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 of how many shawls 6 persons will weave in 15 days, we can use the concept of work done, which is based on the number of persons, the number of days, and the amount of work done.

### Step-by-Step Solution:

1. **Identify the given values:**
- Number of persons (M1) = 5
- Number of shawls woven (W1) = 180
- Number of days (D1) = 12
- Number of persons (M2) = 6
- Number of days (D2) = 15
- Work done (W2) = ?

2. **Set up the formula for work done:**
The formula we will use is:
\[ \frac{M1 \times D1}{W1} = \frac{M2 \times D2}{W2} \]
This means that the work done by the first group of persons over a certain number of days is equal to the work done by the second group of persons over their respective days.

3. **Substitute the known values into the formula:**
\[ \frac{5 \times 12}{180} = \frac{6 \times 15}{W2} \]

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

5. **Set up the equation:**
\[ \frac{1}{3} = \frac{90}{W2} \]
(since \(6 \times 15 = 90\))

6. **Cross-multiply to solve for W2:**
\[ 1 \times W2 = 3 \times 90 \]
\[ W2 = 270 \]

7. **Conclusion:**
Therefore, 6 persons will weave **270 shawls** in 15 days.