If the A.M. between two numbers exceeds their G.M. by 12 and the G.M. exceeds their H.M. by 36/5, then the greater of the two numbers is .
A
72
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B
54
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C
18
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D
48
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Solution
The correct option is B 54 Let the A.M., G.M., and H.M. of the two numbers a and b (a > b) be represented by A, G, and H respectively.
A-G=12 and G-H=36/5 G2=AH=(G+12)(G−365)⇒G2=G2−36G5+12G−4325⇒36G5−12G=−4325⇒−24G5=−4325⇒G=18∴A=30⇒a+b=60G=18⇒√ab=18⇒ab=324∴a=54andb=6asa>b