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Q.

Let G be the geometric mean of two positive numbers a and b, and M be the arithmetic mean of 1a and 1b. If 1M:G is 4 : 5, then a : b can be

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a

1 : 4

b

3 : 4

c

2 : 3

d

1 : 2

answer is A.

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Detailed Solution

G=ab    M=1a+1b2=b+a2ab 1M:G=4:5   ⇒2ab(a+b)ab=45⇒aba+b=25 25 ab=4a2+4b2+8ab⇒4a2-17ab+4b2=0 ⇒(4a-b)(a-4b)=0 ⇒ 4a=b or a=4b

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