Short Tricks to Combine Two or More Ratios

Duration: 16 min

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Module outline

  1. Numerical Ability & Problem Solving: Speed Mathematics and Basic Mathematics, Arithmetic, Number System, HCF LCM, Divisibility Rules, Percentage, Ratio and Proportion (Ratios), Average, Profit and Loss, Simple Interest and Compound Interest, Mixture and Alligation, Time and Work, Pipe and Cistern, Speed Time and Distance, Age Problems, Partnership, Data Interpretation, Mental Ability, Sequence and Series (Series), Powers and Exponents (Surds and Indices), Algebra, Statistics, Logarithm, Mensuration and Geometry, Permutation and Combination, Probability, Sequences and Series, Powers, Surds and Logarithms, Subject-Verb Agreement, Sentence Completion, Geometry, Sentence Structure and Correction, Data Sufficiency, Trigonometry, Measurement and Quantity Take-Off, Signal Space and Optimum Detection, Probability, Statistics, Algebra, Time and Work, Speed, Time and Distance, Data Interpretation, Combinatorics
  2. Logical Reasoning: Series (Number and Letter Series) (Numerical Relations and Reasoning), Coding Decoding, Data Sufficiency, Syllogisms, Deductive and Inductive Reasoning (Logical Deduction and Induction) (Prepositional Reasoning), Seating Arrangements, Blood Relations, Directions (Direction Test), Non Verbal Reasoning (Spatial Aptitude) (Spatial Reasoning) (Visual Reasoning), Analytical Reasoning (Counting Figures Reasoning), Puzzle Solving (Puzzles), Calendar, Clock, Cubes & Dices, Logical Sequence Of Words, Venn Diagram, Data Arrangement, Inequality, Analogy, Ranking, Order and Sequence, Selection Decision Table (Decision Making), Alphabet and Word Tests, Numerical Reasoning, Number System, Averages, Mixtures and Alligation, Percentages, Series Completion, Analogy and Classification, Patterns in Two-Dimensional Figures, Coding and Decoding, Mathematical Operations, Direction Sense, Logical Deduction and Induction, Syllogisms and Venn Diagrams, Critical Reasoning, Order, Ranking and Sequence, Reading Comprehension, Profit, Loss and Discount, Constraint Puzzles, Traverse Surveying, Ratio and Proportion, Mensuration, Permutations and Combinations, Clocks and Calendars, Assembling and Grouping of Shapes, Transformation of Shapes, Three-Dimensional Patterns and Visualization, Cubes and Dice, Vocabulary, Blood Relations
  3. General Knowledge & Current Affairs (India + Rajasthan): History, Geography, Polity, Indian Economy, Static General Knowledge, State Wise GK, GK- Current Affairs, Environment, Physics
  4. Computer Fundamentals & Operating Systems: Basics of COA, Floating Point Rep, Digital Systems & Boolean Basics, Number Representation, Number System, Introduction to OS, File Management, Windows OS, Unix OS, Linux OS, Register Transfer and Microoperations, Virtual Memory
  5. Computer Networks: Introduction to CN, Data Communication, DLL: Error Control, DLL: Access Control, Data Link Layer - Ethernet, Net Layer: IPv4 & Proto, Application Layer, Hardware Basics, Network Security
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  7. Programming (C & OOP): C Fundamentals, Control Flow, Arrays & Pointers, Functions, Storage Classes, Structures & Enums, DMA, Macros, Scoping & File Handling, OOPS with C++, Operators & Expressions, Sorting Algorithms, Java Fundamentals, Java
  8. MS Office & Data Processing: MS Office Applications, Basics of DBMS
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AI summary & chapters

AI Summary

An AI-generated summary of this video lecture.

This lecture by Yash Jain on Ratio and Proportion teaches a systematic shortcut for combining two or more ratios that share common terms. The instructor begins with the foundational example of finding a:b:c given a:b = 2:3 and b:c = 5:6. The core method involves converting the ratios into fractions (a/b and b/c), identifying the common variable, and scaling each ratio so that the shared term has an equal value in both. In the first example, multiplying a/b by 5 and b/c by 3 makes 'b' equal to 15 in both, yielding a:b:c = 10:15:18, which simplifies to 2:3:6. The lesson then progresses to more complex chains, such as finding a:b:c:d from three ratios (a:b = 3:4, b:c = 5:6, c:d = 2:3). Here, the instructor uses a tabular or grid method to align all common terms horizontally. By cross-multiplying the numerators and denominators across the chain, the combined ratio is calculated as 3×5×2 : 4×5×2 : 4×6×2 : 4×6×3, resulting in 30:40:48:72. This is then simplified by dividing by the greatest common divisor to reach the final answer of 15:20:24:36. The video emphasizes that the key to these tricks is maintaining the proportional relationship while making common terms identical, allowing for a direct read-off of the combined ratio.

Chapters

  1. 0:00 – 2:00 00:00-02:00

    The video opens with a title slide for 'Ratio & Proportion' by Yash Jain. The first problem is presented: find a:b:c if a:b = 2:3 and b:c = 5:6. The instructor writes these as fractions, a/b = 2/3 and b/c = 5/6, and begins mapping the values for each variable to identify the common term 'b'.

  2. 2:00 – 5:00 02:00-05:00

    The instructor demonstrates the scaling method for the first example. To make 'b' equal, a/b is multiplied by 5 to become 10/15, and b/c is multiplied by 3 to become 15/18. This allows the combined ratio a:b:c to be written as 10:15:18, which is then simplified by dividing all terms by 5 to reach the final answer of 2:3:6.

  3. 5:00 – 10:00 05:00-10:00

    A second example is solved where a:b = 3:4 and b:c = 7:8. Using the same cross-multiplication logic, the ratios are adjusted to a/b = 21/28 and b/c = 28/32, resulting in a combined ratio of 21:28:32. The instructor then introduces a more complex four-variable problem involving three ratios to find a:b:c:d.

  4. 10:00 – 15:00 10:00-15:00

    The instructor sets up a four-column table for the problem where a:b = 3:4, b:c = 5:6, and c:d = 2:3. Using a grid layout with empty boxes for unknowns, the instructor shows how to multiply terms horizontally across the chain. The products are calculated as 3×5×2 : 4×5×2 : 4×6×2 : 4×6×3, leading to the intermediate ratio 30:40:48:72.

  5. 15:00 – 15:38 15:00-15:38

    The final steps of the four-variable problem are shown. The intermediate ratio 30:40:48:72 is simplified by dividing all terms by 2 (indicated by a '← /2' note). The final boxed answer is presented as 15:20:24:36, with the first two terms circled to emphasize the successful combination of the ratio chain.

The lecture provides a clear, step-by-step progression from simple two-ratio combinations to complex four-variable chains. The central takeaway is the 'common term' rule: by scaling adjacent ratios so that their shared variable matches, students can directly construct the combined ratio. The transition from manual fraction manipulation to a tabular grid method is a key pedagogical shift, offering a more organized 'shortcut' for exams. The use of visual cues like circling common terms and drawing arrows between grid cells helps students track the multiplication steps, ensuring that no term is missed in long ratio chains.

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