CAT Duplicate ratio, triplicate ratio, sub duplicate ratio and sub triplicate ratio - Practice Questions & MCQ

These ratios involve raising the terms of the ratio to certain powers or extracting certain roots to create new ratios. 

Definitions:

1. Duplicate Ratio: The duplicate ratio of  a:b  is 

2. Triplicate Ratio: The triplicate ratio of a:b is

3. Sub Duplicate Ratio: The sub duplicate ratio of  a:b  is 

4. Sub Triplicate Ratio: The sub triplicate ratio of a:b is 

Foundation Building Questions:

Question:

The ratio of two numbers is 4:9. Find the duplicate ratio, the triplicate ratio, and the sub duplicate ratio of these numbers.

Solution:

Given Ratio: 4:9

1. Duplicate Ratio (Squaring both terms): 

2. Triplicate Ratio (Cubing both terms): 

3. Sub Duplicate Ratio (Square rooting both terms): 

Thus, the required ratios are:

- Duplicate Ratio: 16:81

- Triplicate Ratio: 64:729

- Sub Duplicate Ratio: 2:3

Tips and Tricks:

1. Understand the Terms: Duplicate, triplicate, sub duplicate, and sub triplicate are terms related to powers and roots. Don't confuse them.

2. Use Simplifications: If the given ratio can be simplified, do it before performing these operations to ease the calculation. 

3. Check the Context: These concepts may be used in context with other concepts like percentage change or comparison, so be ready to integrate them with other concepts in this chapter.

4. Memorise Definitions: Having a clear understanding of what each term means (duplicate means square, triplicate means cube, etc.) is crucial for quickly answering questions related to this concept.

5. Utilise Previously Covered Concepts: As seen in the previous year question, the ability to manipulate ratios (such as squaring or square rooting them) is an application of basic mathematical principles you've already learned. Connecting the dots between concepts can save time and enhance understanding.

6. Visualise If Needed: For those who find visual aids helpful, sketching a simple diagram or using colour coding for different ratios can assist in quick recall and comprehension.

This concept further strengthens the foundational understanding of ratios by manipulating them through mathematical operations. Practising with real-world problems and previous exam questions helps in cementing these concepts and understanding their practical applications.