Short Trick to bring given set of numbers in proportion

Duration: 14 min

This video lesson is available to enrolled students.

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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 lecture by Yash Jain introduces ratio and proportion, focusing on a shortcut for finding the number to add or subtract from four given numbers (a, b, c, d) so that they become proportional. The instructor first defines a ratio as a comparison of two quantities and presents the general problem: what should be added or subtracted to a, b, c, d so that they are in proportion? A concrete example asks what should be added to each of 5, 9, 11, and 18. The standard algebraic method is demonstrated: introduce a variable y, write the terms as 5+y, 9+y, 11+y, and 18+y, set up the proportion (5+y)/(9+y) = (11+y)/(18+y), cross-multiply to get (5+y)(18+y) = (11+y)(9+y), expand both sides, and simplify to 90 + 23y = 99 + 20y, yielding y = 3. The instructor then introduces a shortcut formula involving |ad - bc| / (a + d) or related expressions, illustrated by subtracting the fractions 5/9 and 11/18 to obtain a difference of 3. A second example with numbers 19, 37, 47, and 86 is worked using cross-multiplication: 19 x 86 = 1634 and 37 x 47 = 1739, with the difference 105 highlighted. The lecture then shifts to the subtraction variant: what should be subtracted from each of 5, 9, 11, and 18? The terms are written as 5-y, 9-y, 11-y, and 18-y, the proportion (5-y)/(9-y) = (11-y)/(18-y) is set up, cross-multiplied and simplified to give y = -3 (or equivalently +3 in the final boxed answer). The video concludes with a thank-you slide.

Chapters

  1. 0:00 – 2:00 00:00-02:00

    The video opens with an introduction slide titled 'RATIO & PROPORTION - BY YASH JAIN', defining a ratio as 'a comparison of 2 quantities'. The instructor presents the general problem: 'What should be added/subtracted to a, b, c, d so that they are in proportion?' and then displays the specific example: 'Que: What should be added to each of 5, 9, 11, 18 to make them in proportion?' with 'each' underlined. The instructor begins writing the terms on the board, introducing a variable x (later y) to represent the unknown number being added, progressively writing 5+x, 9+x, 11+x, and 18+x to set up the proportion.

  2. 2:00 – 5:00 02:00-05:00

    The instructor writes the proportion setup '5+y : 9+y :: 11+y : 18+y' and the fraction form (5+y)/(9+y) = (11+y)/(18+y). Cross-multiplication is shown as '(5+y)(18+y) = (11+y)(9+y)', with the left side expanding to '90 + 18y' and then fully as '90 + 18y + 5y + y² = 99 + 99y + 11y + y²'. The equation simplifies to '90 + 23y = 99 + 20y', and the final value y=3 is calculated and boxed. A new problem with numbers 19, 37, 47, and 86 is briefly introduced before returning to the previous solution.

  3. 5:00 – 10:00 05:00-10:00

    The instructor demonstrates a shortcut trick using the numbers 5, 9, 11, and 18. The fractions 5/9 and 11/18 are set up for subtraction, with calculations '99 - 90 = 9' and '23 - 20 = 3' shown to find the difference. The result is used to form the proportion '9/3 = 3', marked with a checkmark. A general formula involving 'a, b, c, d' and the expression '|ad - bc| / (a + d)' is written down. A second worked example in red shows the question 'Que: What should be added to each of 19, 37, 47, 86 to make them in proportion?' with cross-multiplication '19 x 86 = 1634' and '37 x 47 = 1739', difference '1739 - 1634 = 105' underlined. The final frame switches to a new question: 'Que: What should be subtracted from each of a, b, c, d to make them in proportion?' with terms 'a-y, b-y, c-y, d-y' written.

  4. 10:00 – 13:47 10:00-13:47

    The video demonstrates the subtraction variant: 'What should be subtracted from each of 5, 9, 11, 18 to make them in proportion?' The instructor writes the expressions (5-y), (9-y), (11-y), and (18-y) and sets up the proportion equation '(5-y)/(9-y) = (11-y)/(18-y)'. Cross-multiplication gives '(18-y)(5-y) = (11-y)(9-y)', which is expanded and simplified to '-3y = 9', leading to the final answer y = -3. The instructor highlights the result and shows a verification step using ratios 2/6 and 8/15. The final slide displays the ratio equation in a red box with X marks, and a separate red circle contains the value '+3', followed by a 'THANKS FOR WATCHING' message.

The lecture teaches two methods for solving proportion problems of the form 'what number should be added or subtracted from four given numbers to make them proportional.' The first method is standard algebra: introduce a variable, set up the proportion by equating the ratio of the first two terms to the ratio of the last two, cross-multiply, expand, and solve for the variable. The second method is a shortcut formula involving |ad - bc| / (a + d) or related expressions, which allows faster computation. The instructor demonstrates both methods with the numbers 5, 9, 11, and 18 (yielding y = 3 for addition) and provides a second example with 19, 37, 47, and 86. The subtraction variant is also covered, showing that the same algebraic setup applies with (a-y) terms instead of (a+y) terms, yielding y = -3 (equivalently +3 in the final boxed answer). The key takeaway is that adding or subtracting the same number to all four terms preserves the structure of the proportion, and cross-multiplication is the primary tool for solving such equations.

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