Mastering Ratio and Proportion: Key Concepts and Problem Solving Techniques

Welcome to the second session on Ratio and Proportion, part of the Quantitative Ability series for IPMAT 2021. In this session, we will delve deeper into the concepts introduced in the previous session and solve various problems to enhance our understanding.

Recap of Previous Session

In the first part of this series, we covered the basics of ratio and proportion, including definitions and fundamental principles. It is crucial to have a solid grasp of these concepts as they form the foundation for solving more complex problems.

Engaging with the Audience

Before we dive into problem-solving, I encourage everyone to participate actively. Please feel free to share your thoughts and answers in the chat box as we progress through the session. Your engagement is vital for a fruitful learning experience.

Problem-Solving Techniques

Understanding Partnerships

We will start with a problem related to partnerships, which is a common application of ratios. Consider the following scenario:

• Aruna, Amul, and Alekh started a business together. Aruna invested 1/4 of the total capital, while Amul's investment was equal to Aruna's, and Alekh's investment was the remaining amount.
• If the annual profit of the business is 1280, we need to determine Amul's share of the profit.

To solve this, we can set up the equation based on their investments:

• Let the total capital be represented as 4x. Thus, Aruna's investment is x, Amul's is also x, and Alekh's is 2x.
• The total profit is distributed according to their investments. Therefore, Amul's share of the profit can be calculated as follows: