If one-third of A, one-fourth of B, and one-fifth of C are equal, find the ratio A : B : C.

Introduction / Context:
When scaled parts of quantities are equal, express each original quantity in terms of a common variable. If A/3 = B/4 = C/5 = k, then A, B, C can be written in terms of k and their ratio found directly.

Given Data / Assumptions:

• A/3 = B/4 = C/5
• All quantities are positive.

Concept / Approach:
Let the common value be k. Then A = 3k, B = 4k, C = 5k. Their ratio is simply 3 : 4 : 5 after canceling k.

Step-by-Step Solution:
Assume A/3 = B/4 = C/5 = kA = 3k, B = 4k, C = 5kA : B : C = 3 : 4 : 5

Verification / Alternative check:
Compute A/3, B/4, C/5 with A:B:C = 3:4:5: each gives k, confirming consistency.

Why Other Options Are Wrong:
They invert or permute the order incorrectly; 1/3 : 1/4 : 1/5 restates the given scaled parts, not A:B:C.

Common Pitfalls:
Writing A = k/3 instead of A = 3k; mixing up which number multiplies k.

Final Answer:
3 : 4 : 5