Solving PROFIT & LOSS Questions Using Alligation Rule

Duration: 15 min

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Module outline

  1. About Course: About the Course
  2. Paper 2 | Digital Logic: Digital Systems & Boolean Basics, Logic Gates & Hardware, Boolean Expression, Boolean Minimization, Combinational Circuit, Sequential Circuits, Number System, Number Representation, Floating Point Rep
  3. Paper 2 | Computer Organization And Architecture: Basics of COA, Cache Memory Organization, Input Output Organisation, Pipelining, Control Unit Design, Instr Formats & Modes, Programming the Basic Computer
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  5. Paper 2 | Programming in C: C Fundamentals, Control Flow, Functions, Arrays & Pointers, Storage Classes, Structures & Enums, DMA, Macros, Scoping & File Handling
  6. Paper 2 | Data Structures And Programming: Introduction to DS, Array, Stack, Queue, Linked List, Tree, Graphs, Hashing, Java, OOPS with C++, Java Fundamentals, Array, String, IO & References
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  11. Paper 2 | Information Systems and Software Engineering: Fundamentals of Software Engineering, Software Requirements and Quality Assurance, Software Design, Estimation and Metrics, Software Testing, Software Maintenance and Configuration Management
  12. Paper 2 | Computer Networks: 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
  13. Paper 2 | Internet & Web Technologies: Website, Browser & Services, Internet Fundamentals, Web Design & Development, Protocols & Services, Web Publishing & Hosting, Server Side & Security, Emerging Technologies, HTML Basics, JavaScript-Basics, CSS, XML, HTML5
  14. Paper 2 | Cyber Security And Emerging Technologies: Emerging Tech Trends, Internet of Things
  15. Paper 2 | Cloud Technology: Cloud Computing
  16. Paper 2 | Probability and statistics: Probability, Statistics
  17. Paper-1 English: Vocabulary, Preposition, Articles, Comprehension / Reading Comprehension / Unseen Passages (Critical Reasoning) (Paragraph Questions), Sentence Re-arrangements (Para Jumbles) (Narrative Sequencing), Sentence Correction (Error Correction), Sentence Completion (Fill in the blanks), Cloze Test (Cloze Passage), Sentence Construction
  18. Paper 1 General Mental Ability & Logical reasoning: 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, Series (Number and Letter Series) (Numerical Relations and Reasoning), Coding Decoding, Data Sufficiency, Non Verbal Reasoning (Spatial Aptitude) (Spatial Reasoning) (Visual Reasoning), Percentage, Average, Powers and Exponents (Surds and Indices), Algebra, Profit and Loss, Simple Interest and Compound Interest, Time and Work, Pipe and Cistern, Mensuration and Geometry, Mental Ability, Age Problems, Partnership, Arithmetic, Speed Mathematics and Basic Mathematics, Syllogisms, Deductive and Inductive Reasoning (Logical Deduction and Induction) (Prepositional Reasoning), Seating Arrangements, Blood Relations, Directions (Direction Test), Analytical Reasoning (Counting Figures Reasoning), Puzzle Solving (Puzzles), Calendar, Clock, Cubes & Dices, Selection Decision Table (Decision Making), Logical Sequence Of Words, Venn Diagram, Analogy
  19. Paper-1 General Knowledge & Current Affairs: State Wise GK, History, Geography, GK- Current Affairs, Static General Knowledge
  20. Full Length Mock Test:
AI summary & chapters

AI Summary

An AI-generated summary of this video lecture.

This educational video is a lecture on the mathematical concept of 'Mixtures and Alligations,' presented by an instructor named Yash Jain. The video begins with a title slide and a brief, humorous meme about tea. The core of the lecture consists of two worked examples. The first problem involves a person selling 50 kg of raw tea at two different profit percentages (8% and 18%) to achieve an overall 14% profit, and the instructor uses the alligation method to find the quantity sold at the higher profit. The second problem is a similar mixture problem involving two types of Colgate toothpaste with different costs, where the goal is to find the quantity of the more expensive type to mix with 27 kg of the cheaper type to achieve a 10% gain when sold at a specific price. The instructor demonstrates the alligation method for both problems, using a visual diagram to calculate the ratio of the components and then finding the required quantity. The video concludes with a 'Thanks for watching' screen.

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' visible at the bottom. This transitions to a presentation slide with a geometric background. The slide displays the title 'MIXTURES & ALLIGATIONS' and credits the instructor as 'By Yash Jain'. A small video feed of the instructor, Yash Jain, is visible in the bottom right corner. The instructor begins the lecture, and a humorous meme appears on screen with the text 'Whenever someone asks for चाय ☕ Me:'. The instructor's name and affiliation, 'YASH JAIN SIR KNOWLEDGE GATE EDUCATOR', are displayed in an orange box in the bottom left.

  2. 2:00 – 5:00 02:00-05:00

    The video displays the first problem on a slide. The text reads: 'Que: Kaleb Bhaiya has 50 kg of raw tea, part of which he sells at 8% profit and the rest at 18% profit. He gains 14% on the whole. The quantity sold at 18% profit is __'. The instructor begins to solve this problem using the alligation method. He writes 'total tea = 50 kg' on the board. He then draws a diagram with '8%' and '18%' at the top, and '14%' in the middle, representing the two profit percentages and the average. He calculates the differences: 18 - 14 = 4 and 14 - 8 = 6, establishing a ratio of 4:6, which simplifies to 2:3.

  3. 5:00 – 10:00 05:00-10:00

    The instructor continues solving the first problem. He uses the ratio 2:3 to find the quantity sold at 18% profit. He writes the equation '4/6 = 2/3' and then calculates the quantity as (3/5) * 50 kg, which equals 30 kg. He writes '30 kg' as the final answer. The instructor then transitions to the second problem. The new problem is displayed on the slide: 'Que: How many Kilograms of Colgate costing Rs.9 per kg must be mixed with 27 kg of Colgate costing Rs.7 per kg so that there may be a gain of 10% by selling the mixture at Rs. 9.24 per kg.' He begins to solve this by identifying the selling price (SP) as 9.24 and the profit percentage (P%) as 10%.

  4. 10:00 – 15:00 10:00-15:00

    The instructor calculates the cost price (CP) of the mixture using the formula CP = SP / (1 + P/100). He writes 'CP = 9.24 / (1 + 10/100) = 9.24 / 1.1 = 8.4'. He then applies the alligation method to the second problem. He writes '9 per kg' and '7 per kg' at the top of a diagram, and '8.4' in the middle. He calculates the differences: 9 - 8.4 = 0.6 and 8.4 - 7 = 1.4. This gives a ratio of 0.6:1.4, which simplifies to 6:14 or 3:7. He then sets up a proportion: 3/7 = x/27, where x is the unknown quantity of the Rs.9 per kg Colgate. He solves for x, finding x = (3 * 27) / 7 = 81 / 7 = 11.57 kg, which he rounds to 11.57 kg.

  5. 15:00 – 15:13 15:00-15:13

    The video concludes with a final screen. The background is a dark purple gradient. In the center, the text 'THANKS FOR WATCHING' is displayed in large, white, capital letters. This is the end of the lecture.

The video provides a clear, step-by-step tutorial on solving mixture and alligation problems. It begins by introducing the topic and then presents two distinct problems. For each problem, the instructor first identifies the given values, then applies the alligation method to find the ratio of the components. This ratio is then used to calculate the specific quantity required. The method is demonstrated visually with diagrams and calculations on a digital whiteboard, making the process easy to follow. The lecture effectively connects the abstract concept of alligation to practical, real-world problems involving profit and cost.

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