A wall is 24 m long, 8 m high and 60 cm thick. It is constructed using bricks each of size 24 cm × 12 cm × 8 cm. If 10% of the wall volume is occupied by mortar, how many bricks are required to build the wall?

Introduction / Context:
This construction-based aptitude problem extends the brick-counting idea by adding the realistic detail that some portion of the wall volume is filled with mortar rather than bricks. We must calculate the total wall volume, subtract the part occupied by mortar, and then divide the remaining brick volume by the volume of a single brick. The question tests volume calculations, unit conversions and proportional reasoning.

Given Data / Assumptions:

• Wall dimensions: length = 24 m, height = 8 m, thickness = 60 cm.
• Brick dimensions: 24 cm × 12 cm × 8 cm.
• 10% of the wall volume is mortar, hence 90% is brick volume.
• The wall is assumed solid, apart from mortar gaps.

Concept / Approach:
We treat both the wall and each brick as cuboids. The number of bricks required is the ratio of the volume actually occupied by bricks to the volume of one brick. Because mortar occupies 10% of the wall volume, only 90% of the wall volume is taken up by bricks. Therefore:
Number of bricks = (0.9 * Volume of wall) / Volume of one brick All dimensions must be converted into the same unit, typically centimetres, before computing volumes.

Step-by-Step Solution:
Convert wall dimensions to cm: 24 m = 2400 cm, 8 m = 800 cm, thickness = 60 cm. Volume of wall = 2400 * 800 * 60 cubic centimetres. Volume of wall = 115,200,000 cubic cm. Volume of one brick = 24 * 12 * 8 cubic cm. Volume of one brick = 2304 cubic cm. If there were no mortar, number of bricks = 115,200,000 / 2304 = 50,000. But only 90% of wall volume is brick: brick volume = 0.9 * 115,200,000 = 103,680,000 cubic cm. Number of bricks = 103,680,000 / 2304 = 45,000.

Verification / Alternative check:
We can cross-check quickly: since 10% of the space is mortar, the brick count should be 90% of the no-mortar case. Without mortar, we needed 50,000 bricks, and 90% of 50,000 is 0.9 * 50,000 = 45,000, which matches our detailed calculation. This consistency confirms that our approach and arithmetic are correct.

Why Other Options Are Wrong:
35,000 bricks would correspond to too small a brick volume, implying more mortar than stated. 55,000 and 65,000 are larger than the 50,000 bricks required without mortar, which is impossible. 50,000 bricks would be correct only if mortar were ignored; it does not reflect the 10% mortar content specified in the question.

Common Pitfalls:
One common mistake is forgetting to account for mortar and simply dividing total wall volume by the brick volume. Another is to subtract 10% from the number of bricks instead of 10% from the volume, which in this problem happens to give the same numeric count but may mislead in more complex cases. Students also often mix metres and centimetres, leading to incorrect wall volumes.

Final Answer:
The number of bricks required to build the wall is 45000.