In aptitude (Ratio and Work Problems), 25 buckets of water are required to fill a tank using the current bucket size. If the bucket capacity is reduced to two fifths of its present capacity, how many buckets will be required to fill the same tank?

Introduction / Context:
This question involves proportional reasoning about capacity and quantity. It describes a tank filled using a bucket of a certain size, and then asks how many buckets are needed if each bucket becomes smaller. Problems of this type are common in aptitude tests and help you practice direct inverse proportionality between capacity and number of units required to perform the same job.

Given Data / Assumptions:

• Initially, 25 buckets of water are needed to fill the tank.
• Each original bucket has some capacity, say V units.
• The new bucket has capacity equal to two fifths of the original capacity, that is (2 / 5) * V.
• The tank volume remains the same in both scenarios.
• We must find the number of new buckets required.

Concept / Approach:
The total volume of the tank can be expressed in terms of the original bucket as: Tank volume = 25 * V. With the smaller bucket, each bucket carries only two fifths of V, but the tank volume is unchanged. If N new buckets are needed, then: N * (2 / 5) * V = 25 * V. Since V is nonzero, it cancels out, and we can solve the resulting equation for N. This is a simple example of inverse proportional reasoning: reducing the capacity by a factor causes the number of buckets to increase by the reciprocal factor.

Step-by-Step Solution:
Step 1: Let the original bucket capacity be V units. Step 2: Total tank volume in terms of V is 25 * V. Step 3: New bucket capacity is (2 / 5) * V. Step 4: Let N be the number of new buckets required, so N * (2 / 5) * V = 25 * V. Step 5: Cancel V from both sides: N * (2 / 5) = 25. Step 6: Solve for N: N = 25 * (5 / 2) = 125 / 2. Step 7: Compute 125 / 2 = 62.5. Step 8: Therefore, 62.5 new buckets are required to fill the tank.

Verification / Alternative check:
We can verify with actual units. Assume V = 10 litres for convenience. Then the tank volume is 25 * 10 = 250 litres. New bucket capacity is (2 / 5) * 10 = 4 litres. To supply 250 litres with 4 litre buckets, we need 250 / 4 = 62.5 buckets. This matches our earlier calculation and is consistent with the idea that a smaller bucket means more trips.

Why Other Options Are Wrong:
52.5, 72.5, 82.5, and 50 do not satisfy the basic volume equation N * (2 / 5) = 25. Only N = 62.5 yields the required total of 25V units of water. Any other choice either under fills or overfills the tank based on the assumed capacity.

Common Pitfalls:
Students sometimes scale the number of buckets incorrectly, for example by multiplying by two fifths instead of dividing, or they confuse whether capacity and number vary directly or inversely. Remember that when the size of each unit decreases, you need more units to cover the same total volume. Writing out the equation with an abstract capacity V helps keep the relationships clear.

Final Answer:
When the bucket capacity is reduced to two fifths of its original size, the number of buckets required to fill the tank becomes 62.5.