Cost of flooring a rectangular hall — which statements suffice? I. Length : Breadth = 3 : 2. II. Length = 48 m; flooring rate = $850 per m^2. III. Perimeter = 160 m; flooring rate = $850 per m^2.

Introduction / Context:We need the total cost of flooring, which equals Area * Rate. Thus we must be able to determine the rectangle’s area and have the rate per m^2.

Given Data / Assumptions:

• I: L : B = 3 : 2.
• II: L = 48 m and rate = $850/m^2.
• III: Perimeter P = 160 m (so L + B = 80) and rate = $850/m^2.

Concept / Approach:Any pair that yields both L and B and includes the rate will suffice. With L and B known, Area = L * B, and cost follows directly using the provided rate.

Step-by-Step Solution:

Verification / Alternative check:Each pair independently determines L and B, and includes a rate statement.

Why Other Options Are Wrong:

• Only I and II / Only I and III / Only II and III are each sufficient individually; therefore the most accurate selection is “Any two of the three”.
• All three together is unnecessarily strong.

Common Pitfalls:Forgetting that perimeter with a fixed ratio completely determines both dimensions.

Final Answer:Any two of the three