If a : b = 3 : 5 and a : c = 5 : 7, what is the value of b : c?

Question: If a : b = 3 : 5 and a : c = 5 : 7, what is the value of b : c?

Solution:
a : b = 3 : 5 = (3 × 5) : (5 × 5) = 15 : 25
a : c = 5 : 7 = (5 × 3) : (7 × 3) = 15 : 21

a : b : c = 15 : 25 : 21
∴ b : c = 25 : 21
= 25 : 21