If $40\%$ of $a$ equals $\dfrac{2}{3}$ of $b$, the ratio $a : b$ is:

If $40\%$ of $a$ equals $\dfrac{2}{3}$ of $b$, the ratio $a : b$ is:
  1. $3 : 5$
  2. $4 : 5$
  3. $5 : 3$
  4. $5 : 4$

Solution

$0.4 a = \dfrac{2}{3} b \Rightarrow \dfrac{a}{b} = \dfrac{2/3}{2/5} = \dfrac{2}{3} \times \dfrac{5}{2} = \dfrac{5}{3}$. Ratio $= 5 : 3$.

Asked in: IMO

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