Demo: Types of Ratios with Examples

Duration: 15 min

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Inside: a video lesson and guided study material.

Module outline

  1. Section A | English: Vocabulary, Comprehension / Reading Comprehension / Unseen Passages (Critical Reasoning) (Paragraph Questions), Preposition, Sentence Correction (Error Correction), Sentence Completion (Fill in the blanks), Articles, Sentence Re-arrangements (Para Jumbles) (Narrative Sequencing), Verbal Analogy (Word Based Analogy)
  2. Section A | Quant Aptitude: Ratio and Proportion (Ratios), Mixture and Alligation, Permutation and Combination, Number System, HCF LCM, Sequence and Series (Series), Speed Time and Distance, Arithmetic, Algebra, Powers and Exponents (Surds and Indices), Average, Age Problems, Percentage, Profit and Loss, Partnership, Time and Work, Simple Interest and Compound Interest, Mensuration and Geometry, Probability, Pipe and Cistern
  3. Section A | Reasoning: Series (Number and Letter Series) (Numerical Relations and Reasoning), Coding Decoding, Data Sufficiency, Calendar, Clock, Blood Relations, Directions (Direction Test), Seating Arrangements, Ranking, Order and Sequence, Puzzle Solving (Puzzles)
  4. Section B | C Programming: C Programming by Yash Sir, Coding Questions by Yash Sir
  5. Section B | Data Structures: Algorithm Analysis, Greedy Algorithms, Time Complexity Analysis, Sorting Algorithms, Introduction to DS, Array, Stack, Queue, Linked List, Tree, Graphs
  6. Section B | OOP (C++): Object Oriented Programming (OOPS), Programming in C++
  7. Section B | OS: Introduction to OS, Process Management, CPU Scheduling, Process Synchronization, Threads & Process Creation, Deadlock, Memory Management, Virtual Memory, Disc Scheduling, File Management, Windows OS
  8. Section B | Networking: Introduction to CN, Data Communication, DLL: Access Control, DLL: Flow Control, DLL: Error Control, DLL: Framing, Data Link Layer - Ethernet, Net Layer: IPv4 & Proto, Net Layer: IP Addressing, Net Layer:Routing Protocol, Transport Layer Services, TL: Congestion & UDP, Application Layer, Hardware basics
  9. Section B | AI & Big Data Basics: AI & ML by Arun Sir, Big Data Systems
  10. Section C | Digital Electronics: Digital Systems & Boolean Basics, Logic Gates & Hardware, Boolean Expression, Boolean Minimization, Combinational Circuit, Sequential Circuits, Number System, Number Representation, Analog-Digital Conversion
  11. Section A, C | Comp. Fundamentals, COA: Basics of COA, Floating Point Rep, Cache Memory Organization, Input Output Organisation, Pipelining, Instr Formats & Modes, Control Unit Design, Register Transfer and Microoperations, Multiprocessors, Programming the Basic Computer
  12. MOCK TEST:
AI summary & chapters

AI Summary

An AI-generated summary of this video lecture.

This educational video provides a comprehensive lecture on the types of ratios and their applications in mathematics. The lesson begins by defining ratio as a comparison between two quantities, establishing the foundational notation of a:b. The instructor systematically introduces various specific types of ratios, starting with Duplicate Ratio (a²:b²) and Sub-Duplicate Ratio (√a:√b), using the numerical example 8:1 to demonstrate transformations. The progression continues with Triplicate Ratio (a³:b³) and Sub-Triplicate Ratio, extending the concept of powers and roots to ratio terms. A significant portion of the lecture is dedicated to Inverse Ratio, where the instructor clarifies that while a two-term ratio a:b becomes b:a, three-term ratios like a:b:c require taking reciprocals (1/a : 1/b : 1/c) and simplifying via the Least Common Multiple. The final section covers Compound or Mixed Ratio, defining it as the product of antecedents and consequents across multiple ratios. The video concludes with a worked example calculating the compound ratio of three fractions (2/3, 7/9, and 12/35), demonstrating the multiplication of numerators and denominators followed by simplification.

Chapters

  1. 0:00 – 2:00 00:00-02:00

    The lecture opens with the definition of Ratio & Proportion, explicitly stating that a ratio is a comparison of two quantities. The instructor introduces the general form a:b and immediately applies it to the numerical example 8:1. Key visual cues include on-screen text defining ratio components (part, whole, total) and the transition to Duplicate Ratio. The instructor assigns specific values a=8 and b=1 to set up the calculation for the duplicate form, underlining key terms to emphasize the structure of the ratio before moving into specific transformations.

  2. 2:00 – 5:00 02:00-05:00

    This segment details the definitions and calculations for Duplicate Ratio, Sub-Duplicate Ratio, Triplicate Ratio, and Sub-Triplicate Ratio. The instructor demonstrates that a Duplicate Ratio transforms a:b into a²:b², showing 8:1 becoming 64:1. The lesson then defines Sub-Duplicate Ratio as taking the square root of terms (√a:√b), calculating 8:1 into 2√2 : 1. The progression continues to Triplicate Ratio (a³:b³) and the introduction of Sub-Triplicate Ratio, where the instructor begins setting up cube root calculations. Visual evidence includes handwritten formulas and step-by-step substitutions of numerical values into these power-based ratio definitions.

  3. 5:00 – 10:00 05:00-10:00

    The focus shifts to Inverse Ratio, distinguishing between two-term and three-term ratio inversions. For a:b, the inverse is simply b:a, but for a:b:c, the instructor shows that reversing to c:b:a is incorrect. Instead, the method involves taking reciprocals (1/a : 1/b : 1/c) and simplifying by finding a common denominator. A specific example is worked through using the ratio 3:4:6, where reciprocals are taken (1/3 : 1/4 : 1/6). The instructor calculates the LCM of denominators (3, 4, and 6) as 12, multiplies each term by 12 to clear fractions, and derives the final integer inverse ratio of 4:3:2.

  4. 10:00 – 14:55 10:00-14:55

    The final section defines Compound Ratio (also called Compounded or Mixed Ratio) as the product of antecedents and consequents. The rule is established that for ratios a:b and c:d, the compound ratio is ac:bd. The instructor applies this to a complex problem involving three fractions: 2/3, 7/9, and 12/35. The solution demonstrates multiplying all numerators (2x7x12) and denominators (3x9x35). The instructor then performs simplification by crossing out common factors, reducing the expression to (4x2)/(9x5), illustrating the practical application of multiplying ratios termwise.

The video effectively structures the learning of ratio types by moving from basic definitions to complex transformations. The instructor consistently uses a specific numerical example (8:1) early on to anchor abstract concepts like Duplicate and Sub-Duplicate ratios before generalizing the rules. A critical pedagogical distinction is made regarding Inverse Ratios, where the instructor explicitly corrects the common misconception of simply reversing terms in multi-term ratios. The use of visual aids, such as underlining formulas and crossing out factors during simplification, reinforces the procedural steps required for exams. The progression culminates in Compound Ratio, integrating previous knowledge of multiplication and simplification to solve problems involving multiple fractions. This logical flow ensures students understand not just the formulas but the underlying mathematical operations required to manipulate ratios in various contexts.

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