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

Duration: 10 min

This video lesson is available to enrolled students.

Return to /learn/NTA-UGC-NET-PAPER---1/paper-1-unit-5-mathematical-reasoning-and-aptitude/mixture-and-alligation/ratio/asset-short-trick-to-find-mx-ny-px-qy-given-x-y after enrolling

Inside: a video lesson and guided study material.

Module outline

  1. Paper - 1 | Unit - 1 | Teaching Aptitude: Concept and Objectives of Teaching / शिक्षण की अवधारणा एवं उद्देश्य, Levels of Teaching / शिक्षण के स्तर, Learner's Characteristics / शिक्षार्थी की विशेषताएँ, Learning: Nature and Theories / अधिगम: प्रकृति एवं सिद्धांत, Cognition, Memory and Metacognition / संज्ञान, स्मृति एवं अधिसंज्ञान, Factors Affecting Teaching / शिक्षण को प्रभावित करने वाले कारक, Effective Teaching and the Teacher / प्रभावी शिक्षण एवं शिक्षक, Instructional Objectives and Lesson Planning / अनुदेशनात्मक उद्देश्य एवं पाठ नियोजन, Methods of Teaching / शिक्षण विधियाँ, Offline and Online Teaching Methods / ऑफ़लाइन एवं ऑनलाइन शिक्षण विधियाँ, Teaching Support System / शिक्षण सहायक प्रणाली, Evaluation Systems / मूल्यांकन प्रणाली, Sāṃkhya / सांख्य, Individual Behaviour / व्यक्तिगत व्यवहार, Human Resource Management / मानव संसाधन प्रबंधन, Domains of Child Development / बाल्यावस्था में विकास के क्षेत्र, Biological Basis of Emotion / संवेग का जैविक आधार, Upanishads and Bhagavad Gita / उपनिषद और भगवद्गीता, Central and Peripheral Nervous Systems / केन्द्रीय और परिधीय तंत्रिका तंत्र
  2. Paper - 1 | Unit - 2 | Research Aptitude: Research: Meaning, Features and Scientific Method / अनुसंधान: अर्थ, लक्षण व वैज्ञानिक विधि, Research Paradigms and Approaches / अनुसंधान के प्रतिमान एवं उपागम, Types of Research / अनुसंधान के प्रकार, Variables and Measurement / चर एवं मापन, Methods of Research / अनुसंधान की विधियाँ, Steps of Research / अनुसंधान के चरण, Sampling / प्रतिचयन, Tools and Methods of Data Collection / आँकड़ा संग्रह के उपकरण एवं विधियाँ, Data Analysis and Statistics in Research / आँकड़ा विश्लेषण एवं शोध सांख्यिकी, Thesis and Article Writing / शोध-प्रबंध एवं लेख लेखन, Application of ICT in Research / अनुसंधान में ICT का अनुप्रयोग, Research Ethics / शोध नैतिकता
  3. Paper - 1 | Unit - 3 | Comprehension: Literal Comprehension, Vocabulary and Language in Context, Inferential Comprehension, Critical Comprehension, Comprehension / Reading Comprehension / Unseen Passages (Critical Reasoning) (Paragraph Questions), Restoration and Eighteenth-Century Drama, Modern British Fiction, William Shakespeare, Mid-Twentieth-Century and Contemporary British Fiction, American Drama
  4. Paper - 1 | Unit - 4 | Communication: Communication: Meaning, Nature and Process / संचार: अर्थ, प्रकृति एवं प्रक्रिया, Types and Levels of Communication / संचार के प्रकार एवं स्तर, Verbal and Non-verbal Communication / मौखिक एवं अमौखिक संचार, Semiotics and Meaning / संकेत विज्ञान एवं अर्थ, Models and Theories of Communication / संचार के मॉडल एवं सिद्धांत, Effective Communication / प्रभावी संचार, Barriers to Communication / संचार की बाधाएँ, Classroom Communication / कक्षा संचार, Mass Media: Types and Evolution / जनसंचार माध्यम: प्रकार एवं विकास, Mass Media and Society / जनसंचार एवं समाज, Digital and New Media / डिजिटल एवं नव माध्यम, Static General Knowledge / स्थैतिक सामान्य ज्ञान, Morphology and Syntax, Public Health Nutrition / जन स्वास्थ्य पोषण, Newtonian Motion and Stability, GK- Current Affairs / GK- समसामयिकी, Indian Economy / भारतीय अर्थव्यवस्था, Art and Architecture / कला और स्थापत्य, India after Independence / स्वतंत्रता के बाद भारत
  5. Paper - 1 | Unit - 5 | Mathematical Reasoning and Aptitude: Number System and Simplification / संख्या पद्धति एवं सरलीकरण, Algebra and Ages / बीजगणित एवं आयु, Percentage / प्रतिशतता, Ratio, Proportion, Partnership and Mixtures / अनुपात, समानुपात, साझेदारी एवं मिश्रण, Averages / औसत, Profit, Loss and Discount / लाभ, हानि एवं बट्टा, Simple and Compound Interest / साधारण एवं चक्रवृद्धि ब्याज, Time and Work / समय एवं कार्य, Speed, Time and Distance / चाल, समय एवं दूरी, Mensuration and Geometry / क्षेत्रमिति एवं ज्यामिति, Permutation, Combination and Probability / क्रमचय, संचय एवं प्रायिकता, Series / श्रेणी, Coding-Decoding / कूटलेखन-कूटवाचन, Relationships, Directions and Ranking / संबंध, दिशा एवं क्रम, Arrangements, Puzzles, Clock and Calendar / व्यवस्था, पहेलियाँ, घड़ी एवं कैलेंडर, Mathematical Foundations, Polity / राजव्यवस्था, जीवनी, Deconstruction, Gender and Queer Theory, Modern British and Irish Poetry, Central Force and Scattering, Chemical thermodynamics, Microscopic techniques, Philosophy of the Constitution / संविधान का दर्शन, Waves, Optics and Charged-Particle Motion, Membrane structure and function, Analysis, Markov Chains, Univariate and Joint Distributions
