Calculate the number of bricks, each measuring 25 cm × 15 cm × 8 cm, required to construct a brick wall of dimensions 10 m × 4 m × 0.5 m when 10% of its volume is occupied by concrete.

Introduction / Context:
This question belongs to practical mensuration and volume calculations, often used in civil engineering and construction related aptitude tests. It asks how many standard rectangular bricks are needed to build a brick wall when part of the wall volume is occupied by concrete or mortar. The problem combines unit conversion between metres and centimetres, computation of volumes, and an adjustment for the percentage of concrete used instead of bricks.

Given Data / Assumptions:
• Dimensions of each brick = 25 cm × 15 cm × 8 cm.• Wall dimensions = 10 m × 4 m × 0.5 m (length × height × thickness).• 10% of the wall volume is occupied by concrete or mortar.• Remaining 90% of the wall volume is filled by bricks.

Concept / Approach:
The number of bricks is given by the effective volume of the wall that must be filled by bricks divided by the volume of a single brick. Since the wall dimensions are in metres and the brick dimensions are in centimetres, we first convert the wall dimensions into centimetres. After computing the total wall volume in cubic centimetres, we take 90% of it to account for the space taken up by concrete. Finally, we divide this effective brick volume by the volume of a single brick to get the required number of bricks.

Step-by-Step Solution:
Step 1: Convert wall dimensions into centimetres.10 m = 1000 cm, 4 m = 400 cm, 0.5 m = 50 cm.Step 2: Compute total volume of the wall.Wall volume = 1000 * 400 * 50 cubic centimetres.Wall volume = 1000000 * 20 = 20000000 cm^3.Step 3: Compute effective volume to be filled by bricks.Only 90% is brick volume, so effective volume = 0.9 * 20000000 = 18000000 cm^3.Step 4: Compute volume of one brick.Brick volume = 25 * 15 * 8 = 3000 cm^3.Step 5: Compute the number of bricks.Number of bricks = 18000000 / 3000 = 6000 bricks.

Verification / Alternative check:
We can simplify the ratio before division: 18000000 / 3000 is equal to 18000 / 3 when we divide numerator and denominator by 1000. This equals 6000, which confirms the earlier calculation. The number also looks reasonable for a wall of the given size, since a typical construction uses thousands of bricks for even moderate walls.

Why Other Options Are Wrong:
Option B: 5400 would correspond to a different percentage of concrete or a different thickness and does not match the given 10% concrete assumption.Option C: 3800 is much too low for the volume in question and would not fill 90% of the wall volume.Option D: 4700 is also inconsistent with the computed ratio of volumes and cannot be justified by correct calculations.

Common Pitfalls:
Many learners forget to convert the wall dimensions from metres to centimetres before calculating volume, which leads to a large numerical error. Another frequent mistake is to apply the 10% factor incorrectly, for example subtracting 10 in absolute terms instead of taking 10% of the volume. It is also easy to miscalculate the volume of a brick if the multiplication is rushed. Careful unit handling and stepwise calculation prevent these mistakes.

Final Answer:
The number of bricks required to construct the wall is 6000.