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

Duration: 10 min

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Module outline

  1. Numerical Ability & Problem Solving: Speed Mathematics and Basic Mathematics, Arithmetic, Number System, HCF LCM, Divisibility Rules, Percentage, Ratio and Proportion (Ratios), Average, Profit and Loss, Simple Interest and Compound Interest, Mixture and Alligation, Time and Work, Pipe and Cistern, Speed Time and Distance, Age Problems, Partnership, Data Interpretation, Mental Ability, Sequence and Series (Series), Powers and Exponents (Surds and Indices), Algebra, Statistics, Logarithm, Mensuration and Geometry, Permutation and Combination, Probability, Sequences and Series, Powers, Surds and Logarithms, Subject-Verb Agreement, Sentence Completion, Geometry, Sentence Structure and Correction, Data Sufficiency, Trigonometry, Measurement and Quantity Take-Off, Signal Space and Optimum Detection, Probability, Statistics, Algebra, Time and Work, Speed, Time and Distance, Data Interpretation, Combinatorics
  2. Logical Reasoning: Series (Number and Letter Series) (Numerical Relations and Reasoning), Coding Decoding, Data Sufficiency, Syllogisms, Deductive and Inductive Reasoning (Logical Deduction and Induction) (Prepositional Reasoning), Seating Arrangements, Blood Relations, Directions (Direction Test), Non Verbal Reasoning (Spatial Aptitude) (Spatial Reasoning) (Visual Reasoning), Analytical Reasoning (Counting Figures Reasoning), Puzzle Solving (Puzzles), Calendar, Clock, Cubes & Dices, Logical Sequence Of Words, Venn Diagram, Data Arrangement, Inequality, Analogy, Ranking, Order and Sequence, Selection Decision Table (Decision Making), Alphabet and Word Tests, Numerical Reasoning, Number System, Averages, Mixtures and Alligation, Percentages, Series Completion, Analogy and Classification, Patterns in Two-Dimensional Figures, Coding and Decoding, Mathematical Operations, Direction Sense, Logical Deduction and Induction, Syllogisms and Venn Diagrams, Critical Reasoning, Order, Ranking and Sequence, Reading Comprehension, Profit, Loss and Discount, Constraint Puzzles, Traverse Surveying, Ratio and Proportion, Mensuration, Permutations and Combinations, Clocks and Calendars, Assembling and Grouping of Shapes, Transformation of Shapes, Three-Dimensional Patterns and Visualization, Cubes and Dice, Vocabulary, Blood Relations
  3. General Knowledge & Current Affairs (India + Rajasthan): History, Geography, Polity, Indian Economy, Static General Knowledge, State Wise GK, GK- Current Affairs, Environment, Physics
  4. Computer Fundamentals & Operating Systems: Basics of COA, Floating Point Rep, Digital Systems & Boolean Basics, Number Representation, Number System, Introduction to OS, File Management, Windows OS, Unix OS, Linux OS, Register Transfer and Microoperations, Virtual Memory
  5. Computer Networks: Introduction to CN, Data Communication, DLL: Error Control, DLL: Access Control, Data Link Layer - Ethernet, Net Layer: IPv4 & Proto, Application Layer, Hardware Basics, Network Security
  6. Cyber Security: Cyber Threats and Malware Attacks, Role of Internet and Web Services, Security in Mobile and Wireless Computing, Electronic Data Interchange and E-Commerce, Physical Security and Cryptography Basics, Intrusion Detection Systems (IDS), Cyber Safety and Security, Ethical Hacking
  7. Programming (C & OOP): C Fundamentals, Control Flow, Arrays & Pointers, Functions, Storage Classes, Structures & Enums, DMA, Macros, Scoping & File Handling, OOPS with C++, Operators & Expressions, Sorting Algorithms, Java Fundamentals, Java
  8. MS Office & Data Processing: MS Office Applications, Basics of DBMS
  9. Internet & Web Technology: Society, Law & Ethics, Terms & Abbreviations, Keyboard Shortcuts, Emerging Tech Trends, Artificial Intelligence, Emerging Technologies, Internet Fundamentals, Website, Browser & Services, Web Design & Development, Protocols & Services, Web Publishing & Hosting, Server Side & Security
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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