A wall has a volume such that it is 5 times as high as it is broad and 8 times as long as it is high. If the volume of the wall is 12.8 cubic metres, what is the breadth of the wall, in centimetres?

Introduction / Context:
This problem tests the understanding of proportional dimensions and volume in a three dimensional object. The wall has its height expressed in terms of breadth and its length expressed in terms of height. With the ratios between the three dimensions and the total volume, we must deduce the actual breadth. Such problems are common in aptitude exams where relationships between dimensions are expressed in words instead of directly giving all numerical values.

Given Data / Assumptions:

• Let breadth of the wall be b metres.
• Height is 5 times breadth, so height = 5b metres.
• Length is 8 times height, so length = 8 * (5b) = 40b metres.
• Volume of the wall V = 12.8 cubic metres.
• Wall is rectangular in shape.

Concept / Approach:
Volume of a rectangular solid is given by:
V = length * breadth * height Here each dimension is in terms of b, so we substitute and form an equation in b. After solving for b, we convert the result from metres to centimetres because options are in centimetres.

Step-by-Step Solution:
Step 1: Express all dimensions in terms of b. Breadth = b metres. Height = 5b metres. Length = 40b metres. Step 2: Write volume equation. V = length * breadth * height = 40b * b * 5b. V = 200 * b^3. Given volume V = 12.8 cubic metres. So, 200 * b^3 = 12.8. Step 3: Solve for b^3. b^3 = 12.8 / 200 = 0.064. Step 4: Take cube root. b = cube root of 0.064. Since 0.4^3 = 0.064, b = 0.4 metres. Step 5: Convert to centimetres. b = 0.4 metres = 0.4 * 100 = 40 centimetres. Thus, the breadth of the wall is 40 cm.

Verification / Alternative check:
We can recompute the volume with b = 0.4 metres. Height = 5 * 0.4 = 2 metres. Length = 8 * 2 = 16 metres. Volume V = 16 * 0.4 * 2 = 12.8 cubic metres, which matches the given volume exactly, confirming that the breadth is indeed 0.4 metres or 40 centimetres.

Why Other Options Are Wrong:
Option B (30 cm), Option C (20 cm), and Option D (10 cm) would all produce different volumes when substituted back into the dimensional relationships and thus would not equal 12.8 cubic metres. Option E (50 cm) similarly leads to an incorrect volume. Only 40 cm yields the correct given volume.

Common Pitfalls:
A common error is to misinterpret the phrase 8 times as long as it is high and mistakenly multiply directly by 8 twice, or confuse which dimension is which. Another pitfall is forgetting to convert metres to centimetres at the end, which would result in choosing an option expressed in metres rather than centimetres. Careful reading and unit conversion are crucial.

Final Answer:
The breadth of the wall is 40 cm.