Two numbers are in the ratio 3 : 5. If the sum of the numbers is 184, find the difference between the numbers.

Let the two numbers be 3x and 5x.

The sum of the two numbers is 3x + 5x = 184.
Combining like terms, we get 8x = 184.
Dividing both sides by 8, we find x = 23.
The first number is 3x = 3(23) = 69.
The second number is 5x = 5(23) = 115.
The difference between the numbers is 115 - 69 = <<115-69=46>>46. Answer: \boxed{46}.