Question

(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 )

# 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

Solution