Three positive numbers a, b, c are in continued proportion, with $a = 12$ and $c = 75$. What is $(a + b) : (b + c)$?

Explanation

1. 01

   Continued proportion means $a : b = b : c$, so $b^2 = ac = 12 \times 75 = 900$ and $b = 30$.

2. 02

   $(a + b) : (b + c) = 42 : 105 = 2 : 5$.