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Question

If the harmonic mean between two positive numbers is to their geometric mean as 12:13. The numbers are in the ratio


A

12:13

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B

112:113

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C

4:9

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D

14:19

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Solution

The correct option is D

14:19


By the given condition if the numbers be a and b then
2aba+b:ab=12:13
2aba+b=1213
26ab=12(a+b).
Divisible by 2b
13ab=6(ab+1) put ab=x6x213x+6=0 (2x3)(3x2)=0x=32 or 23=ab
ab=94 or 49
Hence, the numbers are in the ratio 4:9


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