Short Trick to find (mX + nY) (pX + qY) given x y

Duration: 10 min

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Inside: a video lesson and guided study material.

Module outline

  1. About the Course: About the Course
  2. Paper-1 & 2 | Basic Numeracy: अनुपात और समानुपात / Ratio and Proportion, Divisibility Rules, मिश्रण और एलिगेशन / Mixture and Alligation, Permutation and Combination, Logarithm, संख्या पद्धति / Number System, महत्तम समापवर्तक और लघुत्तम समापवर्त्य / HCF and LCM, Sequence and Series (Series), समय, चाल और दूरी / Time, Speed and Distance, प्रतिशत / Percentage, औसत / Average, घन क्षेत्रमिति / Solid Mensuration, Age Problems, Arithmetic, Statistics, Probability, लाभ, हानि और बट्टा / Profit, Loss and Discount, साधारण और चक्रवृद्धि ब्याज / Simple and Compound Interest, Partnership, Speed Mathematics and Basic Mathematics, Algebra, सरलीकरण, घातांक और करणी / Simplification, Indices and Surds, समय और कार्य / Time and Work, Pipe and Cistern, RSSB Specific Videos - Basic Numeracy, समुच्चय, संबंध, फलन और विविक्त गणित / Sets, Relations, Functions and Discrete Mathematics, संख्या पद्धति और संख्या सिद्धांत / Number Systems and Number Theory, निर्देशांक ज्यामिति, सदिश और त्रिविमीय ज्यामिति / Coordinate Geometry, Vectors and 3D Geometry, बहुपद, समीकरण और सम्मिश्र संख्याएँ / Polynomials, Equations and Complex Numbers
  3. Paper-1 & 2 | Data Interpretation: आँकड़ा निर्वचन / Data Interpretation
  4. Paper-1 & 2 | General Mental Ability: Mental Ability, RSSB Specific Videos - Mental Ability
  5. Paper-1 & 2 | Logical Reasoning and Analytical Ability: श्रेणी / Series, कूट लेखन एवं कूट वाचन / Coding-Decoding, Data Sufficiency, अशाब्दिक तर्क / Non-Verbal Reasoning, Syllogisms, बैठक व्यवस्था एवं पहेलियाँ / Seating Arrangement and Puzzles, रक्त संबंध / Blood Relations, दिशा एवं दूरी / Direction and Distance, Analytical Reasoning (Counting Figures Reasoning), गणितीय संक्रियाएँ एवं लुप्त संख्या / Mathematical Operations and Missing Numbers, कैलेंडर एवं घड़ी / Calendar and Clock, Clock, घन, पासा एवं आकृतियों की गिनती / Cubes, Dice and Figure Counting, वेन आरेख, न्याय वाक्य एवं असमानता / Venn Diagrams, Syllogism and Inequalities, सादृश्यता एवं वर्गीकरण / Analogy and Classification, क्रम एवं रैंकिंग / Order and Ranking, कथन आधारित तार्किक विवेचन / Statement-Based Reasoning, Data Arrangement, वर्णमाला एवं संख्या परीक्षण / Alphabet and Number Test, Crypt Arithmetic
  6. Paper-1 & 2 | Decision Making and Problem Solving: आँकड़ों की पर्याप्तता एवं निर्णय क्षमता / Data Sufficiency and Decision Making
  7. Paper-1 | General Science: वैज्ञानिक उपलब्धियाँ और अनुसंधान / Scientific Achievements and Research, Biology, Chemistry, RSSB Specific Videos
  8. Paper-1 | General Awareness: राज्य विशेष सामान्य ज्ञान / State-Specific General Knowledge, समसामयिकी / Current Affairs
  9. Paper - 2 | Digital Logic Systems: Digital Systems & Boolean Basics, Logic Gates & Hardware, Combinational Circuit, Sequential Circuits
  10. Paper-2 | Database Management System: Basics of DBMS, ER Diagram, Relational Model & Functional Dependencies, Keys & Integrity Constraints, Normalization (1NF - BCNF), Decomposition Properties & 4NF, Relational Calculus, Relational Algebra, SQL, NoSQL
