If 27 people, working 8 hours a day, can complete a task in 12 days, then in how many days will 18 people finish the task, working 9 hours a day?

Options

A. 15 days
B. 16 days
C. 18 days
D. 20 days

Answer

To solve the problem, we can use the work formula, which states that:

\[ \text{Work} = \text{Men} \times \text{Days} \times \text{Hours} \]

Given:
- \( m_1 = 27 \) (people)
- \( d_1 = 12 \) (days)
- \( h_1 = 8 \) (hours)
- \( m_2 = 18 \) (people)
- \( h_2 = 9 \) (hours)
- \( d_2 \) = ? (days)

Since the work done is the same in both cases, we can set up the equation:

\[ m_1 \times d_1 \times h_1 = m_2 \times d_2 \times h_2 \]

Substituting the known values into the equation:

\[ 27 \times 12 \times 8 = 18 \times d_2 \times 9 \]

Now, we can simplify this equation step by step.

1. Calculate the left side:
\[ 27 \times 12 = 324 \]
\[ 324 \times 8 = 2592 \]

2. Now, substitute this value back into the equation:
\[ 2592 = 18 \times d_2 \times 9 \]

3. Simplify the right side:
\[ 18 \times 9 = 162 \]
Thus, we have:
\[ 2592 = 162 \times d_2 \]

4. To find \( d_2 \), divide both sides by 162:
\[ d_2 = \frac{2592}{162} \]

5. Now, calculate \( d_2 \):
\[ d_2 = 16 \]

So, the number of days \( d_2 \) that 18 people will take to finish the task working 9 hours a day is **16 days**.