18 men can do 3 units of work in 10 days by doing 8 hours in a day. Then find the required number of days taken by 10 men to complete 5 units of work if they work 6 hours in a day

Options

A. 32 days
B. 45 days
C. 36 days
D. 40 days

Answer

To solve the problem step by step, we will use the relationship between men (m), days (d), time (t), and work (w). The formula we will use is:

\[ \frac{m_1 \cdot d_1 \cdot t_1}{w_1} = \frac{m_2 \cdot d_2 \cdot t_2}{w_2} \]

### Step 1: Identify the given values
From the problem, we have:
- \( m_1 = 18 \) men
- \( d_1 = 10 \) days
- \( t_1 = 8 \) hours/day
- \( w_1 = 3 \) units of work

We need to find:
- \( m_2 = 10 \) men
- \( t_2 = 6 \) hours/day
- \( w_2 = 5 \) units of work
- \( d_2 = ? \) (the number of days we need to find)

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

\[ \frac{18 \cdot 10 \cdot 8}{3} = \frac{10 \cdot d_2 \cdot 6}{5} \]

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

\[ \frac{18 \cdot 10 \cdot 8}{3} = \frac{1440}{3} = 480 \]

So, we have:

\[ 480 = \frac{10 \cdot d_2 \cdot 6}{5} \]

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

\[ \frac{10 \cdot d_2 \cdot 6}{5} = 2 \cdot d_2 \cdot 6 = 12d_2 \]

### Step 5: Set the two sides equal
Now we have:

\[ 480 = 12d_2 \]

### Step 6: Solve for \( d_2 \)
To find \( d_2 \), divide both sides by 12:

\[ d_2 = \frac{480}{12} = 40 \]

### Conclusion
The required number of days taken by 10 men to complete 5 units of work, working 6 hours a day, is **40 days**.