Short Trick to Divide a Given Number X in ratio of M N

Duration: 16 min

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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, Biological Basis of Emotion / संवेग का जैविक आधार, 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)
  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, General Awareness (Legacy Paper 1) / सामान्य जागरूकता (पुराना पेपर 1)
  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, 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, जीवनी, Philosophy of the Constitution / संविधान का दर्शन, Analysis, Indian Polity and Governance (Legacy Unit 10) / भारतीय राजव्यवस्था और शासन (पुराना यूनिट 10)
  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, 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. Paper 2 | Unit 1 | Discrete Structures and Optimization: Propositional and Predicate Logic, Set Theory, Relations, Functions, Permutation, Combination and Probability / क्रमचय, संचय एवं प्रायिकता, Graph Theory, Group Theory, Digital Systems & Boolean Basics, Boolean Expression, Boolean Minimization, Optimization, Markov Chains
  12. Paper 2 | Unit 2 | Computer System Architecture: Logic Gates & Hardware, Combinational Circuit, Sequential Circuits, Number System, Number Representation, Floating Point Rep, Basics of COA, Register Transfer and Microoperations, Programming the Basic Computer, Instr Formats & Modes, Control Unit Design, Pipelining, Input Output Organisation, Cache Memory Organization, Multiprocessors
  13. Paper 2 | Unit 3 | Programming Languages and Computer Graphics: Language Design, C Fundamentals, Control Flow, Functions, Arrays & Pointers, Storage Classes, Structures & Enums, DMA, Macros, Scoping & File Handling, HTML Basics, XML, JavaScript-Basics, Java, Basics of Computer Graphics, 2-D Geometrical Transforms and Viewing, 3-D Object Representation, Geometric Transformations and Viewing, OOPS with C++, Java Fundamentals, Array, String, IO & References, OOPS with Java
  14. Paper 2 | Unit 4 | Database Management Systems: Basics of DBMS, ER Diagram, Relational Model & Functional Dependencies, Keys & Integrity Constraints, Normalization (1NF - BCNF), Decomposition Properties & 4NF, File Organization & Indexing, Relational Algebra, SQL, Relational Calculus, Transaction Management, Concurrency Control, Database Recovery, ORDBMS, Database Security & Authorization, Query Processing & Optimization, Enhanced Data Models, Data Warehousing & Mining, Big Data Systems, NoSQL
  15. Paper 2 | Unit 5 | System Software and Operating System: Introduction to OS, Process Management, CPU Scheduling, Process Synchronization, Threads & Process Creation, Deadlock, Memory Management, Virtual Memory, Disc Scheduling, File Management, Windows OS, Linux OS, Security, Distributed Systems, Virtual Machines
  16. Paper 2 | Unit 6 | Software Engineering: Fundamentals of Software Engineering, Software Requirements and Quality Assurance, Software Design, Estimation and Metrics, Software Testing, Software Maintenance and Configuration Management
  17. Paper 2 | Unit 7 | Data Structures and Algorithms: Introduction to DS, Array, Stack, Queue, Linked List, Tree, Graphs, Hashing, Algorithm Analysis, Time Complexity Analysis, Sorting Algorithms, Greedy Algorithms, Dynamic Programming, Minimum Spanning Trees, Shortest Path Algos, Advanced Algorithms
  18. Paper 2 | Unit 8 | Theory of Computation and Compilers: Introduction to TOC, Deterministic FA (DFA), Non-Deterministic FA, Regular Expressions, Grammar, Regular Language Properties, Moore & Mealy Machines, Pushdown Automata & CFG, Turing Machines, Complexity Theory, Intro to Compilers, Lexical Analysis, Grammar & CFG, Syntax Analysis: Top-Down, Syntax Analysis: Bottom-Up, Semantic Analysis & SDT, Intermediate Code Gen, Code Optimization, Run Time Environment
  19. Paper 2 | Unit 9 | Data Communication and 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, Hardware basics, Network Security, Cloud Computing, Mobile Computing
  20. Paper 2 | Unit 10 | Artificial Intelligence: Approaches to AI, Search Algorithms, Game Playing, Knowledge Representation, Planning, Multi Agent Systems, Fuzzy Sets, Natural Language Processing, Artificial Neural Networks, Genetic Algorithms
  21. Full Notes: Paper 1 Full Notes
  22. Paper 1 | Full Mock Tests:
  23. Paper 2 | Full Mock Tests:
  24. Paper 1 | Previous Year Papers:
  25. Paper 2 | Previous Year Papers:
AI summary & chapters

AI Summary

An AI-generated summary of this video lecture.

