36 persons working 8 hours a day can do 3 units of work in 12 days. How many persons are required to do 5 units of that work in 16 days, if they work for 6 hours a day?

Options

A. 50
B. 55
C. 60
D. 45

Answer

To solve the problem, we will use the formula that relates the number of persons (m), days (d), hours (h), and work units (w). The formula is:

\[ \frac{m_1 \cdot d_1 \cdot h_1}{w_1} = \frac{m_2 \cdot d_2 \cdot h_2}{w_2} \]

### Step 1: Identify the given values
From the problem, we have:
- \( m_1 = 36 \) (number of persons)
- \( d_1 = 12 \) (days)
- \( h_1 = 8 \) (hours per day)
- \( w_1 = 3 \) (units of work)

We need to find \( m_2 \) (number of persons required) for:
- \( w_2 = 5 \) (units of work)
- \( d_2 = 16 \) (days)
- \( h_2 = 6 \) (hours per day)

### Step 2: Substitute the values into the formula
Substituting the known values into the formula:

\[ \frac{36 \cdot 12 \cdot 8}{3} = \frac{m_2 \cdot 16 \cdot 6}{5} \]

### Step 3: Simplify the left side
Calculating the left side:

\[ \frac{36 \cdot 12 \cdot 8}{3} = \frac{3456}{3} = 1152 \]

So, we have:

\[ 1152 = \frac{m_2 \cdot 16 \cdot 6}{5} \]

### Step 4: Simplify the right side
Now, simplify the right side:

\[ \frac{m_2 \cdot 16 \cdot 6}{5} = \frac{96 m_2}{5} \]

### Step 5: Set the equation
Now we can set the equation:

\[ 1152 = \frac{96 m_2}{5} \]

### Step 6: Solve for \( m_2 \)
To isolate \( m_2 \), multiply both sides by 5:

\[ 1152 \cdot 5 = 96 m_2 \]

Calculating the left side:

\[ 5760 = 96 m_2 \]

Now, divide both sides by 96:

\[ m_2 = \frac{5760}{96} = 60 \]

### Conclusion
Thus, the number of persons required to do 5 units of work in 16 days while working 6 hours a day is **60**.

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