The present age of A is three times the present age of B. What is the ratio of the present age of B to the present age of A?

Introduction / Context:
This is a basic ratio question on ages. The present age of A is given as three times the present age of B. We are asked to express the ratio of B's age to A's age. This type of question checks your understanding of how to set up and interpret ratios correctly.

Given Data / Assumptions:

- A's present age is three times B's present age.
- We must find the ratio (B's age) : (A's age).
- Ages are positive real numbers.

Concept / Approach:
Rather than working with actual ages, we can represent B's age with a variable and then express A's age as a multiple of that variable. Ratios are then formed by comparing the two expressions. Since the actual numeric values are not needed, we only need the relative relationship between the two ages.

Step-by-Step Solution:
Step 1: Let B's present age be B years. Step 2: It is given that A's present age is three times B's age, so A's age = 3B years. Step 3: We are asked to find the ratio of the age of B to the age of A, i.e., B : A. Step 4: Substitute the expressions: B : A = B : 3B. Step 5: Divide both terms of the ratio by B (B ≠ 0) to simplify: B / B : 3B / B = 1 : 3.

Verification / Alternative check:
We can verify with a simple example. Suppose B is 5 years old. Then A would be 3 × 5 = 15 years old. The ratio of B's age to A's age is 5 : 15. Dividing both numbers by 5 yields 1 : 3, confirming our simplified ratio. Any other positive value for B will give the same simplified ratio because the relationship is strictly multiplicative.

Why Other Options Are Wrong:
Ratios like 1 : 2, 1 : 4, 2 : 3 or 3 : 1 do not correctly represent the statement "A is three times as old as B" when expressed as B : A. For instance, 3 : 1 would correspond to B being three times as old as A, which is the opposite of the given relationship.

Common Pitfalls:
A very common mistake is to invert the ratio and select 3 : 1 by thinking directly of "three times" without paying attention to the order requested in the question. Always read carefully whether the ratio is A : B or B : A before answering. The first term of the ratio must correspond to the first person mentioned in the question.

Final Answer:
The ratio of the present age of B to the present age of A is 1 : 3.