SHORT TRICK To Apply Alligation Rule on 3 Ingredients

Duration: 14 min

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Module outline

  1. Aptitude: 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, TCS NQT Advanced Quantitative Ability, Speed Mathematics and Basic Mathematics, Arithmetic, Statistics, Partnership, Age Problems, Mental Ability, Mensuration and Geometry, Linear Algebra, Calculus, Trigonometry, Vectors, Gamified / Game Based Aptitude
  2. Reasoning: Series (Number and Letter Series) (Numerical Relations and Reasoning), Coding Decoding, Data Sufficiency, Non Verbal Reasoning (Spatial Aptitude) (Spatial Reasoning) (Visual Reasoning), Deductive and Inductive Reasoning (Logical Deduction and Induction) (Prepositional Reasoning), Syllogisms, TCS NQT Advanced Reasoning Ability, Ranking, Order and Sequence, Analogy, Inequality, Data Arrangement, Venn Diagram, Logical Sequence Of Words, Selection Decision Table (Decision Making), Cubes & Dices, Clock, Calendar, Puzzle Solving (Puzzles), Analytical Reasoning (Counting Figures Reasoning), Directions (Direction Test), Blood Relations, Seating Arrangements
  3. Verbal Ability (English): 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, Adverb, Verb
  4. Mega Test:
  5. Grand Test:
AI summary & chapters

AI Summary

An AI-generated summary of this video lecture.

This educational video, presented by Yash Jain, is a tutorial on solving mixture and alligation problems, specifically focusing on the application of the alligation rule for three ingredients. The video begins with an introduction to the topic, followed by a detailed explanation of the weighted average formula for mixtures. The core of the lesson is a worked example: determining the ratio in which three types of sugar costing Rs. 10, Rs. 12, and Rs. 16 per kg should be mixed to achieve a mixture costing Rs. 13 per kg. The instructor demonstrates the alligation method by first pairing the ingredients (10 and 16, 12 and 16) with the mean price (13), calculating the differences (3 and 3, 1 and 3), and then combining these ratios to find the final ratio of 1:3:2. The video concludes with a summary of the solution and a thank you message.

Chapters

  1. 0:00 – 2:00 00:00-02:00

    The video opens with an animated title card featuring a cartoon scientist in a lab, with the word "MIXTURE" displayed at the bottom. This transitions to a presentation slide with a geometric background, introducing the topic "MIXTURES & ALLIGATIONS" and crediting the instructor, Yash Jain. The instructor, visible in a small window, begins to explain the concept of alligation, writing "Price A", "Price B", and "Mean Price" on the screen to establish the basic framework for the problem.

  2. 2:00 – 5:00 02:00-05:00

    The instructor continues to build the theoretical foundation. He writes the formula for the weighted average of a mixture: x̄ = (n₁x₁ + n₂x₂ + n₃x₃) / (n₁ + n₂ + n₃), where x̄ is the mean price and nᵢ are the quantities. He then introduces the problem: to find the ratio of three types of sugar costing Rs. 10, Rs. 12, and Rs. 16 per kg to make a mixture costing Rs. 13 per kg. He visually represents the prices on a number line, showing that 13 lies between 10 and 16, and between 12 and 16, setting up the alligation process.

  3. 5:00 – 10:00 05:00-10:00

    The instructor applies the alligation rule. He first pairs the cheapest (10) and the most expensive (16) sugar with the mean price (13). He calculates the difference: 13 - 10 = 3 and 16 - 13 = 3, resulting in a ratio of 3:3, which simplifies to 1:1. He then pairs the middle-priced sugar (12) with the most expensive (16), calculating 13 - 12 = 1 and 16 - 13 = 3, resulting in a ratio of 1:3. He then combines these two ratios, 1:1 and 1:3, to find the final ratio of the three ingredients, which he determines to be 1:3:2.

  4. 10:00 – 13:42 10:00-13:42

    The instructor verifies the solution by substituting the ratio 1:3:2 back into the weighted average formula. He calculates the total cost as (1*10 + 3*12 + 2*16) = 10 + 36 + 32 = 78, and the total quantity as 1 + 3 + 2 = 6. The mean price is 78/6 = 13, which matches the required price. He concludes the lesson by summarizing the final answer and the method used. The video ends with a "THANKS FOR WATCHING" screen.

The video provides a clear, step-by-step tutorial on solving a three-ingredient alligation problem. It begins by establishing the fundamental formula for a mixture's mean price and then applies the alligation rule by systematically pairing ingredients with the mean price. The instructor's method of breaking down the problem into two separate two-ingredient alligations and then combining the results is a logical and effective approach. The final verification step reinforces the correctness of the solution, making the entire process a comprehensive and practical guide for students.

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