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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, (m−n)2=(m+n)2−4mn ⇒(m−n)2=(68)2−4×256=3600 ⇒m−n=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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