Carpeting a Rectangular Room — Cost from Width and Rate: Find the total cost of carpeting a room 8 m by 6 m with a carpet 0.75 m wide at ₹20 per metre (length charged by running metre).
Aptitude
Area
Difficulty: Medium
Choose an option
-
A₹ 1300
-
B₹ 1500
-
C₹ 1750
-
D₹ 1280
-
E₹ 1440
Answer
Correct Answer: ₹ 1280
Explanation
Introduction / Context:When carpet is priced per running metre of a fixed width, the payable length equals floor area divided by carpet width. Multiplying this length by the per-metre rate yields the total cost. Unit consistency (metres) is crucial.
Given Data / Assumptions:
- Room: 8 m × 6 m ⇒ area = 48 m^2
- Carpet width = 0.75 m; priced at ₹20 per running metre
- No wastage assumed
Concept / Approach:Length of carpet required = area / width. Cost = (required length) * (rate per metre). Choosing orientation to minimize seams does not affect total length because width is fixed and coverage is full.
Step-by-Step Solution:
Area = 8 * 6 = 48 m^2.Required length = 48 / 0.75 = 64 m.Cost = 64 * ₹20 = ₹1280.Verification / Alternative check:
Rows of width strips: Total strip area = width * length; summing to area forces the same total running metres regardless of direction.Why Other Options Are Wrong:
- ₹1300, ₹1440, ₹1500, ₹1750 arise from rounding or using width 0.8 or 0.7 m mistakenly.
Common Pitfalls:
- Mismatching metres and centimetres or pricing per square metre instead of per running metre.
Final Answer:₹ 1280.