Demo: Types of Ratios with Examples

Duration: 15 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. 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 educational video provides a comprehensive lecture on the types of ratios and their applications in mathematics. The lesson begins by defining ratio as a comparison between two quantities, establishing the foundational notation of a:b. The instructor systematically introduces various specific types of ratios, starting with Duplicate Ratio (a²:b²) and Sub-Duplicate Ratio (√a:√b), using the numerical example 8:1 to demonstrate transformations. The progression continues with Triplicate Ratio (a³:b³) and Sub-Triplicate Ratio, extending the concept of powers and roots to ratio terms. A significant portion of the lecture is dedicated to Inverse Ratio, where the instructor clarifies that while a two-term ratio a:b becomes b:a, three-term ratios like a:b:c require taking reciprocals (1/a : 1/b : 1/c) and simplifying via the Least Common Multiple. The final section covers Compound or Mixed Ratio, defining it as the product of antecedents and consequents across multiple ratios. The video concludes with a worked example calculating the compound ratio of three fractions (2/3, 7/9, and 12/35), demonstrating the multiplication of numerators and denominators followed by simplification.

Chapters

  1. 0:00 – 2:00 00:00-02:00

    The lecture opens with the definition of Ratio & Proportion, explicitly stating that a ratio is a comparison of two quantities. The instructor introduces the general form a:b and immediately applies it to the numerical example 8:1. Key visual cues include on-screen text defining ratio components (part, whole, total) and the transition to Duplicate Ratio. The instructor assigns specific values a=8 and b=1 to set up the calculation for the duplicate form, underlining key terms to emphasize the structure of the ratio before moving into specific transformations.

  2. 2:00 – 5:00 02:00-05:00

    This segment details the definitions and calculations for Duplicate Ratio, Sub-Duplicate Ratio, Triplicate Ratio, and Sub-Triplicate Ratio. The instructor demonstrates that a Duplicate Ratio transforms a:b into a²:b², showing 8:1 becoming 64:1. The lesson then defines Sub-Duplicate Ratio as taking the square root of terms (√a:√b), calculating 8:1 into 2√2 : 1. The progression continues to Triplicate Ratio (a³:b³) and the introduction of Sub-Triplicate Ratio, where the instructor begins setting up cube root calculations. Visual evidence includes handwritten formulas and step-by-step substitutions of numerical values into these power-based ratio definitions.

  3. 5:00 – 10:00 05:00-10:00

    The focus shifts to Inverse Ratio, distinguishing between two-term and three-term ratio inversions. For a:b, the inverse is simply b:a, but for a:b:c, the instructor shows that reversing to c:b:a is incorrect. Instead, the method involves taking reciprocals (1/a : 1/b : 1/c) and simplifying by finding a common denominator. A specific example is worked through using the ratio 3:4:6, where reciprocals are taken (1/3 : 1/4 : 1/6). The instructor calculates the LCM of denominators (3, 4, and 6) as 12, multiplies each term by 12 to clear fractions, and derives the final integer inverse ratio of 4:3:2.

  4. 10:00 – 14:55 10:00-14:55

    The final section defines Compound Ratio (also called Compounded or Mixed Ratio) as the product of antecedents and consequents. The rule is established that for ratios a:b and c:d, the compound ratio is ac:bd. The instructor applies this to a complex problem involving three fractions: 2/3, 7/9, and 12/35. The solution demonstrates multiplying all numerators (2x7x12) and denominators (3x9x35). The instructor then performs simplification by crossing out common factors, reducing the expression to (4x2)/(9x5), illustrating the practical application of multiplying ratios termwise.

The video effectively structures the learning of ratio types by moving from basic definitions to complex transformations. The instructor consistently uses a specific numerical example (8:1) early on to anchor abstract concepts like Duplicate and Sub-Duplicate ratios before generalizing the rules. A critical pedagogical distinction is made regarding Inverse Ratios, where the instructor explicitly corrects the common misconception of simply reversing terms in multi-term ratios. The use of visual aids, such as underlining formulas and crossing out factors during simplification, reinforces the procedural steps required for exams. The progression culminates in Compound Ratio, integrating previous knowledge of multiplication and simplification to solve problems involving multiple fractions. This logical flow ensures students understand not just the formulas but the underlying mathematical operations required to manipulate ratios in various contexts.

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