The geometric mean and harmonic mean of two non-negative observations are $10$ and $8$ respectively. Then what is the arithmetic mean of the observations equal to?

4

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9

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12.5

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25

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Solution

The correct option is B $12.5$
Relation between A.M, G.M and H.M is ${(G M)}^{2} = (A M) \times (H M)$
Given : $G M = 10$
$H M = 8$
So, $A M = \frac{10^{2}}{8} = \frac{100}{8} = 12.5$
Hence, $A M = 12.5$

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