  11. Paper-2 | Data Structures & Algorithms: Introduction to DS, Array, Stack, Queue, Linked List, Tree, Graphs, Algorithm Analysis, Sorting Algorithms, Intro to Compilers, Hashing
  12. Paper 2 | Data Communication and Network Security: Introduction to CN, Data Communication, Data Link Layer - Ethernet, DLL: Error Control, Net Layer: IPv4 & Proto, Net Layer: IP Addressing, Application Layer, Hardware basics, Network Security, Ethical Hacking
  13. Paper-2 | Operating Systems: Introduction to OS, Process Management, Memory Management, File Management, Deadlock
  14. Paper-2 | Computer Organization and Architecture: Basics of COA, Floating Point Rep, Cache Memory Organization, Input Output Organisation, Instr Formats & Modes, Control Unit Design, Register Transfer and Microoperations, Programming the Basic Computer, Number System, Number Representation
  15. Paper 2 | System Analysis and Design: Fundamentals of Systems and Information Systems, Fundamentals of Software Engineering, SDLC and Development Approaches, Software Documentation and Software Requirements Specification (SRS), SDD and Quality Assurance, Security, Risk Management & Maintenance, Software Testing
  16. Paper-2 | C Programming: C Fundamentals, Control Flow, Functions, Arrays & Pointers, Storage Classes, Structures & Enums, DMA, Macros, Scoping & File Handling
  17. Paper 2 | OOPS , C++ , JAVA: Language Design, OOPS with C++, Java, .Net Programming, Java Fundamentals
  18. Paper 2 | Python: Introduction to Python, Tokens, Variables, Data Types, I/O, Operators & Expressions, Control Flow & Looping, Collections & Strings, Functions & Modules, File Handling & Data Analysis
  19. Emerging Trends and AI: Emerging Tech Trends, कंप्यूटर के मूल सिद्धांत / Computer Fundamentals, व्यापार, विपणन एवं उपभोक्ता संरक्षण / Trade, Marketing and Consumer Protection
  20. Paper-2 | Data Processing (Ms-Office): MS Office Applications, कंप्यूटर सॉफ़्टवेयर / Computer Software, ऑपरेटिंग सिस्टम / Operating System, वर्ड प्रोसेसिंग (MS Word) / Word Processing (MS Word), प्रेज़ेंटेशन (MS PowerPoint) / Presentation Software (MS PowerPoint)
  21. Paper-2 | Internet and Web Technologies: HTML Basics, CSS, XML, JavaScript-Basics, Internet Fundamentals, Protocols & Services, Web Publishing & Hosting, Server Side & Security, Emerging Technologies, Terms & Abbreviations, Cyber Threats and Malware Attacks, Role of Internet and Web Services, Security in Mobile and Wireless Computing, साइबर सुरक्षा / Cyber Safety and Security, कंप्यूटर नेटवर्क / Computer Networks
  22. Paper 2 | Pedagogy: वृद्धि और विकास / Growth and Development, विकास के सिद्धांत / Theories of Development, Concept of Pedagogy, समावेशी शिक्षा / Inclusive Education, Experiential Pedagogy, आकलन और मूल्यांकन / Assessment and Evaluation, संज्ञानात्मक प्रक्रियाएँ / Cognitive Processes, समाजीकरण और जेंडर / Socialisation and Gender, National Education Policy (NEP) 2020
  23. Live Classes: RSSB Live Sessions
  24. Paper 1 - Full Mock Tests:
  25. Paper 2 - Full Mock Tests:
  26. BCI Previous Year Papers:
AI summary & chapters

