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 use the concept of work done, which can be calculated using the formula:

\[ \text{Work} = \text{Number of Persons} \times \text{Hours per Day} \times \text{Days} \]

### Step 1: Calculate the total work done in the first scenario
Given:
- Number of persons (M1) = 18
- Hours per day (H1) = 8
- Days (D1) = 10
- Units of work (W1) = 3

Using the formula, we can calculate the total work done in terms of person-hours:
\[ \text{Total Work} = M1 \times H1 \times D1 = 18 \times 8 \times 10 = 1440 \text{ person-hours} \]

### Step 2: Calculate the work done per unit
Since 3 units of work are completed in 1440 person-hours, the work done per unit can be calculated as:
\[ \text{Work per unit} = \frac{\text{Total Work}}{\text{Units of Work}} = \frac{1440}{3} = 480 \text{ person-hours per unit} \]

### Step 3: Calculate the total work required for the second scenario
Now, we need to find out how much work is required for 5 units of work:
\[ \text{Total Work Required} = 5 \times \text{Work per unit} = 5 \times 480 = 2400 \text{ person-hours} \]

### Step 4: Set up the equation for the second scenario
Now we need to find out how many persons (M2) are required to complete this work in the second scenario:
- Hours per day (H2) = 6
- Days (D2) = 16

Using the formula for work, we have:
\[ \text{Total Work Required} = M2 \times H2 \times D2 \]
Substituting the known values:
\[ 2400 = M2 \times 6 \times 16 \]

### Step 5: Solve for M2
Now, we can solve for M2:
\[ 2400 = M2 \times 96 \]
\[ M2 = \frac{2400}{96} = 25 \]

### 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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