  6. Paper - 1 | Unit - 6 | Logical Reasoning: Structure of Arguments / युक्ति की संरचना, Terms, Definitions and Uses of Language / पद, परिभाषा एवं भाषा के उपयोग, Categorical Propositions / निरुपाधिक प्रतिज्ञप्तियाँ, Categorical Syllogism / निरुपाधिक न्यायवाक्य, Venn Diagrams / वेन आरेख, Deduction, Induction and Analogy / निगमन, आगमन एवं सादृश्यता, Fallacies / तर्कदोष, Indian Logic: Pramanas / भारतीय तर्कशास्त्र: प्रमाण, Anumana and Vyapti / अनुमान एवं व्याप्ति, Hetvabhasa / हेत्वाभास, Non Verbal Reasoning (Spatial Aptitude) (Spatial Reasoning) (Visual Reasoning), Aristotle / अरस्तू, Western Schools of Philosophy / पाश्चात्य दर्शन की विचारधाराएँ, Kant / कांट, Sadhana Paada, Vaiśeṣika / वैशेषिक
  7. Paper - 1 | Unit - 7 | Data Interpretation: Data and Graphical Representation / आँकड़े एवं आलेखीय निरूपण, Data Interpretation: Tables / आँकड़ा निर्वचन: तालिका
  8. Paper - 1 | Unit - 8 | Information and Communication Technology: Computer Fundamentals and Hardware, Memory, Storage and Data Representation, Computer Software, Office Applications, Multimedia and File Formats, Computer Networks, Internet and World Wide Web, Email and Online Communication, Cyber Security, Digital Ethics, IPR and Society, Cloud and Distributed Computing, Emerging Technologies, ICT in Education and Governance, Cyber Threats and Malware Attacks, Role of Internet and Web Services, Electronic Data Interchange and E-Commerce, Internet Fundamentals, Web Design & Development, Web Publishing & Hosting, Emerging Technologies, Terms & Abbreviations, Basics of COA, Introduction to OS, Introduction to CN, Data Communication, Net Layer: IP Addressing, Network Security, Number System, Number Representation, Society, Law & Ethics, Keyboard Shortcuts, Website, Browser & Services, Protection of Geographical Indications / भौगोलिक संकेतों का संरक्षण
  9. Paper - 1 | Unit - 9 | People Development and Environment: Ecosystems and Biodiversity / पारितंत्र और जैव विविधता, Human and Environment Interaction / मानव और पर्यावरण की अंतःक्रिया, Development and Environment / विकास और पर्यावरण, Natural Resources – Forests, Water and Soil / प्राकृतिक संसाधन: वन, जल और मृदा, Energy Resources / ऊर्जा संसाधन, Air Pollution / वायु प्रदूषण, Water Pollution and Treatment / जल प्रदूषण और उपचार, Noise Pollution / ध्वनि प्रदूषण, Waste Management / अपशिष्ट प्रबंधन, Environmental Health and Toxicology / पर्यावरणीय स्वास्थ्य और विषविज्ञान, Climate Change and Global Environmental Issues / जलवायु परिवर्तन और वैश्विक पर्यावरणीय समस्याएँ, Natural Hazards and Disaster Management / प्राकृतिक प्रकोप और आपदा प्रबंधन, Indian Environmental Laws and Policies / भारतीय पर्यावरण कानून और नीतियाँ, International Environmental Agreements / अंतर्राष्ट्रीय पर्यावरण समझौते, Environment / पर्यावरण, Geography / भूगोल, Factory and Industry Systems / कारखाना और उद्योग व्यवस्थाएँ, Earth Materials, Surface Features and Processes, Communicable Diseases and Immunization / संक्रामक रोग और प्रतिरक्षण
  10. Paper - 1 | Unit - 10 | Higher Education System: Education in Ancient India / प्राचीन भारत में शिक्षा, Ancient Centres of Higher Learning / प्राचीन भारत के उच्च शिक्षा केंद्र, Colonial Education Policies and Commissions / औपनिवेशिक काल की शिक्षा नीतियाँ और आयोग, Colonial Colleges, Universities and Reformers / औपनिवेशिक कॉलेज, विश्वविद्यालय व सुधारक, Education Commissions and Policies after Independence / स्वतंत्र भारत में शिक्षा आयोग और नीतियाँ, National Education Policy 2020 / राष्ट्रीय शिक्षा नीति 2020, Types of Higher Education Institutions / उच्च शिक्षा संस्थानों के प्रकार, Learning Programmes and Academic Credits / अधिगम कार्यक्रम और अकादमिक क्रेडिट, Professional, Technical and Skill-Based Education / व्यावसायिक, तकनीकी और कौशल आधारित शिक्षा, Value Education and Environmental Education / मूल्य शिक्षा और पर्यावरण शिक्षा, Governance, Administration and Financing / शासन, प्रशासन और वित्तपोषण, Regulation, Accreditation and Ranking / उच्च शिक्षा का नियमन, प्रत्यायन और रैंकिंग
  11. Live Classes: NTA UGC NET 2025 Live Class
  12. Full Mock Tests:
  13. 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.

Loading lesson…