Solve using a given proportional relation If x / (2y) = 3 / 2, find the exact value of (2x + y) / (x − 2y).

Introduction / Context:
Converting a proportion into an explicit relationship between x and y simplifies complex rational expressions. This is a common step in algebraic simplification and aptitude problems.

Given Data / Assumptions:

• x / (2y) = 3 / 2.
• Compute (2x + y) / (x − 2y).
• Assume y ≠ 0 and denominators stay nonzero.

Concept / Approach:
From x / (2y) = 3 / 2, deduce x = 3y. Substituting this into the target expression collapses both numerator and denominator to simple multiples of y. The variable cancels out, leaving a pure number.

Step-by-Step Solution:
Given x/(2y) = 3/2 ⇒ x = 3y.Numerator: 2x + y = 2*(3y) + y = 6y + y = 7y.Denominator: x − 2y = 3y − 2y = y.Thus (2x + y)/(x − 2y) = 7y / y = 7.

Verification / Alternative check:
Choose y = 1 ⇒ x = 3. Then (2*3 + 1)/(3 − 2) = 7/1 = 7, agreeing with the symbolic solution.

Why Other Options Are Wrong:
1/7 is the reciprocal of the correct result, often from flipping numerator and denominator.7.1 is a rounding-type distractor; all arithmetic here is exact.None of these is incorrect because 7 is attainable exactly.

Common Pitfalls:
Misreading x/(2y) as (x/2)/y; substituting x = (3/2)y incorrectly; or forgetting to subtract 2y in the denominator. Maintain the relation x = 3y exactly.

Final Answer:
7