Scaled carpet order and cost comparison\nAn initial carpet has breadth 6 m and length 1.44 times the breadth. A second carpet has its length increased by 40% and breadth increased by 25% over the first. If cost is ₹45 per m², what is the cost of the second carpet?

Introduction / Context:
This involves proportional scaling of dimensions followed by area and cost computation. Percentage increases act as multiplicative factors on the original dimensions.

Given Data / Assumptions:

• Original breadth B = 6 m; original length L = 1.44 * 6 = 8.64 m
• New length = 1.4 * 8.64 = 12.096 m
• New breadth = 1.25 * 6 = 7.5 m
• Rate = ₹45 per m^2

Concept / Approach:
Compute new area and multiply by rate to obtain the total cost.

Step-by-Step Solution:

Verification / Alternative check:
Original area = 8.64 * 6 = 51.84 m^2. Scale factors 1.4 and 1.25 multiply area by 1.4 * 1.25 = 1.75, and 51.84 * 1.75 = 90.72 (consistent).

Why Other Options Are Wrong:
The other amounts do not align with the precise area scaling and rate multiplication.

Common Pitfalls:
Adding percentages instead of multiplying scale factors, or applying the rate to a single dimension instead of the area.

Final Answer:
₹4,082.40