Finding ratio of 2 numbers from their sum & difference

Duration: 3 min

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Module outline

  1. Mathematics: Ratio and Proportion (Ratios), Divisibility Rules, Data Interpretation, Mixture and Alligation, Permutation and Combination, Logarithm, Number System, HCF LCM, Sequence and Series (Series), Speed Time and Distance, Percentage, Average, Powers and Exponents (Surds and Indices), Algebra, Probability, Profit and Loss, Simple Interest and Compound Interest, Time and Work, Pipe and Cistern, Mensuration and Geometry, Mental Ability, Age Problems, Partnership, Statistics, Arithmetic, Speed Mathematics and Basic Mathematics
  2. General Intelligence & Reasoning: 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. General Awareness: Polity, Evolution of Indian Banking (Banking & Financial Awareness), Physics, Biology, Chemistry, History, Geography, Indian Economy, Static General Knowledge, GK- Current Affairs, NEP 2020, Environment
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.

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