TCS Previous Year Question on Alligation Rule

Duration: 11 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: संख्या पद्धति / Number System, महत्तम समापवर्तक और लघुत्तम समापवर्त्य / HCF and LCM, Divisibility Rules, प्रतिशत / Percentage, अनुपात और समानुपात / Ratio and Proportion, औसत / Average, लाभ, हानि और बट्टा / Profit, Loss and Discount, समय और कार्य / Time and Work, घन क्षेत्रमिति / Solid Mensuration, साधारण और चक्रवृद्धि ब्याज / Simple and Compound Interest, समय, चाल और दूरी / Time, Speed and Distance, Age Problems, मिश्रण और एलिगेशन / Mixture and Alligation, Algebra, सरलीकरण, घातांक और करणी / Simplification, Indices and Surds, Pipe and Cistern, Trigonometry, Statistics, आँकड़ा निर्वचन / Data Interpretation, Arithmetic, 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. Logical Reasoning: श्रेणी / Series, कूट लेखन एवं कूट वाचन / Coding-Decoding, सादृश्यता एवं वर्गीकरण / Analogy and Classification, रक्त संबंध / Blood Relations, दिशा एवं दूरी / Direction and Distance, क्रम एवं रैंकिंग / Order and Ranking, अशाब्दिक तर्क / Non-Verbal Reasoning, बैठक व्यवस्था एवं पहेलियाँ / Seating Arrangement and Puzzles, Syllogisms, वेन आरेख, न्याय वाक्य एवं असमानता / Venn Diagrams, Syllogism and Inequalities, गणितीय संक्रियाएँ एवं लुप्त संख्या / Mathematical Operations and Missing Numbers, वर्णमाला एवं संख्या परीक्षण / Alphabet and Number Test, कथन आधारित तार्किक विवेचन / Statement-Based Reasoning, Analytical Reasoning (Counting Figures Reasoning), घन, पासा एवं आकृतियों की गिनती / Cubes, Dice and Figure Counting, कैलेंडर एवं घड़ी / Calendar and Clock, Clock
  4. General Knowledge: वैज्ञानिक उपलब्धियाँ और अनुसंधान / Scientific Achievements and Research, Chemistry, Biology, History, Geography, Polity, Indian Economy, समसामयिकी / Current Affairs, Static General Knowledge, राज्य विशेष सामान्य ज्ञान / State-Specific General Knowledge
  5. Art of Teaching: शिक्षण-अधिगम प्रक्रिया एवं कक्षा प्रबंधन / Teaching-Learning Process and Classroom Management, Learners & Learning Process, Factors Affecting Teaching, शिक्षण विधियाँ एवं उपागम / Teaching Methods and Approaches, सूक्ष्म शिक्षण एवं कक्षा संप्रेषण / Microteaching and Classroom Communication, शिक्षण सहायक सामग्री एवं शैक्षिक तकनीकी / Teaching Aids and Educational Technology, आकलन एवं मूल्यांकन / Assessment and Evaluation, शिक्षक: गुण, व्यावसायिक नैतिकता एवं विकास / Teacher: Qualities, Professional Ethics and Development, शैक्षिक नीतियाँ, अधिनियम एवं प्रशासन / Educational Policies, Acts and Administration, पाठ्यचर्या, कला एवं सह-शैक्षिक क्षेत्र / Curriculum, Arts and Co-curricular Areas, निर्देशन एवं परामर्श / Guidance and Counselling, दिव्यांग बच्चों की शिक्षा / Education of Children with Disabilities, Micro-Teaching & Teaching Skills, पाठ योजना / Lesson Planning
  6. Environmental Science: Environment
  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, कंप्यूटर नेटवर्क / 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):
AI summary & chapters

AI Summary

An AI-generated summary of this video lecture.

This educational video, presented by Yash Jain, is a comprehensive tutorial on solving mixture and alligation problems, a common topic in competitive exams like the TCS exam. The lecture begins with an introduction to the core concept of alligation, which is a method to find the ratio in which two or more ingredients at different prices must be mixed to achieve a desired average price. The instructor first explains the 'Basic Rule of Alligation' using a diagram that visually represents the relationship between the lower price, higher price, and the average price, leading to the formula: (Higher Price - Average Price) : (Average Price - Lower Price). To demonstrate this, a practical example is solved using the traditional algebraic approach, where the prices of Item A (Rs. 450 per kg) and Item B (Rs. 510 per kg) are used to find the ratio for a mixture costing Rs. 475 per kg. The video then introduces a faster, more efficient method known as the 'X short trick,' which simplifies the calculation by directly subtracting the prices from the average price to get the ratio. The video concludes with a final 'Thanks for Watching' screen.

Chapters

  1. 0:00 – 2:00 00:00-02:00

    The video opens with an animated title card featuring a cartoon scientist in a lab, with the word 'MIXTURE' visible at the bottom. This transitions to a presentation slide with a geometric background, displaying the title 'MIXTURES & ALLIGATIONS' and the instructor's name, 'By Yash Jain'. A small video feed of the instructor, Yash Jain, is in the bottom right corner. He introduces the topic, explaining that the video will cover mixture and alligation problems, which are frequently asked in competitive exams such as the TCS exam.

  2. 2:00 – 5:00 02:00-05:00

    The instructor begins explaining the 'Alligation Rule'. The screen shows a handwritten note titled 'Basic Rule of Alligation'. The text explains that if item 'A' is sold at a lower price (x) and item 'B' at a higher price (y), and they are mixed in a ratio to get an average price (a), the required ratio is (y-a) : (a-x). A diagram is drawn with 'lower price (x)', 'higher price (y)', and 'average price (a)' connected by lines, visually representing the rule. The instructor then introduces a problem: 'Item A is sold at Rs. 450 per kg & Item B is sold at Rs. 510 per kg. In what ratio A & B should be mixed so that the mixture costs Rs. 475 per kg?'. He labels this as a 'Traditional Approach' and begins to solve it by setting up variables p and q for the quantities of A and B, respectively.

  3. 5:00 – 10:00 05:00-10:00

    The instructor continues the traditional approach. He writes the total cost as '450p + 510q' and the total quantity as 'p + q'. He then sets up the equation for the average price: (450p + 510q) / (p + q) = 475. He proceeds to solve this equation algebraically, multiplying both sides by (p + q) to get 450p + 510q = 475p + 475q. By rearranging terms, he finds 35q = 25p, which simplifies to the ratio p:q = 35:25, or 7:5. He then transitions to a faster method, the 'X short trick', by drawing a diagram with the prices 450, 510, and the average 475. He shows the differences: 510 - 475 = 35 and 475 - 450 = 25, and states that the ratio is 35:25, which simplifies to 7:5, matching the traditional method.

  4. 10:00 – 11:05 10:00-11:05

    The video concludes with a final screen. The background is a dark purple gradient. In the center, the text 'THANKS FOR WATCHING' is displayed in large, white, capitalized letters. This is the end of the lecture, summarizing the key takeaway that the 'X short trick' provides a quick and efficient way to solve alligation problems, which is particularly useful for time-constrained competitive exams.

The video provides a clear, step-by-step tutorial on solving mixture and alligation problems. It effectively contrasts the traditional, algebraic method with a faster, more intuitive 'X short trick'. The core concept, the alligation rule, is introduced with a visual diagram and a clear formula. The example problem is solved using both methods, demonstrating that they yield the same result (a 7:5 ratio) but that the shortcut is significantly quicker. The progression from theory to practical application, and from a slower method to a faster one, makes the content highly effective for students preparing for competitive exams.

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