Finding ratio of 2 numbers from their sum & difference

Duration: 3 min

This video lesson is available to enrolled students.

Return to /learn/SSC-CGL-TIER-2/mathematical-abilities-part-a-sec-i-paper-i/ratio-and-proportion-ratios/division-of-quantity-in-a-given-ratio/asset-finding-ratio-of-2-numbers-from-their-sum-difference after enrolling

Inside: a video lesson and guided study material.

Module outline

  1. Paper-I | Mathematical Abilities: Ratio and Proportion (Ratios), Divisibility Rules, Data Interpretation, Mixture and Alligation, Number System, Speed Time and Distance, Arithmetic, Percentage, Average, Simple Interest and Compound Interest, Profit and Loss, Partnership, Time and Work, Algebra, Mensuration and Geometry, Trigonometry, Linear Algebra
  2. Paper-I | Reasoning & General Intelligence: Series (Number and Letter Series) (Numerical Relations and Reasoning), Coding Decoding, Data Sufficiency, Non Verbal Reasoning (Spatial Aptitude) (Spatial Reasoning) (Visual Reasoning), Syllogisms, Deductive and Inductive Reasoning (Logical Deduction and Induction) (Prepositional Reasoning), Seating Arrangements, Blood Relations, Directions (Direction Test), Analytical Reasoning (Counting Figures Reasoning), Puzzle Solving (Puzzles), Calendar, Clock, Cubes & Dices, Selection Decision Table (Decision Making), Logical Sequence Of Words, Crypt Arithmetic, Venn Diagram, Data Arrangement, Inequality, Analogy, Ranking, Order and Sequence, Clerical Aptitude, Verbal Classification
  3. Paper-I | English Language & Comprehension: Vocabulary, Noun, Subject Verb Agreement (Verb Noun Agreement), Adjectives, Tenses, Pronoun, Preposition, Articles, Direct and Indirect Speech, Conjunction, Modals, Sentence Re-arrangements (Para Jumbles) (Narrative Sequencing), Sentence Correction (Error Correction), Sentence Completion (Fill in the blanks), Comprehension / Reading Comprehension / Unseen Passages (Critical Reasoning) (Paragraph Questions), Cloze Test (Cloze Passage), Verbal Analogy (Word Based Analogy), Sentence Construction, Active Passive Voice (Voice), Determiner, Facts, Inference and Judgements
  4. Paper-I | General Awareness: Polity, Physics, Biology, Chemistry, Environment, GK- Current Affairs, Static General Knowledge, History, Geography, Indian Economy
  5. Paper-I | Computer Knowledge/Proficiency): Basics of COA, Transport Layer Services, Keyboard Shortcuts, MS Office Applications, MS Office by Yash Sir, Emerging Tech Trends, Society, Law & Ethics, Website, Browser & Services, Internet Fundamentals, Web Design & Development, Introduction to CN, Hardware basics, Network Security, Application Layer, Cyber and Info Security, Cyber Threats and Malware Attacks, Cyber Safety and Security, Role of Internet and Web Services, Security in Mobile and Wireless Computing
  6. Paper-II | Statistics: Statistics, Probability, Research Process Steps
AI summary & chapters

AI Summary

An AI-generated summary of this video lecture.

This short math lesson teaches how to find the ratio of two numbers when given the ratio of their sum and difference. The instructor introduces variables a and b, sets up (a+b)/(a-b) = given ratio, then solves the example where sum:diff = 9:2. Cross-multiplication gives 2(a+b) = 9(a-b), leading to 11b = 7a and a/b = 11/7. A shortcut formula a/b = (9+2)/(9-2) confirms the result 11:7. The video ends with a thanks screen.

Chapters

  1. 0:00 – 2:00 00:00-02:00

    The lesson opens with the title 'Finding Ratio of Numbers Given Ratio of Sum & Difference'. The instructor defines two numbers as a and b, writes 'a, b = x ?', and establishes the core relationship (a+b)/(a-b) = given ratio, with a circled 'a/b' indicating the target. The example question appears: 'Ratio of sum & difference of two numbers is 9 : 2. Find the ratio of numbers.' The instructor writes 'Sum/Diff = 9/2' and begins forming the equation (a+b)/(a-b) = 9/2, setting up the algebraic method.

  2. 2:00 – 3:11 02:00-03:11

    The instructor solves the equation by cross-multiplying: 2(a+b) = 9(a-b). Expanding and simplifying yields 11b = 7a, so a/b = 11/7. A shortcut formula is then shown: a/b = (9+2)/(9-2) = 11/7, confirming the ratio of numbers is 11:7. The video concludes with a closing screen displaying 'THANKS FOR WATCHING' in bold text on a black background, with an orange highlight box around 'THANKS' and an underline beneath the message.

The central concept is deriving a/b from (a+b)/(a-b) = m/n. The standard method uses cross-multiplication: n(a+b) = m(a-b), which simplifies to (m-n)a = (m+n)b, giving a/b = (m+n)/(m-n). For the example m=9, n=2: a/b = 11/7. The shortcut formula directly applies this result. Key teaching cues include variable setup, cross-multiplication to eliminate fractions, and verification via the shortcut. The lesson is concise and focused on one problem type with a clear worked example.

Loading lesson…