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Question

For two positive real number's a and b, If the A.M. exceeds their G.M. by 2 and the G.M. exceeds their H.M. by 85, then the value of a+b is

A
20
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B
30
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C
40
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D
50
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Solution

The correct option is A 20
Let the A.M., G.M. and H.M. be A,G and H respectively,
AG=2(1)
GH=85(2)
We know that,
G2=AH
Using equation (1) and (2),
G2=(G+2)(G85)G2=G2+(285)G1652G5=165G=8
Now,
A=a+b2=2+Ga+b=20

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