Ratio 1 | CAT Preparation 2024 | Arithmetic | Quantitative Aptitude

Summary

In this educational video, Ravi Prakash introduces the concepts of ratios, proportions, and their applications in mathematics. He explains the literal meaning of ratios, using examples like dividing 56 rupees between two people in a 4:3 ratio. Prakash further delves into combining ratios and illustrates how to find the combined ratio of multiple variables. He also discusses methods for converting ratios with fractions into whole numbers for easier calculation. The video serves as a comprehensive guide to understanding and applying ratios in various mathematical problems.

Takeaways

• 📚 The class focuses on the concepts of ratios, proportions, and their applications in mathematics.
• 🔢 Ratios are expressed as A:B and can be understood as dividing a quantity into parts according to the ratio.
• 💡 The script explains how to distribute a sum of money, like 56 rupees, among two people based on a given ratio.
• 📈 An example is provided to illustrate how to calculate the distribution of 171 rupees between two individuals with a ratio of 11:8.
• 🌐 The importance of maintaining the same multiple for each part when distributing according to a ratio is emphasized.
• 🔄 The script demonstrates how to simplify ratios by canceling out common factors to make calculations easier.
• ➡️ A method to combine multiple ratios is introduced, which involves aligning and adding the parts of each ratio.
• 🧩 The concept of finding a combined ratio when given separate ratios for different pairs of items is explained.
• 💡 The script teaches how to convert ratios involving fractions into whole numbers by finding the least common multiple (LCM).
• 📝 A practical problem-solving approach is showcased, where the distribution of money is calculated based on given ratios and conditions.

Q & A

What is the basic concept of a ratio as explained in the script?

A ratio is a way to compare two or more quantities. It is written in the form 'a to b', which means 'a' is to 'b' as in the fraction 'a/b'. It can also represent how a whole is divided into parts, such as dividing 56 rupees into two persons 'a' and 'b' in the ratio of 4:3.

How does the script illustrate dividing money in a ratio?

The script uses the example of dividing 56 rupees between two persons 'a' and 'b' in the ratio of 4:3. It explains that if the total parts are 7 (4+3), each part is worth 56/7 = 8 rupees, so 'a' gets 4 parts (32 rupees) and 'b' gets 3 parts (24 rupees).

What is the meaning of 'k' in the context of the script when dealing with ratios?

In the script, 'k' is used as a variable to represent a common multiple that scales the ratio parts. For example, if 'a' gets 7 parts and 'b' gets 9 parts, 'a' can be represented as 7k and 'b' as 9k, where 'k' is the common multiple that, when multiplied by the ratio parts, gives the actual values.

How does the script explain combining ratios?

The script explains combining ratios by aligning the parts that correspond to the same entity across different ratios. For example, if 'a' has a ratio of 7 to 'b' and 'b' has a ratio of 8 to 'c', then 'a', 'b', and 'c' can be combined into a single ratio by making 'b' the common part and adjusting 'a' and 'c' accordingly.

What is the significance of the least common multiple (LCM) in combining ratios?

The LCM is significant in combining ratios because it helps to convert the parts of the ratios into whole numbers, which are easier to work with. By multiplying each part of the ratio by the LCM of the denominators, the fractions are converted into integers, simplifying calculations.

How does the script handle ratios where the parts are not whole numbers?

The script suggests converting the fractional parts of a ratio into whole numbers by multiplying by a common factor, typically the LCM of the denominators of the fractions, to make the calculations simpler and more straightforward.

What is the strategy for solving problems where ratios are given as fractions?

The script recommends converting the fractional ratios into whole numbers by multiplying with the LCM of the denominators. This conversion simplifies the problem-solving process, making it easier to apply the concepts of ratios and proportions.

How does the script demonstrate the application of combined ratios in a problem?

The script demonstrates the application of combined ratios by solving a problem where a certain amount is distributed among 'a', 'b', 'c', and 'd' in a given ratio. It shows how to find the individual amounts by understanding the combined ratio and using it to set up equations that can be solved for the values.

What is the method to find the individual values when given a combined ratio and a condition like one value being less than another?

The script suggests setting up the combined ratio and then using the given condition to find the difference in parts. By understanding the value of one part (unit) of the ratio, the individual values can be calculated by multiplying the number of parts each entity has by the value of one part.

How does the script approach a problem involving ratios and ages?

The script approaches age-related ratio problems by first finding the combined ratio of the ages and then using the given age difference to determine the value of one unit of the ratio. By multiplying the number of units each person has by the value of one unit, the individual ages can be calculated.