Short Tricks to Combine Two or More Ratios

Duration: 16 min

This video lesson is available to enrolled students.

Return to /learn/UPPSC-COMPUTER-OPERATOR-GRADE-B/reasoning/ratio-and-proportion-ratios/successive-combined-ratio-problems/asset-short-tricks-to-combine-two-or-more-ratios after enrolling

Inside: a video lesson and guided study material.

Module outline

  1. English Comprehension: Comprehension / Reading Comprehension / Unseen Passages (Critical Reasoning) (Paragraph Questions), Reading Comprehension, Vocabulary, Idioms and Phrases, Narrative Sequencing, Critical Reasoning
  2. Reasoning and Aptitude: Series (Number and Letter Series) (Numerical Relations and Reasoning), Coding Decoding, Analogy, Non Verbal Reasoning (Spatial Aptitude) (Spatial Reasoning) (Visual Reasoning), Blood Relations, Directions (Direction Test), Ranking, Order and Sequence, Logical Sequence Of Words, Seating Arrangements, Puzzle Solving (Puzzles), Syllogisms, Deductive and Inductive Reasoning (Logical Deduction and Induction) (Prepositional Reasoning), Data Sufficiency, Selection Decision Table (Decision Making), Calendar, Clock, Cubes & Dices, Data Arrangement, Venn Diagram, Analytical Reasoning (Counting Figures Reasoning), Number System, HCF LCM, Percentage, Ratio and Proportion (Ratios), Average, Profit and Loss, Simple Interest and Compound Interest, Speed Time and Distance, Mensuration and Geometry, Arithmetic, Mixture and Alligation, Age Problems, Data Interpretation, 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, Simplification and Approximation, Assembling and Grouping of Shapes, Transformation of Shapes, Three-Dimensional Patterns and Visualization, Cubes and Dice, Algebra, Traverse Surveying, Clocks and Calendars, Order, Ranking and Sequence, Constraint Puzzles, Syllogisms and Venn Diagrams, Ratio and Proportion, Mensuration, Permutations and Combinations, Project Monitoring, Resources and Safety, Profit, Loss and Discount, Sequences and Series, Powers, Surds and Logarithms, Subject-Verb Agreement, Sentence Completion, Geometry, Probability, Trigonometry, Measurement and Quantity Take-Off, Statistics, Data Sufficiency, Blood Relations, Speed, Time and Distance, Time and Work, Data Interpretation, Sequence and Series (Series), Algebra, Permutation and Combination, Combinatorics
  3. General Awareness: Physics, Chemistry, Biology, Geography, History, Polity, Indian Economy
  4. Computer Fundamentals: Basics of COA, Number System, Number Representation, Semiconductor Memories and Programmable Logic, Timing, Hazards and Testing, Processor Organization and Instructions, Number Systems and Codes, Combinational Logic Design, Combinational Logic Circuits, Number Systems and Codes
  5. Operating System: Introduction to OS, Unix OS, Linux OS
  6. C Programming: C Fundamentals, Control Flow, Functions, Arrays & Pointers, Storage Classes, Structures & Enums, DMA, Macros, Scoping & File Handling
  7. OOPS with C++ & Java: OOPS with C++, Java
  8. Database Management System: Basics of DBMS, SQL
  9. MS Office: MS Office Applications
  10. Internet & Web Technologies: Website, Browser & Services, Internet Fundamentals, Web Design & Development, Protocols & Services
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.

Loading lesson…