Symbolic unitary method (wire pricing at a constant rate): If the cost of x meters of wire is d rupees at a fixed rate, what is the cost (in rupees) of y meters of the same wire at that identical rate? Express the answer in terms of x, y, and d.

Introduction / Context:This is a symbolic unitary-method question. We know the total price for x meters and must compute the price for y meters at the same linear rate. The answer requires expressing unit price and scaling it by the new length, maintaining dimensional consistency (rupees per meter * meters = rupees).

Given Data / Assumptions:

• x meters cost d rupees
• Rate is constant (direct proportion between length and cost)
• We need the cost for y meters in terms of x, y, and d

Concept / Approach:When cost is proportional to length, unit cost = d / x rupees per meter. The cost for y meters is unit cost multiplied by y. Carefully preserve variable positions to avoid algebraic mistakes.

Step-by-Step Solution:Unit cost = d / xCost for y meters = (d / x) * ySimplify: Cost = (d * y) / x = dy / x

Verification / Alternative check:Dimensional check: (rupees / meter) * meter = rupees → (d / x) * y → dy / x rupees, which is dimensionally correct and consistent with direct proportion.

Why Other Options Are Wrong:d / y and x * d / y invert or misplace variables; x * y / d is inverse proportionality; d + y is not proportional and mixes incompatible units arithmetically.

Common Pitfalls:Writing yx/d or yd*x without a division bar; always express clear fraction dy / x to reflect unit cost times quantity.

Final Answer:dy / x