
\[ x \times 96 = 2400 \]
Now, solving for \( x \):
\[ x = \frac{2400}{96} = 25 \]

### Conclusion:

Thus, the number of persons required to complete 5 units of work in 16 days working 6 hours a day is **25**.

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