Aspire Faculty ID #15390 · Topic: MAH MCA CET 2023 · Just now
MAH MCA CET 2023

$x$ is a G.M., $y$ is a H.M. of two numbers. If $\dfrac{x}{y} = \dfrac{5}{4}$, then the numbers are in ratio

Solution

Let numbers be $a, b$. Then $\dfrac{x}{y} = \dfrac{\sqrt{ab}}{\dfrac{2ab}{a+b}} = \dfrac{a+b}{2\sqrt{ab}} = \dfrac{5}{4}$. Let $\dfrac{a}{b} = r$, then $\dfrac{r+1}{2\sqrt{r}} = \dfrac{5}{4}$. On solving, $r = 4$ or $\dfrac{1}{4}$. Hence ratio = $1:4$.
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