Percentage Relation between a and b

CMAT 2024 · Quantitative Techniques & Data Interpretation · Easy · Arithmetic

If $a\%$ of $a + b\%$ of $b = 2\%$ of $ab$ , then what percent of $a$ is $b$ ?

Answer

$\frac{a^2}{100} + \frac{b^2}{100} = \frac{2ab}{100} \implies a^2 + b^2 - 2ab = 0 \implies (a - b)^2 = 0 \implies a = b$

Thus, $b$ is $100\%$ of $a$ .

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