Symbolic pricing at a constant rate (clean algebraic form): If the cost of x meters of wire is d rupees, determine the cost of y meters of wire at the same rate. Provide a simplified algebraic expression.

Introduction / Context:
This algebraic unitary-method question asks for the general formula to scale cost with length at a constant price per meter. Clarity in forming the unit price and then multiplying by the new length is key to avoiding misplaced variables or inverted fractions.

Given Data / Assumptions:

• x meters cost d rupees
• We seek the cost for y meters
• Rate is constant and linear

Concept / Approach:
Unit price = d / x (rupees per meter). Multiply by the desired length y to obtain the total cost. Keep variables symbolic until the final expression to maintain generality.

Step-by-Step Solution:
Unit price = d / xCost for y meters = (d / x) * yCost = dy / x

Verification / Alternative check:
Dimensional reasoning: (rupees/meter) * meter = rupees. The expression dy / x has dimensions of rupees, as required, and scales linearly with y and inversely with x, which is expected if d is fixed for x meters.

Why Other Options Are Wrong:
xd and yd ignore the needed division by x; yd / x equals dy / x (same correct form); d / (x * y) inverts proportionality and is dimensionally inconsistent for total cost.

Common Pitfalls:
Writing xy/d or mixing numerator and denominator. Always start from unit price to avoid algebraic mistakes.

Final Answer:
dy / x