What is the compounded ratio obtained by combining the ratios (2 : 3), (6 : 11) and (11 : 2)?

Introduction / Context:
This question checks the understanding of compounded ratio, which is formed by multiplying corresponding terms of two or more ratios. It is a straightforward but important concept in ratio and proportion used in many competitive exams.

Given Data / Assumptions:

• First ratio = 2 : 3
• Second ratio = 6 : 11
• Third ratio = 11 : 2
• We have to find the compounded ratio of these three ratios.

Concept / Approach:
The compounded ratio of several ratios is obtained by multiplying together all the antecedents (first terms) to get the new antecedent and multiplying together all the consequents (second terms) to get the new consequent. After that, we simplify the resulting ratio to its lowest terms by dividing both sides by their greatest common divisor.

Step-by-Step Solution:
Step 1: Identify the antecedent and consequent of each ratio. Step 2: Antecedents are 2, 6 and 11. Consequents are 3, 11 and 2. Step 3: Multiply the antecedents: 2 * 6 * 11 = 132. Step 4: Multiply the consequents: 3 * 11 * 2 = 66. Step 5: So the compounded ratio before simplification is 132 : 66. Step 6: Divide both sides by their greatest common divisor 66 to simplify. Step 7: 132 ÷ 66 = 2 and 66 ÷ 66 = 1, so the simplified compounded ratio is 2 : 1.

Verification / Alternative check:
We can quickly check by seeing that 132 : 66 clearly has a factor of 66 common to both terms. Dividing both by 66 is exact and yields 2 : 1. No further simplification is possible, so 2 : 1 is the final simplest form of the compounded ratio.

Why Other Options Are Wrong:
Ratios like 1 : 2, 11 : 24 or 36 : 121 come from incorrect multiplication or from reducing with a wrong common factor. For example, 11 : 24 would suggest that 132 and 66 were not multiplied correctly, while 36 : 121 would correspond to a completely different pair of products. These do not match the actual arithmetic of 2 * 6 * 11 and 3 * 11 * 2.

Common Pitfalls:
A common error is to add ratios instead of multiplying them or to mix antecedents with consequents incorrectly. Some students also forget to simplify the final ratio to lowest terms. Remember that compounded ratio must be formed by multiplying corresponding terms and then always simplified by dividing by the greatest common divisor.

Final Answer:
The compounded ratio is 2 : 1.