Short Trick to bring given set of numbers in proportion

Duration: 14 min

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  1. About the course: About the Course
  2. Mathematical Aptitude / गणितीय अभिक्षमता: Number System / संख्या पद्धति, HCF and LCM / महत्तम समापवर्तक और लघुत्तम समापवर्त्य, Divisibility Rules / विभाज्यता के नियम, Percentage / प्रतिशत, Ratio and Proportion / अनुपात और समानुपात, Average / औसत, Profit, Loss and Discount / लाभ, हानि और बट्टा, Time and Work / समय और कार्य, Solid Mensuration / घन क्षेत्रमिति, Simple and Compound Interest / साधारण और चक्रवृद्धि ब्याज, Time, Speed and Distance / समय, चाल और दूरी, Age Problems / आयु संबंधी प्रश्न, Mixture and Alligation / मिश्रण और एलिगेशन, Algebra / बीजगणित, Simplification, Indices and Surds / सरलीकरण, घातांक और करणी, Pipe and Cistern / नल और टंकी, Trigonometry / त्रिकोणमिति, Statistics / सांख्यिकी, Data Interpretation / आँकड़ा निर्वचन, Arithmetic / अंकगणित, Sets, Relations, Functions and Discrete Mathematics / समुच्चय, संबंध, फलन और विविक्त गणित, Number Systems and Number Theory / संख्या पद्धति और संख्या सिद्धांत, Coordinate Geometry, Vectors and 3D Geometry / निर्देशांक ज्यामिति, सदिश और त्रिविमीय ज्यामिति, Polynomials, Equations and Complex Numbers / बहुपद, समीकरण और सम्मिश्र संख्याएँ
  3. Logical Reasoning / तार्किक तर्कशक्ति: Series / श्रेणी, Coding-Decoding / कूट लेखन एवं कूट वाचन, Analogy and Classification / सादृश्यता एवं वर्गीकरण, Blood Relations / रक्त संबंध, Direction and Distance / दिशा एवं दूरी, Order and Ranking / क्रम एवं रैंकिंग, Non-Verbal Reasoning / अशाब्दिक तर्क, Seating Arrangement and Puzzles / बैठक व्यवस्था एवं पहेलियाँ, Syllogisms / न्यायवाक्य, Venn Diagrams, Syllogism and Inequalities / वेन आरेख, न्याय वाक्य एवं असमानता, Mathematical Operations and Missing Numbers / गणितीय संक्रियाएँ एवं लुप्त संख्या, Alphabet and Number Test / वर्णमाला एवं संख्या परीक्षण, Statement-Based Reasoning / कथन आधारित तार्किक विवेचन, Analytical Reasoning (Counting Figures Reasoning) / विश्लेषणात्मक तर्क (आकृति गणना तर्क), Cubes, Dice and Figure Counting / घन, पासा एवं आकृतियों की गिनती, Calendar and Clock / कैलेंडर एवं घड़ी, Clock / घड़ी
  4. General Knowledge / सामान्य ज्ञान: Scientific Achievements and Research / वैज्ञानिक उपलब्धियाँ और अनुसंधान, Chemistry / रसायन विज्ञान, Biology / जीव विज्ञान, History / इतिहास, Geography / भूगोल, Polity / राजव्यवस्था, Indian Economy / भारतीय अर्थव्यवस्था, Current Affairs / समसामयिकी, Static General Knowledge / स्थैतिक सामान्य ज्ञान, State-Specific General Knowledge / राज्य विशेष सामान्य ज्ञान
  5. Art of Teaching / शिक्षण कला: Teaching-Learning Process and Classroom Management / शिक्षण-अधिगम प्रक्रिया एवं कक्षा प्रबंधन, Learners & Learning Process / अधिगमकर्ता और अधिगम प्रक्रिया, Factors Affecting Teaching / शिक्षण को प्रभावित करने वाले कारक, Teaching Methods and Approaches / शिक्षण विधियाँ एवं उपागम, Microteaching and Classroom Communication / सूक्ष्म शिक्षण एवं कक्षा संप्रेषण, Teaching Aids and Educational Technology / शिक्षण सहायक सामग्री एवं शैक्षिक तकनीकी, Assessment and Evaluation / आकलन एवं मूल्यांकन, Teacher: Qualities, Professional Ethics and Development / शिक्षक: गुण, व्यावसायिक नैतिकता एवं विकास, Educational Policies, Acts and Administration / शैक्षिक नीतियाँ, अधिनियम एवं प्रशासन, Curriculum, Arts and Co-curricular Areas / पाठ्यचर्या, कला एवं सह-शैक्षिक क्षेत्र, Guidance and Counselling / निर्देशन एवं परामर्श, Education of Children with Disabilities / दिव्यांग बच्चों की शिक्षा, Micro-Teaching & Teaching Skills / सूक्ष्म शिक्षण और शिक्षण कौशल, Lesson Planning / पाठ योजना