AI Summary

An AI-generated summary of this video lecture.

This educational video, presented by Yash Jain from Knowledge Gate Eduventures, focuses on the mathematical topic of "Ratio & Proportion". The lecture begins by defining a ratio as a comparison of two quantities, visually supported by a slide with colorful dots. The instructor then introduces a general algebraic problem type: given a ratio x:y, find the value of a compound ratio (mx+ny):(px+qy) where m, n, p, and q are constants. He demonstrates this concept with a sample ratio x/y = 5/7. The core of the lecture involves solving specific numerical problems using this general framework. The first problem asks to find 3x+2y : 2x+5y given x:y = 2:3. The instructor meticulously solves this using multiple methods, including direct substitution and assuming a constant of proportionality (k). He then applies the same logic to a second problem involving subtraction: finding 3x-7y : 9x-11y given x:y = 7:9. The video serves as a practical guide for students preparing for exams involving ratio and proportion problems.

Chapters

  1. 0:00 – 2:00 00:00-02:00

    The video starts with a title slide featuring the text "RATIO & PROPORTION" and a 3D pie chart. The instructor introduces the definition of a ratio as "a comparison of 2 quantities", shown on a slide with colorful dots representing parts and wholes. He then presents a general problem statement on a pink background with space-themed doodles: "Given x : y, find (mx + ny) : (px + qy) where m,n,p,q are constants". To make this concrete, he writes a specific example on the top right: x/y = 5/7. This section sets the theoretical foundation for the algebraic manipulation of ratios that follows. The slide background is pink with space-themed doodles like a rocket and a planet.

  2. 2:00 – 5:00 02:00-05:00

    The instructor transitions to a specific numerical question: "If x : y = 2 : 3, find the value of 3x + 2y : 2x + 5y ?". He begins the solution by writing the ratio as a fraction x/y = 2/3. He then attempts to substitute x = 2y/3 into the target expression (3x+2y)/(2x+5y). He writes out the substitution clearly: 3[2y/3] + 2y in the numerator and 2[2y/3] + 5y in the denominator. He then factors out 'y' from both the numerator and the denominator, showing that y cancels out, leaving a numerical expression. This demonstrates the first method of solving such problems. He also writes the final simplified form on the board.

  3. 5:00 – 10:00 05:00-10:00

    Continuing the solution, the instructor simplifies the expression to (3(2/3) + 2) / (2(2/3) + 5). He calculates the numerator as 2 + 2 = 4 and the denominator as 4/3 + 5 = 19/3. This results in 4 / (19/3), which simplifies to 12/19. He then introduces a second, often faster method: assuming x = 2k and y = 3k. Substituting these into the expression gives (3(2k) + 2(3k)) / (2(2k) + 5(3k)) = (6k + 6k) / (4k + 15k) = 12k / 19k = 12/19. He then moves to a new problem: "If x : y = 7 : 9, find the value of 3x - 7y : 9x - 11y ?". He solves this by substituting x=7 and y=9 directly into the expression, showing the calculation (21-63)/(63-99). He writes the intermediate steps clearly on the screen.

  4. 10:00 – 10:17 10:00-10:17

    The instructor completes the calculation for the second problem. He writes (3(7) - 7(9)) / (9(7) - 11(9)) which equals (21 - 63) / (63 - 99). This simplifies to -42 / -36. He simplifies this fraction to 7/6. The video concludes with a black screen displaying "THANKS FOR WATCHING" in white and orange text, signaling the end of the lecture. The instructor is visible in the bottom right corner throughout the problem-solving sections, providing verbal guidance and ensuring students follow the steps.

The lecture effectively bridges the gap between abstract ratio concepts and practical problem-solving. By starting with a general formula and then applying it to specific numerical examples, the instructor reinforces the method of substitution and simplification. The use of multiple methods (substitution vs. assuming constants) for the same problem highlights the flexibility in solving ratio problems, a key skill for exams. The progression from simple definitions to complex algebraic expressions ensures a comprehensive understanding of the topic. The instructor's clear handwriting and step-by-step approach make the complex algebra accessible to students.

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