Simplification with proportional variables: If 0.764 × B = 1.236 × A, compute the value of the expression (B − A) / (B + A). Provide the exact decimal value.

Introduction / Context:This problem checks your ability to transform a proportional relationship between two variables into a simple ratio expression. Given 0.764 × B = 1.236 × A, you are asked to evaluate (B − A) / (B + A) without finding A and B individually. Such questions are common in aptitude tests because they reward algebraic manipulation and careful handling of ratios.

Given Data / Assumptions:

• Equation: 0.764 * B = 1.236 * A.
• Expression to find: (B − A) / (B + A).
• A and B are positive real numbers (typical in simplification tasks).

Concept / Approach:From 0.764 * B = 1.236 * A, write the ratio r = B / A = 1.236 / 0.764. Then substitute B = rA into (B − A) / (B + A) to get (rA − A) / (rA + A) = (r − 1) / (r + 1). This reduces the expression to a function of r alone.

Step-by-Step Solution:

Verification / Alternative check:Let A = 0.764 and B = 1.236 (any proportional pair works). Then (B − A) / (B + A) = (1.236 − 0.764) / (1.236 + 0.764) = 0.472 / 2.000 = 0.236, confirming the result.

Why Other Options Are Wrong:0.764 and 0.472 are intermediate numbers from the equation, not the final ratio. 2 and 0.618 do not satisfy the derived identity (r − 1) / (r + 1) for r = 1.236 / 0.764.

Common Pitfalls:Solving for A and B individually (unnecessary), or inverting the ratio A / B instead of B / A when substituting, which changes the sign or value of the final expression.

Final Answer:0.236