A tank can be completely filled by 18 buckets of water when each bucket has a capacity of 8 litres. How many buckets will be required to fill the same tank if each new bucket has a capacity of 12 litres?

Introduction / Context:
This is a straightforward application of ratio and proportion involving volume. The question describes a fixed tank capacity that can be filled using buckets of one size, and then asks how many buckets of a different size are required to fill the same tank. It tests basic understanding of volume conservation and proportional scaling, which is essential for many aptitude problems.

Given Data / Assumptions:

The tank is completely filled by 18 buckets.

Each of the original buckets has a capacity of 8 litres.

New buckets each have a capacity of 12 litres.

The tank capacity remains the same in both cases and there are no spills or losses.

Concept / Approach:
The volume of the tank is the total water contained when using the first set of buckets. This is simply the number of buckets multiplied by the capacity of each bucket. Once the total tank volume is known, the number of new buckets required is the tank volume divided by the new bucket capacity. This is a direct proportional calculation and involves only basic arithmetic.

Step-by-Step Solution:
Compute the total volume of the tank using the first scenario.Number of original buckets = 18.Capacity of each original bucket = 8 litres.Total volume of the tank = 18 * 8 = 144 litres.Now consider the new buckets.Capacity of each new bucket = 12 litres.Let the required number of new buckets be n.Then 12 * n = total tank volume = 144 litres.Solve for n: n = 144 / 12 = 12.So exactly 12 of the new buckets are needed to fill the tank.
Verification / Alternative check:
Check by direct comparison of bucket capacities.Original bucket capacity : new bucket capacity = 8 : 12 = 2 : 3.To keep the same total volume, the number of buckets must change inversely in the ratio 3 : 2.Original number of buckets = 18, so new number = 18 * (2/3) = 12.This matches the computed value, confirming the answer.
Why Other Options Are Wrong:
10 or 15 buckets would give total volumes of 120 litres and 180 litres respectively, which do not equal 144 litres and therefore would not fill the tank exactly. 13.5 buckets is not meaningful in this context because the question asks for a whole number of buckets. 18 buckets of 12 litres each would exceed the required volume significantly and overfill the tank.

Common Pitfalls:
A common mistake is to think directly in terms of subtracting the capacities or to divide the number of buckets instead of the total volume. Some students also forget that the number of buckets must usually be a whole number in such practical situations. The key is always to compute the total volume first and then divide by the new capacity, keeping units consistent throughout.

Final Answer:
12 buckets of 12 litres each will be required to fill the tank.