Solving PROFIT & LOSS Questions Using Alligation Rule

Duration: 15 min

This video lesson is available to enrolled students.

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Inside: a video lesson and guided study material.

Module outline

  1. About the Course: About the Course
  2. Paper-1 & 2 | Basic Numeracy / आधारभूत संख्यात्मक योग्यता: Ratio and Proportion / अनुपात और समानुपात, Divisibility Rules / विभाज्यता के नियम, Mixture and Alligation / मिश्रण और एलिगेशन, Permutation and Combination / क्रमचय और संचय, Logarithm / लघुगणक, Number System / संख्या पद्धति, HCF and LCM / महत्तम समापवर्तक और लघुत्तम समापवर्त्य, Sequences, Series and Combinatorics / अनुक्रम, श्रेणी और संयोजन, Time, Speed and Distance / समय, चाल और दूरी, Percentage / प्रतिशत, Average / औसत, Solid Mensuration / घन क्षेत्रमिति, Age Problems / आयु संबंधी प्रश्न, Arithmetic / अंकगणित, Statistics / सांख्यिकी, Probability / प्रायिकता, Profit, Loss and Discount / लाभ, हानि और बट्टा, Simple and Compound Interest / साधारण और चक्रवृद्धि ब्याज, Partnership / साझेदारी, Speed Mathematics and Basic Mathematics / द्रुत गणित और आधारभूत गणित, Algebra / बीजगणित, Simplification, Indices and Surds / सरलीकरण, घातांक और करणी, Time and Work / समय और कार्य, Pipe and Cistern / नल और टंकी, RSSB Specific Videos - Basic Numeracy / RSSB विशेष वीडियो - आधारभूत संख्यात्मक योग्यता, Sets, Relations, Functions and Discrete Mathematics / समुच्चय, संबंध, फलन और विविक्त गणित, Number Systems and Number Theory / संख्या पद्धति और संख्या सिद्धांत, Coordinate Geometry, Vectors and 3D Geometry / निर्देशांक ज्यामिति, सदिश और त्रिविमीय ज्यामिति, Polynomials, Equations and Complex Numbers / बहुपद, समीकरण और सम्मिश्र संख्याएँ
  3. Paper-1 & 2 | Data Interpretation / आँकड़ों की व्याख्या: Data Interpretation / आँकड़ा निर्वचन
  4. Paper-1 & 2 | General Mental Ability / सामान्य मानसिक योग्यता: Mental Ability / मानसिक योग्यता, RSSB Specific Videos - Mental Ability / RSSB विशेष वीडियो - मानसिक योग्यता
  5. Paper-1 & 2 | Logical Reasoning and Analytical Ability / तार्किक तर्कणा एवं विश्लेषणात्मक क्षमता: Series / श्रेणी, Coding-Decoding / कूट लेखन एवं कूट वाचन, Data Sufficiency / आँकड़ों की पर्याप्तता, Non-Verbal Reasoning / अशाब्दिक तर्क, Syllogisms / न्यायवाक्य, Seating Arrangement and Puzzles / बैठक व्यवस्था एवं पहेलियाँ, Blood Relations / रक्त संबंध, Direction and Distance / दिशा एवं दूरी, Analytical Reasoning (Counting Figures Reasoning) / विश्लेषणात्मक तर्क (आकृति गणना तर्क), Mathematical Operations and Missing Numbers / गणितीय संक्रियाएँ एवं लुप्त संख्या, Calendar and Clock / कैलेंडर एवं घड़ी, Clock / घड़ी, Cubes, Dice and Figure Counting / घन, पासा एवं आकृतियों की गिनती, Venn Diagrams, Syllogism and Inequalities / वेन आरेख, न्याय वाक्य एवं असमानता, Analogy and Classification / सादृश्यता एवं वर्गीकरण, Order and Ranking / क्रम एवं रैंकिंग, Statement-Based Reasoning / कथन आधारित तार्किक विवेचन, Data Arrangement / आँकड़ों की व्यवस्था, Alphabet and Number Test / वर्णमाला एवं संख्या परीक्षण, Crypt Arithmetic / कूट अंकगणित
  6. Paper-1 & 2 | Decision Making and Problem Solving / निर्णय लेना एवं समस्या समाधान: Data Sufficiency and Decision Making / आँकड़ों की पर्याप्तता एवं निर्णय क्षमता
  7. Paper-1 | General Science / सामान्य विज्ञान: Scientific Achievements and Research / वैज्ञानिक उपलब्धियाँ और अनुसंधान, Biology / जीव विज्ञान, Chemistry / रसायन विज्ञान, RSSB Specific Videos / RSSB विशेष वीडियो
  8. Paper-1 | General Awareness / सामान्य जागरूकता: State-Specific General Knowledge / राज्य विशेष सामान्य ज्ञान, Current Affairs / समसामयिकी
  9. Paper-2 | Fundamentals of Computer: Basics of COA, Number System, Floating Point Rep, Number Representation
  10. Paper - 2 | Digital Logic Systems: Digital Systems & Boolean Basics, Logic Gates & Hardware, Boolean Expression, Boolean Minimization, Combinational Circuit, Sequential Circuits
  11. Paper-2 | Operating Systems: Introduction to OS, Process Management, CPU Scheduling, Process Synchronization, Deadlock, Threads & Process Creation, Memory Management, Virtual Memory, Disc Scheduling, File Management, Linux OS, Distributed Systems
  12. Paper-2 | Database Management System: Basics of DBMS, ER Diagram, Relational Model & Functional Dependencies, Keys & Integrity Constraints, Normalization (1NF - BCNF), Decomposition Properties & 4NF, Relational Algebra, SQL, Relational Calculus, File Organization & Indexing, Transaction Management, Concurrency Control
  13. Paper-2 | Data Structures: Introduction to DS, Array, Stack, Queue, Linked List, Tree, Graphs, Hashing
  14. Paper-2 | C Programming: C Fundamentals, Control Flow, Functions, Arrays & Pointers, Storage Classes, Structures & Enums, DMA, Macros, Scoping & File Handling
  15. Paper 2 | Oops, C++, Java: Language Design, OOPS with C++, Java, .Net Programming, Java Fundamentals
  16. Paper 2 | Python: Introduction to Python, Tokens, Variables, Data Types, I/O, Operators & Expressions, Control Flow & Looping, Collections & Strings, Functions & Modules, File Handling & Data Analysis
  17. Paper 2 | Emerging Trends and AI: Emerging Tech Trends, Computer Fundamentals, Trade, Marketing and Consumer Protection / व्यापार, विपणन एवं उपभोक्ता संरक्षण, Computer Networks, Internet of Things, Cloud Computing
  18. Paper-2 | Algorithms: Algorithm Analysis, Time Complexity Analysis, Sorting Algorithms, Greedy Algorithms, Advanced Algorithms
  19. Paper 2 | Data Communication and Network Security: Introduction to CN, Data Communication, DLL: Access Control, DLL: Flow Control, DLL: Error Control, 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, Network Security, Ethical Hacking
  20. Paper-2 I Software Engineering: Fundamentals of Software Engineering, Software Requirements and Quality Assurance, Software Design, Estimation and Metrics, Software Testing, Software Maintenance and Configuration Management
  21. Paper-2 | Computer Organization and Architecture: Cache Memory Organization, Input Output Organisation, Instr Formats & Modes, Control Unit Design, Register Transfer and Microoperations
  22. Paper-2 | Web Development: JavaScript-Basics, HTML Basics, CSS, XML
  23. Pedagogy / शिक्षाशास्त्र: Growth and Development / वृद्धि और विकास, Concept of Pedagogy / शिक्षाशास्त्र की संकल्पना, Cognitive Processes / संज्ञानात्मक प्रक्रियाएँ, Theories of Development / विकास के सिद्धांत, Inclusive Education / समावेशी शिक्षा, Experiential Pedagogy / अनुभवात्मक शिक्षाशास्त्र, Socialisation and Gender / समाजीकरण और जेंडर, National Education Policy (NEP) 2020 / राष्ट्रीय शिक्षा नीति (NEP) 2020
  24. Live Sessions: RSSB Live Sessions
  25. RSSB Paper 1 - Full Mock Tests:
  26. RSSB Paper 2 - Full Mock Tests:
  27. SCI Previous Year Papers:
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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