Introduction / Context:
The number of bricks required equals (volume of wall) / (volume of one brick). Multiplying the brick count by the rate per 1000 gives the total cost. Unit consistency (meters vs centimeters) is essential.
Given Data / Assumptions:
- Wall: 200 m × 1.8 m × 0.375 m
- Brick: 25 cm × 12.5 cm × 7.5 cm = 0.25 m × 0.125 m × 0.075 m
- Rate: Rs 750 per 1000 bricks
- Ignore mortar allowances (ideal packing).
Concept / Approach:
- Compute both volumes in the same units.
- Number of bricks = V_wall / V_brick; Cost = (bricks / 1000) * rate.
Step-by-Step Solution:
V_wall = 200 * 1.8 * 0.375 = 135 m3.V_brick = 0.25 * 0.125 * 0.075 = 0.00234375 m3.Bricks needed = 135 / 0.00234375 = 57,600.Cost = 57.6 * 750 = Rs 43,200.
Verification / Alternative check:
In cm3: wall 135,000,000; brick 2343.75; 135,000,000 / 2343.75 = 57,600 (same count).
Why Other Options Are Wrong:
- Rs. 42, 600 / 41, 860 / 40, 750: Result from rounding, wrong brick volume, or rate errors.
Common Pitfalls:
- Mistaking cm for m in one dimension.
- Forgetting to divide by 1000 before multiplying by rate.
Final Answer:
Rs. 43, 200
Discussion & Comments