If P = x% of y and Q = y% of x, then which of following is true?

The correct answer is Option (1) → P = Q

“\(x\)% of \(y\)” means \(\frac{x}{100}\times y\). Written out, both expressions are the same product \(\frac{xy}{100}\), because the order of multiplication does not matter.

• \(\displaystyle P=\frac{x}{100}\times y=\frac{xy}{100}\)

• \(\displaystyle Q=\frac{y}{100}\times x=\frac{xy}{100}\)

So P \(=\) Q for any values of \(x\) and \(y\); for example, 20% of 50 and 50% of 20 are both 10.