Short Trick to Find A B C given some mA = nB = pC

Duration: 5 min

This video lesson is available to enrolled students.

Return to /learn/UPPSC-COMPUTER-OPERATOR-GRADE-B/reasoning/ratio-and-proportion-ratios/successive-combined-ratio-problems/asset-short-trick-to-find-a-b-c-given-some-ma-nb-pc after enrolling

Inside: a video lesson and guided study material.

Module outline

  1. English Comprehension: Comprehension / Reading Comprehension / Unseen Passages (Critical Reasoning) (Paragraph Questions), Reading Comprehension, Vocabulary, Idioms and Phrases, Narrative Sequencing, Critical Reasoning
  2. Reasoning and Aptitude: Series (Number and Letter Series) (Numerical Relations and Reasoning), Coding Decoding, Analogy, Non Verbal Reasoning (Spatial Aptitude) (Spatial Reasoning) (Visual Reasoning), Blood Relations, Directions (Direction Test), Ranking, Order and Sequence, Logical Sequence Of Words, Seating Arrangements, Puzzle Solving (Puzzles), Syllogisms, Deductive and Inductive Reasoning (Logical Deduction and Induction) (Prepositional Reasoning), Data Sufficiency, Selection Decision Table (Decision Making), Calendar, Clock, Cubes & Dices, Data Arrangement, Venn Diagram, Analytical Reasoning (Counting Figures Reasoning), Number System, HCF LCM, Percentage, Ratio and Proportion (Ratios), Average, Profit and Loss, Simple Interest and Compound Interest, Speed Time and Distance, Mensuration and Geometry, Arithmetic, Mixture and Alligation, Age Problems, Data Interpretation, 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, Simplification and Approximation, Assembling and Grouping of Shapes, Transformation of Shapes, Three-Dimensional Patterns and Visualization, Cubes and Dice, Algebra, Traverse Surveying, Clocks and Calendars, Order, Ranking and Sequence, Constraint Puzzles, Syllogisms and Venn Diagrams, Ratio and Proportion, Mensuration, Permutations and Combinations, Project Monitoring, Resources and Safety, Profit, Loss and Discount, Sequences and Series, Powers, Surds and Logarithms, Subject-Verb Agreement, Sentence Completion, Geometry, Probability, Trigonometry, Measurement and Quantity Take-Off, Statistics, Data Sufficiency, Blood Relations, Speed, Time and Distance, Time and Work, Data Interpretation, Sequence and Series (Series), Algebra, Permutation and Combination, Combinatorics
  3. General Awareness: Physics, Chemistry, Biology, Geography, History, Polity, Indian Economy
  4. Computer Fundamentals: Basics of COA, Number System, Number Representation, Semiconductor Memories and Programmable Logic, Timing, Hazards and Testing, Processor Organization and Instructions, Number Systems and Codes, Combinational Logic Design, Combinational Logic Circuits, Number Systems and Codes
  5. Operating System: Introduction to OS, Unix OS, Linux OS
  6. C Programming: C Fundamentals, Control Flow, Functions, Arrays & Pointers, Storage Classes, Structures & Enums, DMA, Macros, Scoping & File Handling
  7. OOPS with C++ & Java: OOPS with C++, Java
  8. Database Management System: Basics of DBMS, SQL
  9. MS Office: MS Office Applications
  10. Internet & Web Technologies: Website, Browser & Services, Internet Fundamentals, Web Design & Development, Protocols & Services
AI summary & chapters

AI Summary

An AI-generated summary of this video lecture.

This educational video provides a comprehensive tutorial on solving ratio problems involving three variables, specifically focusing on the scenario where variables are related by a common equation. The instructor, Yash Jain, explains how to find the ratio A:B:C when given an equation where the variables are multiplied by different constants, such as mA = nB = pC. The core technique involves setting the equation to a constant 'k' to isolate each variable, expressing them as fractions, and then finding the Least Common Multiple (LCM) of the denominators to simplify the result into whole numbers. This method is presented as a standard approach for competitive exams.

Chapters

  1. 0:00 – 2:00 00:00-02:00

    The video begins with a title slide displaying "RATIO & PROPORTION" in bold black text next to a colorful 3D pie chart. The instructor, Yash Jain, appears in a small window and introduces the topic. A slide defines "Ratio" as "a comparison of 2 quantities," accompanied by a diagram illustrating parts and a whole. The lesson then transitions to a specific problem type titled "Finding A:B:C where mA = nB = pC". The first example problem is displayed on a yellow background: "If 3A = 5B = 6C, find A : B : C?". The instructor underlines the numbers 3, 5, and 6 to identify them as the coefficients m, n, and p.

  2. 2:00 – 5:00 02:00-05:00

    The instructor demonstrates the solution by setting the entire equation equal to a constant variable 'k', writing "3A = 5B = 6C = k". He isolates each variable to express them in terms of k: A = k/3, B = k/5, and C = k/6. He then constructs the ratio A:B:C as k/3 : k/5 : k/6. To simplify this into whole numbers, he calculates the Least Common Multiple (LCM) of the denominators 3, 5, and 6, which is 30. He multiplies each term of the ratio by 30, resulting in the final integer ratio 10 : 6 : 5. He also writes the general formula A:B:C = 1/m : 1/n : 1/p.

  3. 5:00 – 5:27 05:00-05:27

    The instructor briefly presents a second example problem: "If 2A = 3B = 4C, find A : B : C?". He applies the general formula A:B:C = 1/2 : 1/3 : 1/4. He calculates the LCM of 2, 3, and 4 as 12. Multiplying the terms by 12 yields the ratio 6 : 4 : 3. The video concludes with a black screen displaying the text "THANKS FOR WATCHING" in orange and white font.

The lesson progresses logically from basic definitions of ratio to complex algebraic applications. The key takeaway is the method of equating terms to a constant 'k' to isolate variables, followed by finding the LCM to convert fractional ratios into integers. The instructor demonstrates this with two distinct examples, reinforcing the concept that the ratio of variables is the inverse of their coefficients. This systematic approach ensures accuracy in solving ratio and proportion problems found in competitive exams, providing students with a reliable shortcut for similar questions.

Loading lesson…