This lecture teaches a shortcut for dividing a given number x in the ratio m:n by first finding the value of one part and then multiplying it by each ratio term. The instructor opens with a definition of ratio as the comparison of two quantities, noting that it can be written in colon, word, or fraction form. The main method is introduced as “Dividing a given number 'x' in the ratio 'm:n'.” A story-based example uses Suresh and Mahesh, with a 153 lakh property to be divided in the ratio 4:5. The total number of parts is found as 4 + 5 = 9, so one part equals 153/9 = 17 lakh. Suresh’s share is then calculated as 4 × 17 = 68 lakh, and Mahesh’s share as 5 × 17 = 85 lakh. The instructor verifies the answer by adding the two shares back to 153 lakh. A second example involves Jethalal, Sunderlal, and Taarak Bhai sharing a profit of Rs. 10,85,000 in the efficiency ratio 7:11:13. The total number of parts is 7 + 11 + 13 = 31, so one part equals 10,85,000/31 = Rs. 35,000. Sunderlal’s share is highlighted as 11 × 35,000 = Rs. 3,85,000. A third example introduces chained ratios: Rs. 200 is divided among Neha, Tony, and Sonu such that N:T = 2:3 and T:S = 3:5. The instructor combines these into a single ratio N:T:S = 2:3:5, giving 10 parts equal to 200. One part is therefore 20, so Neha’s share is 2 × 20 = 40 and Tony’s share is 3 × 20 = 60. The final example extends the chained-ratio method to four people: Rs. 5000 is divided among Guddu, Munna, JP Yadav, and Kaleen Bhaiya with ratios G:M = 1:2, M:J = 2:3, and J:K = 3:4. These are combined into G:M:J:K = 1:2:3:4, giving 10 parts equal to 5000. One part is 500, so Munna’s share is 2 × 500 = Rs. 1000, which is circled as the answer. The lesson ends with a “THANKS FOR WATCHING” screen.

Chapters

  1. 0:00 – 2:00 00:00-02:00

    The video opens with a slide titled “RATIO & PROPORTION” that defines ratio as “a comparison of 2 quantities” and states it can be written in colon, word, or fraction form. The instructor then introduces the specific topic: “Dividing a given number 'x' in the ratio 'm:n'.” A “Story Time” segment begins with an illustration of three men, two of whom are labeled “Suresh” and “Mahesh,” followed by a house illustration labeled “Father.” This sets up the contextual word problem that will be solved using the ratio-division shortcut.

  2. 2:00 – 5:00 02:00-05:00

    The story problem is formalized as “153 lakh property into two parts in the ratio 4:5,” with Suresh associated with 4 and Mahesh with 5. The instructor writes “153 -> 9 parts” and “9 parts -> 153 lakh,” then calculates one part as 153/9 = 17 lakh. The individual shares are found by multiplying: “Suresh -> 4 x 17 lakh = 68 lakh” and “Mahesh -> 5 x 17 = 85 lakh.” A verification step adds the two shares back to confirm they total 153 lakh, reinforcing that the parts must sum to the original amount.

  3. 5:00 – 10:00 05:00-10:00

    A partnership problem is presented in an orange panel: Jethalal, Sunderlal, and Taarak Bhai have an efficiency ratio of 7:11:13 and a total profit of Rs. 10,85,000. The instructor labels the ratio as “Bhag ← efficiency ratio” and computes the total parts: 7 + 11 + 13 = 31. One part is then found as 10,85,000/31 = Rs. 35,000. Each partner’s share is obtained by multiplying their ratio term by 35,000; Sunderlal’s share of 11 × 35,000 = Rs. 3,85,000 is circled as the answer. This example demonstrates applying the same one-part method to a three-way division.

  4. 10:00 – 15:00 10:00-15:00

    The lesson moves to chained ratios. First, Rs. 200 is divided among Neha, Tony, and Sonu with N:T = 2:3 and T:S = 3:5. The instructor writes the fractions N/T = 2/3 and T/S = 3/5, then combines them into the single ratio N:T:S = 2:3:5. Since 2 + 3 + 5 = 10 parts equal 200, one part is 20. Neha’s share is calculated as 2 × 20 = 40 and Tony’s as 3 × 20 = 60. A second chained-ratio problem then introduces Rs. 5000 divided among Guddu, Munna, JP Yadav, and Kaleen Bhaiya with G:M = 1:2, M:J = 2:3, and J:K = 3:4.

  5. 15:00 – 15:30 15:00-15:30

    The final chained-ratio problem is completed. The ratios G:M = 1:2, M:J = 2:3, and J:K = 3:4 are combined into G:M:J:K = 1:2:3:4, giving 1 + 2 + 3 + 4 = 10 parts equal to 5000. One part is therefore 500, and the four shares are labeled 500, 1000, 1500, and 2000. Munna’s share of (2/10) × 5000 = Rs. 1000 is circled as the answer, and the video ends with a “THANKS FOR WATCHING” screen.

The central idea of the lecture is a consistent shortcut for dividing a number in a given ratio: sum the ratio terms to get the total number of parts, divide the original amount by that sum to find the value of one part, and then multiply each ratio term by this unit value to obtain individual shares. This method is first demonstrated with a simple two-way division (153 lakh in the ratio 4:5), where one part equals 17 lakh and the shares are 68 and 85 lakh. It is then extended to a three-way partnership division (Rs. 10,85,000 in the ratio 7:11:13), where one part equals Rs. 35,000 and Sunderlal’s share is Rs. 3,85,000. The most important conceptual extension involves chained ratios, where separate pairwise ratios must first be combined into a single multi-term ratio before applying the one-part method. In the Neha-Tony-Sonu example, N:T = 2:3 and T:S = 3:5 are combined into N:T:S = 2:3:5 because the common term Tony is already consistent (3 in both ratios). In the final four-person example, G:M = 1:2, M:J = 2:3, and J:K = 3:4 are combined into G:M:J:K = 1:2:3:4, again because the overlapping terms match. The verification step in the first example—adding the calculated shares back to the original total—is a useful habit that confirms correctness. The lecture uses story-based framing and character names to make the abstract ratio concept concrete, but the underlying arithmetic is identical across all examples: total parts → value of one part → individual shares.

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