Short Trick to Find A C when A B & B C is given

Duration: 6 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 provides a step-by-step guide to solving ratio problems, specifically focusing on finding the combined ratio A:C when given two separate ratios A:B and B:C. The instructor begins by defining a ratio as a comparison of two quantities and then presents a specific problem: If A:B = 3:4 and B:C = 6:7, find A:C. He demonstrates the standard method of equating the common term B using the Least Common Multiple (LCM). He then introduces a faster shortcut method involving the multiplication of fractions. The lesson is reinforced with a second example and a review of the first problem using the shortcut, ensuring students understand both the conceptual and procedural aspects of the topic.

Chapters

  1. 0:00 – 2:00 00:00-02:00

    The video begins with a title slide "RATIO & PROPORTION" followed by a definition card stating "Ratio a comparison of 2 quantities". The instructor then presents the core problem: "If A : B = 3 : 4 and B : C = 6 : 7, find A : C?". He writes the ratios vertically, underlining the common term B in both. He explains that to combine them, the value of B must be the same in both ratios. He identifies the Least Common Multiple (LCM) of 4 and 6 as 12. To achieve this, he multiplies the entire first ratio (3:4) by 3, resulting in 9:12. Simultaneously, he multiplies the second ratio (6:7) by 2, resulting in 12:14. This aligns the ratios to form a combined sequence A:B:C as 9:12:14. Consequently, the ratio of A to C is derived as 9:14.

  2. 2:00 – 5:00 02:00-05:00

    Next, a second example is introduced: "If A : B = 4 : 7 and B : C = 2 : 3, find A : C?". The instructor repeats the process of aligning the common term B. He notes the LCM of 7 and 2 is 14. He multiplies the first ratio (4:7) by 2 to get 8:14 and the second ratio (2:3) by 7 to get 14:21. This creates the combined ratio A:B:C as 8:14:21, yielding A:C = 8:21. He then introduces a shortcut method, writing the equation A/C = (A/B) x (B/C). He substitutes the fractions 4/7 and 2/3 into the equation. The multiplication yields 8/21, confirming the previous result. This method is highlighted as a quicker alternative to finding LCMs.

  3. 5:00 – 6:03 05:00-06:03

    The instructor returns to the first problem to demonstrate the shortcut method in detail. He writes the equation A/B x B/C = A/C. He substitutes the values 3/4 and 6/7. He explicitly shows the cross-simplification step where the 6 in the numerator and the 4 in the denominator are both divided by 2. This simplifies the expression to (3/2) x (3/7). The final multiplication gives 9/14. He circles the final answer to emphasize correctness. The video concludes with a black screen displaying "THANKS FOR WATCHING" in orange and white text, signaling the end of the lesson on combining ratios.

The lesson effectively bridges the gap between basic ratio definitions and more complex combined ratio problems. By first establishing the need for a common term (B) and then introducing the fraction multiplication shortcut, the instructor provides students with two distinct strategies. The visual progression from vertical alignment to fraction multiplication reinforces the mathematical logic behind the operations.

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