Simple Ratio — Find the Antecedent Two numbers are in the ratio 2 : 3. If the consequent (the second term) is 24, determine the antecedent (the first term).

Introduction / Context:
Understanding the terms antecedent (first) and consequent (second) is fundamental in ratio questions. Once you recognize which term is fixed, you can scale the entire ratio by the same factor to find the unknown counterpart accurately and quickly.

Given Data / Assumptions:

• Ratio of two numbers: 2 : 3.
• Consequent (second term) = 24.
• Find the antecedent (first term).

Concept / Approach:
Let the numbers be 2k and 3k. If 3k = 24, then k = 24/3 = 8. The antecedent is 2k = 16. This direct scaling avoids any unnecessary computations and ensures proportional consistency.

Step-by-Step Solution:
Represent numbers as 2k and 3k.Set 3k = 24 → k = 8.Antecedent = 2k = 2 * 8 = 16.Answer: 16.

Verification / Alternative check:
Check ratio: 16 : 24 reduces by dividing both by 8 to 2 : 3, confirming the correct scaling factor.

Why Other Options Are Wrong:
36 and 48 would correspond to wrong multipliers for the first term; 72 is 3 times 24, mixing positions; 12 corresponds to k = 6, which would make the consequent 18, not 24.

Common Pitfalls:
Confusing antecedent with consequent; scaling the wrong term; failing to simplify the resulting ratio to confirm correctness.

Final Answer:
16