If 3 persons weave 168 shawls in 14 days, how many shawls will 8 persons weave in 5 days ?

Options

A. 90
B. 105
C. 126
D. 160

Answer

To solve the problem step by step, we will use the concept of direct proportionality between the number of persons, the number of days, and the amount of work done (shawls woven).

### Step 1: Understand the relationship between persons, days, and work
We know that the amount of work done is directly proportional to the number of persons and the number of days. This can be expressed as:
\[ \text{Work} \propto \text{Persons} \times \text{Days} \]

### Step 2: Set up the equation based on the given information
From the problem, we know:
- 3 persons can weave 168 shawls in 14 days.

Let’s denote:
- \( M_1 = 3 \) (persons)
- \( D_1 = 14 \) (days)
- \( W_1 = 168 \) (shawls)

We want to find out how many shawls \( W_2 \) can be woven by:
- \( M_2 = 8 \) (persons)
- \( D_2 = 5 \) (days)

### Step 3: Set up the proportion
Using the formula for direct proportionality:
\[ \frac{M_1 \times D_1}{W_1} = \frac{M_2 \times D_2}{W_2} \]

Substituting the known values:
\[ \frac{3 \times 14}{168} = \frac{8 \times 5}{W_2} \]

### Step 4: Cross-multiply to solve for \( W_2 \)
Cross-multiplying gives:
\[ 3 \times 14 \times W_2 = 168 \times (8 \times 5) \]

Calculating the right side:
\[ 8 \times 5 = 40 \]
So,
\[ 168 \times 40 = 6720 \]

Now the equation becomes:
\[ 42 W_2 = 6720 \]

### Step 5: Solve for \( W_2 \)
Now, divide both sides by 42:
\[ W_2 = \frac{6720}{42} \]

Calculating this gives:
\[ W_2 = 160 \]

### Conclusion
Thus, 8 persons will weave **160 shawls** in 5 days.