Finding ratio of 2 numbers from their sum & difference

Duration: 3 min

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  1. About the course: About the Course
  2. Mathematical Aptitude / गणितीय अभिक्षमता: Number System / संख्या पद्धति, HCF and LCM / महत्तम समापवर्तक और लघुत्तम समापवर्त्य, Divisibility Rules / विभाज्यता के नियम, Percentage / प्रतिशत, Ratio and Proportion / अनुपात और समानुपात, Average / औसत, Profit, Loss and Discount / लाभ, हानि और बट्टा, Time and Work / समय और कार्य, Solid Mensuration / घन क्षेत्रमिति, Simple and Compound Interest / साधारण और चक्रवृद्धि ब्याज, Time, Speed and Distance / समय, चाल और दूरी, Age Problems / आयु संबंधी प्रश्न, Mixture and Alligation / मिश्रण और एलिगेशन, Algebra / बीजगणित, Simplification, Indices and Surds / सरलीकरण, घातांक और करणी, Pipe and Cistern / नल और टंकी, Trigonometry / त्रिकोणमिति, Statistics / सांख्यिकी, Data Interpretation / आँकड़ा निर्वचन, Arithmetic / अंकगणित, Sets, Relations, Functions and Discrete Mathematics / समुच्चय, संबंध, फलन और विविक्त गणित, Number Systems and Number Theory / संख्या पद्धति और संख्या सिद्धांत, Coordinate Geometry, Vectors and 3D Geometry / निर्देशांक ज्यामिति, सदिश और त्रिविमीय ज्यामिति, Polynomials, Equations and Complex Numbers / बहुपद, समीकरण और सम्मिश्र संख्याएँ
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  24. Full Length Mock Tests — General Paper:
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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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