4 mat-weavers can weave 4 mats in 4 days. At the same rate how many mats would be woven by 8 mat-weavers in 8 days ?

Options

A. 4
B. 8
C. 12
D. 16

Answer

To solve the problem, we will use the relationship between the number of workers (mat-weavers), the number of days they work, and the amount of work done (number of mats woven).

### Step-by-Step Solution:

1. **Understanding the Given Information**:
- 4 mat-weavers can weave 4 mats in 4 days.
- We need to find out how many mats can be woven by 8 mat-weavers in 8 days.

2. **Calculate the Work Done by 4 Mat-Weavers**:
- The total work done (in terms of mats) by 4 mat-weavers in 4 days is 4 mats.
- Therefore, the work done by 1 mat-weaver in 4 days is:
\[ \text{Work by 1 mat-weaver} = \frac{4 \text{ mats}}{4 \text{ mat-weavers}} = 1 \text{ mat} \]

3. **Calculate the Work Done by 1 Mat-Weaver in 1 Day**:
- Since 1 mat-weaver weaves 1 mat in 4 days, the work done by 1 mat-weaver in 1 day is:
\[ \text{Work by 1 mat-weaver in 1 day} = \frac{1 \text{ mat}}{4 \text{ days}} = \frac{1}{4} \text{ mat} \]

4. **Calculate the Work Done by 8 Mat-Weavers in 1 Day**:
- If 1 mat-weaver can weave \(\frac{1}{4}\) mat in a day, then 8 mat-weavers can weave:
\[ \text{Work by 8 mat-weavers in 1 day} = 8 \times \frac{1}{4} = 2 \text{ mats} \]

5. **Calculate the Total Work Done by 8 Mat-Weavers in 8 Days**:
- If 8 mat-weavers can weave 2 mats in 1 day, then in 8 days they can weave:
\[ \text{Total work in 8 days} = 2 \text{ mats/day} \times 8 \text{ days} = 16 \text{ mats} \]

6. **Conclusion**:
- Therefore, 8 mat-weavers can weave **16 mats** in 8 days.

### Final Answer:
**16 mats**

---