If 12 carpenters working 6 hours a day can make 460 chairs in 240 days, then find the number of chairs made by 18 carpenters in 360 days each working 8 hours a day?

Options

A. 1. 1320
B. 2. 1380
C. 3. 1260
D. 4. 920

Answer

To solve the problem, we will use the relationship between the number of workers, the number of days they work, the number of hours they work each day, and the total work done (in this case, the number of chairs made). We can use the formula:

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

Where:
- \(m_1\) = number of carpenters in the first scenario (12)
- \(d_1\) = number of days in the first scenario (240)
- \(h_1\) = hours worked per day in the first scenario (6)
- \(w_1\) = work done in the first scenario (460 chairs)
- \(m_2\) = number of carpenters in the second scenario (18)
- \(d_2\) = number of days in the second scenario (360)
- \(h_2\) = hours worked per day in the second scenario (8)
- \(w_2\) = work done in the second scenario (unknown)

### Step-by-Step Solution:

1. **Identify the known values:**
- \(m_1 = 12\)
- \(d_1 = 240\)
- \(h_1 = 6\)
- \(w_1 = 460\)
- \(m_2 = 18\)
- \(d_2 = 360\)
- \(h_2 = 8\)

2. **Set up the equation using the formula:**
\[ \frac{12 \cdot 240 \cdot 6}{460} = \frac{18 \cdot 360 \cdot 8}{w_2} \]

3. **Calculate the left side of the equation:**
\[ \text{Left Side} = \frac{12 \cdot 240 \cdot 6}{460} \]
- Calculate \(12 \cdot 240 = 2880\)
- Then, \(2880 \cdot 6 = 17280\)
- Finally, \(\frac{17280}{460} = 37.478\) (approximately)

4. **Calculate the right side of the equation:**
\[ \text{Right Side} = \frac{18 \cdot 360 \cdot 8}{w_2} \]
- Calculate \(18 \cdot 360 = 6480\)
- Then, \(6480 \cdot 8 = 51840\)

5. **Set the two sides equal to each other:**
\[ 37.478 = \frac{51840}{w_2} \]

6. **Solve for \(w_2\):**
- Cross-multiply to get:
\[ 37.478 \cdot w_2 = 51840 \]
- Now, divide both sides by \(37.478\):
\[ w_2 = \frac{51840}{37.478} \approx 1380 \]

### Final Answer:
The number of chairs made by 18 carpenters in 360 days, each working 8 hours a day, is approximately **1380 chairs**.