If A = x% of y and B = y% of x, then which of the following is true?

Definitions

• A = x% of y = 𝑥 100 × 𝑦 100 x ​ ×y
• B = y% of x = 𝑦 100 × 𝑥 100 y ​ ×x

Step 1: Compare A and B
A = 𝑥 100 × 𝑦 100 x ​ ×y = 𝑥 𝑦 100 100 xy ​ B = 𝑦 100 × 𝑥 100 y ​ ×x = 𝑥 𝑦 100 100 xy ​

Conclusion

• Both expressions are identical for all real x and y.

Final Answer
A = B.