A wall has dimensions 10 m in length, 6 m in height and 4 cm in thickness. Each brick measures 25 cm × 15 cm × 8 cm. If mortar occupies 10 percent of the wall volume, calculate the number of bricks required to construct the wall.

Introduction / Context:
This problem tests your understanding of volume calculations and percentage adjustments in practical construction scenarios. You must calculate the volume of a wall, account for mortar occupying part of the volume, and then determine how many bricks are needed to fill the remaining volume of solid material.

Given Data / Assumptions:

• Wall length = 10 m
• Wall height = 6 m
• Wall thickness = 4 cm
• Brick dimensions = 25 cm × 15 cm × 8 cm
• Mortar occupies 10 percent of wall volume
• Remaining 90 percent of volume is occupied by bricks

Concept / Approach:
First, convert all dimensions into the same unit, preferably metres or centimetres. Then compute the total volume of the wall. Since 10 percent is mortar, calculate 90 percent of the wall volume as the brick volume. Next, compute the volume of a single brick. Finally, divide the total brick volume by the volume of one brick to obtain the number of bricks required.

Step-by-Step Solution:
Convert thickness 4 cm to metres: 4 cm = 0.04 m Wall volume = length * height * thickness = 10 * 6 * 0.04 = 2.4 m^3 Brick volume: convert brick dimensions to metres: 25 cm = 0.25 m, 15 cm = 0.15 m, 8 cm = 0.08 m Volume of one brick = 0.25 * 0.15 * 0.08 = 0.003 m^3 Only 90 percent of wall volume is brick: brick volume total = 0.9 * 2.4 = 2.16 m^3 Number of bricks = total brick volume / volume of one brick = 2.16 / 0.003 = 720

Verification / Alternative check:
You can cross check by multiplying 720 * 0.003 = 2.16 m^3. Adding mortar volume 0.24 m^3 (10 percent of 2.4) gives total 2.4 m^3, which matches the wall volume exactly. This confirms that 720 bricks are required.

Why Other Options Are Wrong:
600 and 660: These correspond to incorrect usage of the wall volume or mortar percentage and give brick volume less than required. 6000: This is far too large and would represent a huge overestimate of the number of bricks. 540: Also underestimates the volume and does not satisfy the volume balance check.

Common Pitfalls:
Mixing centimetres and metres without converting units. Ignoring the mortar volume and assuming the wall is fully solid brick. Forgetting to apply the 90 percent factor for bricks. Errors in volume calculation, especially with three dimensional multiplication.

Final Answer:
The number of bricks required to construct the wall is 720