There are two buckets, smaller bucket can hold only 3/5th of the water as compared to the larger bucket. If 6000 buckets of larger capacity are needed to fill a pond, then how many smaller capacity buckets are needed to fill the same pond?

Options

A. 8000
B. 10000
C. 12000
D. 15000

Answer

To solve the problem step by step, we will follow the reasoning provided in the video transcript:

1. **Understanding the relationship between the buckets**:
- Let the capacity of the larger bucket be represented as \( L \).
- The smaller bucket can hold \( \frac{3}{5} \) of the larger bucket's capacity. Therefore, the capacity of the smaller bucket, \( S \), can be expressed as:
\[ S = \frac{3}{5}L \]

2. **Calculating the total volume of water required to fill the pond**:
- We know that 6000 larger buckets are needed to fill the pond. Thus, the total volume of water required to fill the pond can be calculated as:
\[ \text{Total volume} = 6000 \times L \]

3. **Substituting the capacity of the smaller bucket**:
- We can express the total volume in terms of the smaller bucket's capacity. Since \( S = \frac{3}{5}L \), we can rearrange this to find \( L \):
\[ L = \frac{5}{3}S \]
- Now substituting \( L \) in the total volume equation:
\[ \text{Total volume} = 6000 \times \left(\frac{5}{3}S\right) = 6000 \times \frac{5}{3}S = 10000S \]

4. **Finding the number of smaller buckets needed**:
- Since the total volume required to fill the pond is \( 10000S \) and each smaller bucket holds \( S \), the number of smaller buckets needed is:
\[ \text{Number of smaller buckets} = \frac{\text{Total volume}}{S} = \frac{10000S}{S} = 10000 \]

5. **Conclusion**:
- Therefore, the number of smaller capacity buckets needed to fill the pond is:
\[ \text{Number of smaller buckets} = 10000 \]