If 25% of (X + Y) = 50% of (X − Y), then Y is what percentage of X?

The correct answer is Option (2) → 33.33%

Writing both percentages as fractions turns the condition into an equation between X and Y, which gives the ratio of Y to X; a ratio is then turned into a percentage by multiplying by 100.

• 25% is one-fourth and 50% is one-half: \(\displaystyle\frac{X+Y}{4}=\frac{X-Y}{2}\)

• \(X+Y=2X-2Y\), which gives \(X=3Y\): X is three times Y

• So Y is one-third of X: \(\displaystyle\frac{Y}{X}\times100=\frac{100}{3}=33.33\%\)