The ratio of the geometric mean and arithmetic mean of two numbers is 3:5, find the ratio of the smaller number to the larger number.

Step-by-step explanation:

Let the numbers be x,y, where x>y

The geometric mean is

The Arithmetic mean is

The ratio of the geometric mean and arithmetic mean of two numbers is 3:5.

We can write the equation;

or

l

and

or

Make y the subject in equation 2

Put equation 3 in 1

When x=1, y=10-1=9

When x=9, y=10-9=1

Therefore x=9, and y=1

The ratio of the smaller number to the larger number is