Reverse ratio required: Given A : B = 2 : 3 and B : C = 4 : 5, compute C : A by first forming A : B : C and then inverting the order to obtain the required pair.

Introduction / Context: Often a problem asks for C : A rather than A : C. The proper method is still to combine the given ratios by matching the common term (here, B) and then read off the required order.

Given Data / Assumptions:

• A : B = 2 : 3.
• B : C = 4 : 5.

Concept / Approach: Make B the same in both ratios, derive A : B : C, and then express C : A directly from the obtained triple.

Step-by-Step Solution:

Verification / Alternative check: Subratios check: A : B = 8 : 12 = 2 : 3; B : C = 12 : 15 = 4 : 5.

Why Other Options Are Wrong: 8 : 15 reverses the order; 12 : 10, 8 : 5, and 5 : 8 do not match the combined ratio.

Common Pitfalls: Answering A : C instead of C : A, or failing to align B properly before concluding.

Final Answer: 15 : 8