If 20% of (x+Y) = 50%, of (X-Y) then X: Y is equal to

Convert the percentages to fractions first: 0.2(x+y) = 0.5(x−y). Multiply through by 10 to get 2(x+y) = 5(x−y), so 2x + 2y = 5x − 5y. Bringing like terms together gives 7y = 3x, which means x : y = 7 : 3. So the answer is C.

Checking the wrong options by substitution makes the trap clear:

• A) 3:7 gives x = 3, y = 7. The left side is 0.2 × 10 = 2 and the right side is 0.5 × (−4) = −2. The signs do not match. This ratio comes from flipping the equation.
• B) 5:7 gives 0.2 × 12 = 2.4 against 0.5 × (−2) = −1. Not equal.
• D) 7:5 gives 0.2 × 12 = 2.4 against 0.5 × 2 = 1. Not equal.

The core concept is converting a linear relation between two variables into a ratio. This kind of simplification shows up in Quantitative Aptitude and in data interpretation in Mains.

Trap: Aspirants often write the ratio in the order in which the equation was set up, or they stop at 7y = 3x and invert it. Always confirm which variable is in the numerator before you tick the option.