  6. Environmental Science / पर्यावरण विज्ञान: Environment / पर्यावरण
  7. Unit 1 | Digital Electronics: Digital Systems & Boolean Basics, Logic Gates & Hardware, Boolean Expression, Boolean Minimization, Combinational Circuit, Sequential Circuits, Number System, Number Representation
  8. Unit 2 | COA: 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
  9. Unit 3 | C Programming: C Fundamentals, Control Flow, Functions, Arrays & Pointers, Storage Classes, Structures & Enums, DMA, Macros, Scoping & File Handling
  10. Unit 3 | Data Structures: Introduction to DS, Array, Stack, Queue, Linked List, Tree, Graphs, Hashing
  11. Unit 4 | Algorithms: Algorithm Analysis, Time Complexity Analysis, Sorting Algorithms, Dynamic Programming, Minimum Spanning Trees, Shortest Path Algos, Advanced Algorithms
  12. Unit 5 | Operating System: Introduction to OS, Process Management, CPU Scheduling, Process Synchronization, Threads & Process Creation, Deadlock, Memory Management, Virtual Memory, Disc Scheduling, File Management
  13. Unit 6 | Database Management System: Basics of DBMS, ER Diagram, Relational Model & Functional Dependencies, Keys & Integrity Constraints, Normalization (1NF - BCNF), Decomposition Properties & 4NF, File Organization & Indexing, Relational Algebra, SQL, Transaction Management, Concurrency Control
  14. Unit 7 | Computer Networks: Introduction to CN, Data Communication, DLL: Access Control, DLL: Flow Control, DLL: Error Control, DLL: Framing, Data Link Layer - Ethernet, Net Layer: IPv4 & Proto, Net Layer: IP Addressing, Net Layer:Routing Protocol, Transport Layer Services, TL: Congestion & UDP, Application Layer
  15. Unit 8 | Software Engineering: Fundamentals of Software Engineering, Software Requirements and Quality Assurance, Software Design, Estimation and Metrics, Software Testing, Software Maintenance and Configuration Management
  16. Unit 9 | Object Oriented Programming: OOPS with C++
  17. Unit 10 | Web Development: HTML Basics, CSS, JavaScript-Basics, XML, Node.js, Git & Github, PHP
  18. Unit 11 | Theory Of Computation: Introduction to TOC, Deterministic FA (DFA), Non-Deterministic FA, Regular Expressions, Grammar, Regular Language Properties, Moore & Mealy Machines, Pushdown Automata & CFG, Turing Machines
  19. Unit 12 | IoT: Emerging Tech Trends, Cloud Computing, Computer Networks, Internet of Things
  20. Unit 13 | Artificial Intelligence: Approaches to AI, Search Algorithms, Game Playing, Knowledge Representation, Natural Language Processing, Artificial Neural Networks, Genetic Algorithms
  21. Unit 14 | E-Commerce: Electronic Data Interchange and E-Commerce, Role of Internet and Web Services, Security in Mobile and Wireless Computing, Physical Security and Cryptography Basics, Cyber Safety and Security
  22. Unit 15 | Multimedia: Multimedia
  23. Unit 16 | Python: Introduction to Python, Tokens, Variables, Data Types, I/O, Operators & Expressions, Control Flow & Looping, Collections & Strings, Functions & Modules, File Handling & Data Analysis, DSA using Python
  24. Full Length Mock Tests — General Paper:
  25. Full Length Mock Tests — Computer Science (Paper II):
  26. Full Length Mock Test – General + Computer Science:
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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