Short Trick to find (mX + nY) (pX + qY) given x y

Duration: 10 min

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Module outline

  1. Quantitative Aptitude: Ratio and Proportion (Ratios), Data Interpretation, Mixture and Alligation, Permutation and Combination, Number System, Sequence and Series (Series), Speed Time and Distance, Speed Mathematics and Basic Mathematics, Algebra, Percentage, Profit and Loss, Simple Interest and Compound Interest, Powers and Exponents (Surds and Indices), Time and Work, Mensuration and Geometry, Partnership
  2. Reasoning Ability: Series (Number and Letter Series) (Numerical Relations and Reasoning), Coding Decoding, Data Sufficiency, Seating Arrangements, Deductive and Inductive Reasoning (Logical Deduction and Induction) (Prepositional Reasoning), Directions (Direction Test), Ranking, Order and Sequence, Syllogisms, Blood Relations, Puzzle Solving (Puzzles), Inequality, Machine Input-Output
  3. English Language: Vocabulary, Noun, Subject Verb Agreement (Verb Noun Agreement), Adjectives, Tenses, Comprehension / Reading Comprehension / Unseen Passages (Critical Reasoning) (Paragraph Questions), Cloze Test (Cloze Passage), Sentence Correction (Error Correction), Sentence Completion (Fill in the blanks), Sentence Re-arrangements (Para Jumbles) (Narrative Sequencing), Sentence Construction, Pronoun, Preposition, Conjunction, Adverb, Verb, Modals, Articles, Determiner, Interjection
  4. General Awareness: Evolution of Indian Banking (Banking & Financial Awareness), GK- Current Affairs, Static General Knowledge, Indian Economy
  5. C Concepts + MCQs (IT Specialist): C Programming by Yash Sir, C Language Core
  6. Java (IT Specialist): Java
  7. Python (IT Specialist): Python for Placements by Yash Sir, Python Basics
  8. OOPs (IT Specialist): Object Oriented Programming (OOPS)
  9. DBMS (IT Specialist): Basics of DBMS, ER Diagram, Relational Model & Functional Dependencies, Keys & Integrity Constraints, Normalization (1NF - BCNF), Decomposition Properties & 4NF, File Organization & Indexing, Relational Algebra, 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
  10. SQL (IT Specialist): SQL
  11. Software Engineering (IT Specialist): Fundamentals of Software Engineering, Software Requirements and Quality Assurance, Software Design, Estimation and Metrics, Software Testing, Software Maintenance and Configuration Management
  12. Data Structure (IT Specialist): Introduction to DS, Array, Stack, Queue, Linked List, Tree, Graphs, Hashing
  13. Operating System (IT Specialist): Introduction to OS, Process Management, CPU Scheduling, Process Synchronization, Deadlock, Threads & Process Creation, Memory Management, Virtual Memory, Disc Scheduling, File Management, Windows OS, Linux OS, Security, Distributed Systems, Virtual Machines
  14. Compiler Design (IT Specialist): 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
  15. Computer Architecture (IT Specialist): Basics of COA, Floating Point Rep, Cache Memory Organization, Input Output Organisation, Pipelining, Instr Formats & Modes, Control Unit Design, Register Transfer and Microoperations, Multiprocessors, Programming the Basic Computer
  16. Data Communication & Networking (IT Specialist): 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
  17. Descriptive Test (Main Exam): English Writing Ability
AI summary & chapters

AI Summary

An AI-generated summary of this video lecture.

This educational video, presented by Yash Jain from Knowledge Gate Eduventures, focuses on the mathematical topic of "Ratio & Proportion". The lecture begins by defining a ratio as a comparison of two quantities, visually supported by a slide with colorful dots. The instructor then introduces a general algebraic problem type: given a ratio x:y, find the value of a compound ratio (mx+ny):(px+qy) where m, n, p, and q are constants. He demonstrates this concept with a sample ratio x/y = 5/7. The core of the lecture involves solving specific numerical problems using this general framework. The first problem asks to find 3x+2y : 2x+5y given x:y = 2:3. The instructor meticulously solves this using multiple methods, including direct substitution and assuming a constant of proportionality (k). He then applies the same logic to a second problem involving subtraction: finding 3x-7y : 9x-11y given x:y = 7:9. The video serves as a practical guide for students preparing for exams involving ratio and proportion problems.

Chapters

  1. 0:00 – 2:00 00:00-02:00

    The video starts with a title slide featuring the text "RATIO & PROPORTION" and a 3D pie chart. The instructor introduces the definition of a ratio as "a comparison of 2 quantities", shown on a slide with colorful dots representing parts and wholes. He then presents a general problem statement on a pink background with space-themed doodles: "Given x : y, find (mx + ny) : (px + qy) where m,n,p,q are constants". To make this concrete, he writes a specific example on the top right: x/y = 5/7. This section sets the theoretical foundation for the algebraic manipulation of ratios that follows. The slide background is pink with space-themed doodles like a rocket and a planet.

  2. 2:00 – 5:00 02:00-05:00

    The instructor transitions to a specific numerical question: "If x : y = 2 : 3, find the value of 3x + 2y : 2x + 5y ?". He begins the solution by writing the ratio as a fraction x/y = 2/3. He then attempts to substitute x = 2y/3 into the target expression (3x+2y)/(2x+5y). He writes out the substitution clearly: 3[2y/3] + 2y in the numerator and 2[2y/3] + 5y in the denominator. He then factors out 'y' from both the numerator and the denominator, showing that y cancels out, leaving a numerical expression. This demonstrates the first method of solving such problems. He also writes the final simplified form on the board.

  3. 5:00 – 10:00 05:00-10:00

    Continuing the solution, the instructor simplifies the expression to (3(2/3) + 2) / (2(2/3) + 5). He calculates the numerator as 2 + 2 = 4 and the denominator as 4/3 + 5 = 19/3. This results in 4 / (19/3), which simplifies to 12/19. He then introduces a second, often faster method: assuming x = 2k and y = 3k. Substituting these into the expression gives (3(2k) + 2(3k)) / (2(2k) + 5(3k)) = (6k + 6k) / (4k + 15k) = 12k / 19k = 12/19. He then moves to a new problem: "If x : y = 7 : 9, find the value of 3x - 7y : 9x - 11y ?". He solves this by substituting x=7 and y=9 directly into the expression, showing the calculation (21-63)/(63-99). He writes the intermediate steps clearly on the screen.

  4. 10:00 – 10:17 10:00-10:17

    The instructor completes the calculation for the second problem. He writes (3(7) - 7(9)) / (9(7) - 11(9)) which equals (21 - 63) / (63 - 99). This simplifies to -42 / -36. He simplifies this fraction to 7/6. The video concludes with a black screen displaying "THANKS FOR WATCHING" in white and orange text, signaling the end of the lecture. The instructor is visible in the bottom right corner throughout the problem-solving sections, providing verbal guidance and ensuring students follow the steps.

The lecture effectively bridges the gap between abstract ratio concepts and practical problem-solving. By starting with a general formula and then applying it to specific numerical examples, the instructor reinforces the method of substitution and simplification. The use of multiple methods (substitution vs. assuming constants) for the same problem highlights the flexibility in solving ratio problems, a key skill for exams. The progression from simple definitions to complex algebraic expressions ensures a comprehensive understanding of the topic. The instructor's clear handwriting and step-by-step approach make the complex algebra accessible to students.

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