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Question

If 34 and 16 are the arithmetic mean and geometric mean of two positive numbers respectively, Find the numbers


A

125 and 5

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B

64 and 4

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C

60 and 68

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D

16 and 256

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Solution

The correct option is B

64 and 4


Let the two numbers be m and n. Then
Arithmetic Mean = 34
m+n2=34
m+n=68
And
Geometric Mean = 16
mn=16
mn=256 ............................... (i)
Therefore, (mn)2=(m+n)24mn
(mn)2=(68)24×256=3600
mn=60 ............................... (ii)
On solving (i) and (ii), we get m = 64 and n = 4.
Hence, the required numbers are 64 and 4.


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