Brief Summary
This YouTube video by SSC Wallah provides a comprehensive guide to ratio and proportion, essential for arithmetic math and various exams. The instructor emphasizes patience in learning and encourages viewers to practice with pen and paper. The lecture covers basic definitions, comparisons, and manipulations of ratios, including multiplying, dividing, and distributing values. It also explains how to merge ratios using common elements and shifting methods, and addresses complex ratio problems involving combined ratios and fractional ratios. The video concludes with practice questions from previous CHSL exams, covering topics like distribution, merging ratios, and proportional relationships.
- Importance of ratio and proportion in arithmetic math.
- Methods for merging ratios and solving complex problems.
- Practical application through previous year exam questions.
Introduction to Ratio and Proportion
The instructor begins by highlighting the importance of ratio and proportion as a fundamental concept in arithmetic math, alongside percentage. This chapter is crucial for exams and has broad applications across various mathematical problems. The instructor promises practice sessions and resources, including PDF notes on the application, to enhance understanding and speed.
Basic Concepts of Ratio
The lecture defines a ratio as a comparison between two or more quantities. It explains that ratios can be manipulated by multiplying or dividing by the same value without changing the proportion. The instructor illustrates this with examples, showing how to find equivalent ratios and solve for unknown values.
Parts of a Ratio and Distribution
This section explains how to determine the parts of a whole that each component of a ratio represents. For a ratio A:B, the part of A is A/(A+B) and the part of B is B/(A+B). The instructor extends this concept to distribution problems, demonstrating how to divide a total quantity into parts according to a given ratio, using examples involving mixtures of milk, water, and wine.
Merging Ratios
The instructor introduces the concept of merging two ratios, A:B and B:C, into a single ratio A:B:C. The first method involves making the common element (B) equal in both ratios. The second method, known as the shifting method, involves writing the ratios in a specific format and shifting adjacent numbers to fill vacant places, then multiplying to find the combined ratio.
Advanced Ratio Problems
This section covers more complex ratio problems, such as finding the ratio A:B:C when given A:(B+C) and B:(C+A). The key is to ensure that the total quantity (A+B+C) is the same in both expressions. If not, adjust the ratios to equalize the totals before comparing individual components.
Fractional Ratios and Proportionality
The lecture addresses ratios involving fractions, emphasizing that ratios should not be left in fractional form. To resolve this, find the least common multiple (LCM) of the denominators and multiply each term in the ratio by the LCM. The instructor also covers scenarios where expressions like 2A = 3B = 5C are given, explaining how to find the ratio A:B:C by taking the reciprocals of the coefficients.
Proportions: Direct, Third and Fourth
The instructor explains the concepts of first, second, third, and fourth proportions. The middle proportion is also discussed, with the formula B = √(AC) for a continuous proportion A:B = B:C. Examples are provided to illustrate how to calculate these proportions.
Practice Questions: Part 1
The instructor begins solving practice questions from previous CHSL exams. These questions cover a range of topics, including merging ratios, distributing amounts according to ratios, and dealing with fractional ratios. The instructor emphasizes the importance of understanding the question and applying the appropriate method.
Practice Questions: Part 2
Continuing with practice questions, the instructor tackles problems involving multiple ratios and distributions. The problems include scenarios with three or more variables and require careful application of ratio concepts to arrive at the correct solution.
Practice Questions: Part 3
The session continues with more practice questions, focusing on scenarios where quantities are added or subtracted from ratios. These problems often require setting up equations and solving for unknown variables.
Practice Questions: Part 4
The instructor solves additional practice questions, including those that involve adding a number to each term of a ratio to make it proportional. The instructor recommends using the option method to solve this type of question.
Practice Questions: Part 5
More practice questions are addressed, including a complex problem involving the distribution of money among several individuals with varying conditions. The instructor emphasizes the importance of carefully reading and understanding the question before attempting to solve it.
Practice Questions: Part 6
The lecture continues with additional practice questions, including a problem involving coins and their values. The instructor guides viewers through the steps to solve these problems, emphasizing the importance of converting all values to the same unit.
Practice Questions: Part 7
The instructor tackles problems where water or milk is added to a mixture, changing the ratio. The key is to recognize that the quantity of one component (usually milk) remains constant, allowing for the establishment of a common base for comparison.
Practice Questions: Part 8
The session continues with practice questions involving the removal and addition of quantities to a mixture. The instructor introduces the cross product method as a versatile technique for solving these types of problems.
Practice Questions: Part 9
The instructor continues to solve practice questions, demonstrating the application of the cross product method in various scenarios. The importance of understanding the underlying concepts and applying the appropriate method is emphasized.
Practice Questions: Part 10
The lecture continues with more practice questions, including a problem involving the distribution of money among several individuals with varying conditions. The instructor emphasizes the importance of carefully reading and understanding the question before attempting to solve it.
Practice Questions: Part 11
The session continues with additional practice questions, including those that involve adding a number to each term of a ratio to make it proportional. The instructor emphasizes the importance of understanding the question and applying the appropriate method.
Practice Questions: Part 12
More practice questions are addressed, including a problem involving the distribution of money among several individuals with varying conditions. The instructor emphasizes the importance of carefully reading and understanding the question before attempting to solve it.
Practice Questions: Part 13
The instructor solves additional practice questions, including those that involve finding the ratio of land and water in the southern hemisphere given the ratio for the entire earth and the northern hemisphere.
