If 5 persons weave 180 shawls in 12 days, How many shawls will 6 persons weave in 15 days?

Options

A. 260
B. 370
C. 270
D. 360

Answer

To solve the problem, we will use the concept of direct variation, which states that if the number of persons and the number of days are increased, the number of shawls woven will also increase proportionally.

### Step-by-Step Solution:

1. **Identify the given values:**
- Number of persons (m1) = 5
- Number of days (d1) = 12
- Number of shawls woven (w1) = 180
- Number of persons in the second scenario (m2) = 6
- Number of days in the second scenario (d2) = 15
- Number of shawls woven in the second scenario (w2) = ?

2. **Set up the proportion using the formula:**
\[ \frac{m1 \cdot d1}{w1} = \frac{m2 \cdot d2}{w2} \]

3. **Substitute the known values into the equation:**
\[ \frac{5 \cdot 12}{180} = \frac{6 \cdot 15}{w2} \]

4. **Calculate the left side of the equation:**
\[ \frac{60}{180} = \frac{1}{3} \]

5. **Now, substitute this into the equation:**
\[ \frac{1}{3} = \frac{90}{w2} \]

6. **Cross-multiply to solve for w2:**
\[ 1 \cdot w2 = 3 \cdot 90 \]
\[ w2 = 270 \]

7. **Conclusion:**
The number of shawls that 6 persons will weave in 15 days is **270**.