Twelve buckets of water, each of capacity 13.5 litres, are just enough to fill a tank. How many buckets will be required to fill the same tank completely if each bucket now has a capacity of 9 litres?

Introduction / Context:
This is a direct capacity and volume comparison problem. The tank capacity remains fixed, but the size of each bucket changes. The idea is to compute the volume of the tank from the first situation and then find how many smaller buckets are needed to hold the same volume of water.

Given Data / Assumptions:
- Number of buckets in the first case = 12
- Capacity of each bucket in the first case = 13.5 litres
- Capacity of each bucket in the second case = 9 litres
- The tank is completely filled in both situations
- No water is spilled or wasted in either case

Concept / Approach:
We use the relationship:
- Tank capacity = number of buckets * capacity per bucket.
The tank capacity found from the first situation must equal total water from the second situation. Then the required number of buckets in the second case is tank capacity divided by capacity of each smaller bucket.

Step-by-Step Solution:
Step 1: Compute tank capacity from the first case: capacity = 12 * 13.5 litres. Step 2: 12 * 13.5 = 162, so the tank holds 162 litres. Step 3: In the second case, capacity of each bucket = 9 litres. Step 4: Required number of buckets = total volume / capacity of one new bucket. Step 5: Number of buckets = 162 / 9 = 18.

Verification / Alternative check:
We can verify by multiplying back: 18 buckets * 9 litres per bucket = 162 litres, which matches the tank capacity found earlier. Therefore the count of 18 buckets is consistent and correct.

Why Other Options Are Wrong:
8 buckets: 8 * 9 = 72 litres, which is much less than the required 162 litres.
15 buckets: 15 * 9 = 135 litres, still short of the full tank capacity.
16 buckets: 16 * 9 = 144 litres, also less than 162 litres, so the tank would not be full.

Common Pitfalls:
A common mistake is to assume that if the capacity reduces by a certain factor, the number of buckets changes by the same numeric difference rather than by a ratio. Students may also confuse 13.5 with 13 or 14 while doing mental multiplication. Writing the intermediate step for the tank capacity avoids such careless errors.

Final Answer:
The tank will be filled completely by 18 buckets of capacity 9 litres each.