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+1 vote

If the harmonic mean between two positive numbers is to their geometric mean as $12 : 13$, then the numbers could be in the ratio:

- $12: 13$
- $1/12: 1/13$
- $4:9$
- $2:3$

+1 vote

Best answer

We know :

a) Harmonic mean of two positive numbers a and b = 2ab/(a + b)

b) Geometric mean of two positive numbers a and b = √ab

So given , H.M. / G.M. = 12 / 13

==> [2ab / (a+b)] / √ab = 12 / 13

==> √ab / (a+b) = 6 / 13

==> ab / (a+b)^{2} = 36 / 169

==> a = 4k and b = 9k

**Hence the ratio a : b = 4 : 9**

**Hence C) should be the correct option.**

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