The problem states:

To fill a tank, 25 buckets of water are required. How many buckets of water will be required to fill the same tank if the capacity of the bucket is reduced to two-fifths of its present capacity?

Solution:

Step 1: Calculate the total tank capacity.

If 25 buckets are required to fill the tank, and the capacity of each bucket is $C$ (present bucket capacity), the total capacity of the tank is: $\text{Tank Capacity} = 25 \times C$

Step 2: Adjust for the reduced bucket capacity.

If the new bucket capacity is reduced to two-fifths of its original capacity, the new bucket capacity becomes: $\text{New Bucket Capacity} = \frac{2}{5} \times C$

Step 3: Determine the new number of buckets required.

The number of buckets required to fill the tank is now given by: $\text{New Buckets Required} = \frac{\text{Tank Capacity}}{\text{New Bucket Capacity}}$

Substituting values: $\text{New Buckets Required} = \frac{25 \times C}{\frac{2}{5} \times C}$

Canceling $C$ from numerator and denominator: $\text{New Buckets Required} = \frac{25}{\frac{2}{5}}$

Simplify: $\text{New Buckets Required} = 25 \times \frac{5}{2} = 62.5$

Step 4: Interpret the result.

Since buckets must be whole numbers in practical terms, the result means that 63 buckets will be required to completely fill the tank (rounding up to the next whole number).

Final Answer:

63 buckets are required if the bucket's capacity is reduced to two-fifths of its original size.

Would you like a deeper breakdown or have further questions?

Related Questions:

1. What would happen if the bucket capacity were reduced to half instead of two-fifths?
2. How many buckets would be needed if the bucket size is increased to double its capacity?
3. How is rounding handled in real-world situations like this?
4. What if the tank's capacity were doubled—how would the calculation change?
5. Can you derive a general formula for buckets required given any proportional reduction?

Tip:

Always check whether the values in real-world problems like this one require rounding up or down to ensure practical feasibility!