Practice Questions: Part 14
The session continues with practice questions, including a problem involving the division of a picture into two parts with different ratios of blue and yellow colors.
Practice Questions: Part 15
The instructor tackles problems where two containers with different ratios of milk and water are mixed. The key is to equalize the capacities of the containers before adding the quantities.
Practice Questions: Part 16
The lecture continues with more practice questions, including a problem involving the number of male and female employees in an office and their technical skills. The instructor emphasizes the importance of considering the total value to simplify the calculations.
Practice Questions: Part 17
The session continues with additional practice questions, including those that involve finding the ratio of the original numbers after adding a certain value. The instructor emphasizes the importance of understanding the question and applying the appropriate method.
Practice Questions: Part 18
More practice questions are addressed, including a problem involving the distribution of sweets among several customers with varying conditions. The instructor emphasizes the importance of carefully reading and understanding the question before attempting to solve it.
Practice Questions: Part 19
The instructor solves additional practice questions, including those that involve finding the ratio of the original numbers after adding a certain value. The instructor emphasizes the importance of understanding the question and applying the appropriate method.
Practice Questions: Part 20
The session continues with practice questions, including a problem involving the distribution of money among several individuals with varying conditions. The instructor emphasizes the importance of carefully reading and understanding the question before attempting to solve it.
Practice Questions: Part 21
More practice questions are addressed, including a problem involving a diamond broken into three pieces. The instructor emphasizes the importance of understanding the question and applying the appropriate method.
Practice Questions: Part 22
The instructor solves additional practice questions, including those that involve finding the ratio of the original numbers after adding a certain value. The instructor emphasizes the importance of understanding the question and applying the appropriate method.
Practice Questions: Part 23
The session continues with practice questions, including a problem involving the distribution of money among several individuals with varying conditions. The instructor emphasizes the importance of carefully reading and understanding the question before attempting to solve it.
Practice Questions: Part 24
More practice questions are addressed, including a problem involving the distribution of sweets among several customers with varying conditions. The instructor emphasizes the importance of carefully reading and understanding the question before attempting to solve it.
Practice Questions: Part 25
The instructor solves additional practice questions, including those that involve finding the ratio of the original numbers after adding a certain value. The instructor emphasizes the importance of understanding the question and applying the appropriate method.
Practice Questions: Part 26
The session continues with practice questions, including a problem involving the distribution of money among several individuals with varying conditions. The instructor emphasizes the importance of carefully reading and understanding the question before attempting to solve it.
Practice Questions: Part 27
More practice questions are addressed, including a problem involving a diamond broken into three pieces. The instructor emphasizes the importance of understanding the question and applying the appropriate method.
Practice Questions: Part 28
The instructor solves additional practice questions, including those that involve finding the ratio of the original numbers after adding a certain value. The instructor emphasizes the importance of understanding the question and applying the appropriate method.
Practice Questions: Part 29
The session continues with practice questions, including a problem involving the distribution of money among several individuals with varying conditions. The instructor emphasizes the importance of carefully reading and understanding the question before attempting to solve it.
Practice Questions: Part 30
More practice questions are addressed, including a problem involving a diamond broken into three pieces. The instructor emphasizes the importance of understanding the question and applying the appropriate method.
Practice Questions: Part 31
The instructor solves additional practice questions, including those that involve finding the ratio of the original numbers after adding a certain value. The instructor emphasizes the importance of understanding the question and applying the appropriate method.
Practice Questions: Part 32
The session continues with practice questions, including a problem involving the distribution of money among several individuals with varying conditions. The instructor emphasizes the importance of carefully reading and understanding the question before attempting to solve it.
Practice Questions: Part 33
More practice questions are addressed, including a problem involving a diamond broken into three pieces. The instructor emphasizes the importance of understanding the question and applying the appropriate method.
Practice Questions: Part 34
The instructor solves additional practice questions, including those that involve finding the ratio of the original numbers after adding a certain value. The instructor emphasizes the importance of understanding the question and applying the appropriate method.
Practice Questions: Part 35
The session continues with practice questions, including a problem involving the distribution of money among several individuals with varying conditions. The instructor emphasizes the importance of carefully reading and understanding the question before attempting to solve it.
Practice Questions: Part 36
More practice questions are addressed, including a problem involving a diamond broken into three pieces. The instructor emphasizes the importance of understanding the question and applying the appropriate method.
Practice Questions: Part 37
The instructor solves additional practice questions, including those that involve finding the ratio of the original numbers after adding a certain value. The instructor emphasizes the importance of understanding the question and applying the appropriate method.
Practice Questions: Part 38
The session continues with practice questions, including a problem involving the distribution of money among several individuals with varying conditions. The instructor emphasizes the importance of carefully reading and understanding the question before attempting to solve it.
Practice Questions: Part 39
More practice questions are addressed, including a problem involving a diamond broken into three pieces. The instructor emphasizes the importance of understanding the question and applying the appropriate method.
Practice Questions: Part 40
The instructor solves additional practice questions, including those that involve finding the ratio of the original numbers after adding a certain value. The instructor emphasizes the importance of understanding the question and applying the appropriate method.
Conclusion and Next Steps
The instructor concludes the session, emphasizing the importance of patience and continuous learning. He announces that the next topic will be profit and loss with discount, and promises to bring practice sessions for previously covered topics.
