Mathematics

Problem

Let

G

be the geometric mean of two positive numbers

a

and

b

, and

M

be the arithmetic mean of

\frac{1}{a}

and

\frac{1}{b}

. If

\frac{1}{M} : G

4 : 5

, then

a : b

can be: [JEE-MAIN ONLINE - 2014] (1) 2 : 3 (2) 1 : 4 (3) 1 : 2 (4) 3 : 4