116. Arithmetic mean progression of...
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116. Arithmetic mean progression of two numbers is 6 more than the geometric mean progression of the numbers. The ratio of numbers is 9:1, then numbers are (a) 27, 3 (b) 16,3 (c) 15,4 (d) None of these

JEE/Engineering Exams
Maths
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(a) Let ( a ) and ( b ) be numbers. Now, Arithmetic mean ( =frac{a+b}{2} ) and Geometric mean ( =sqrt{a b} ) According to question, Arithmetic mean ( = ) Geometric mean +6 ( Rightarrow quad frac{a+b}{2}=sqrt{a b}+6 ) and ( quad frac{a}{b}=frac{9}{1} ) ( Rightarrow quad a=9 b ) From Eqs. (i) and (ii), we get ( frac{9 b+b}{2}=sqrt{9 b^{2}}+6 ) ( Rightarrow ) ( 5 b=3 b+6 ) ( Rightarrow quad 2 b=6 ) ( Rightarrow quad b=3 ) ( because quad a=9 b=9 times 3=27 )
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