Average - Cricket Based Problems on Average (Part 2)

Duration: 10 min

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Module outline

  1. About Course: About the Course
  2. Section A: General Awareness: Polity, Physics, Biology, Chemistry, Static General Knowledge, History, Geography, Indian Economy, GK- Current Affairs, Evolution of Indian Banking (Banking & Financial Awareness), Environment
  3. Section A: General Intelligence & Reasoning ability: Series (Number and Letter Series) (Numerical Relations and Reasoning), Coding Decoding, Data Sufficiency, Non Verbal Reasoning (Spatial Aptitude) (Spatial Reasoning) (Visual Reasoning), Analytical Reasoning (Counting Figures Reasoning), Blood Relations, Syllogisms, Deductive and Inductive Reasoning (Logical Deduction and Induction) (Prepositional Reasoning), Seating Arrangements, Directions (Direction Test), Puzzle Solving (Puzzles), Calendar, Clock, Cubes & Dices, Selection Decision Table (Decision Making), Logical Sequence Of Words, Crypt Arithmetic, Venn Diagram, Data Arrangement, Inequality, Analogy, Ranking, Order and Sequence, TCS NQT Advanced Reasoning Ability
  4. Section A: Arithmetical & Numerical Ability: 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, Percentage, Average, Profit and Loss, Simple Interest and Compound Interest, Time and Work, Pipe and Cistern, Mensuration and Geometry, Powers and Exponents (Surds and Indices), Algebra, Probability, Mental Ability, Age Problems, Partnership, Statistics, Arithmetic, Speed Mathematics and Basic Mathematics, Miscellaneous
  5. Section A: English Language & Comprehension: Vocabulary, Subject Verb Agreement (Verb Noun Agreement), Adjectives, Tenses, Comprehension / Reading Comprehension / Unseen Passages (Critical Reasoning) (Paragraph Questions), Articles, Sentence Construction, Preposition, Direct and Indirect Speech, Sentence Completion (Fill in the blanks), Sentence Re-arrangements (Para Jumbles) (Narrative Sequencing), Modals, Active Passive Voice (Voice), Sentence Correction (Error Correction), Adverb, Conjunction, Cloze Test (Cloze Passage)
  6. Section A: Hindi Language & Comprehension: भाषा, लिपि, ध्वनि, वर्ण, अक्षर, स्वर, व्यंजन, मात्रा और संयुक्ताक्षर, वर्तनी, वर्ण-विन्यास, अनुस्वार, अनुनासिक, चंद्रबिंदु और ‘र’ के रूप, शब्द, पद और शब्द-भेद, संज्ञा और सर्वनाम, विशेषण और क्रिया, लिंग, वचन, पुरुष और कारक, काल, वाच्य, वाक्य और वाक्य-भेद, संधि, समास, विलोम शब्द, पर्यायवाची शब्द, सामान्य अशुद्धियाँ, अनेक शब्दों के लिए एक शब्द, मुहावरे और लोकोक्तियाँ, अपठित गद्यांश और अपठित पद्यांश, Multi-Topic Content (Cross-Concept Material), वर्णमाला
  7. Section B: Programming, Data Structures, OOP & Java: C Fundamentals, Control Flow, Functions, Arrays & Pointers, Storage Classes, Structures & Enums, DMA, Macros, Scoping & File Handling, Introduction to DS, Array, Stack, Queue, Linked List, Tree, Graphs, Hashing, Java, OOPS with C++, Language Design, Intro to Compilers, Visual Basics, Syntax Analysis: Bottom-Up, Object Oriented Technology
  8. Section B: Computer Networks, TCP/IP & Network Security: Introduction to CN, Data Communication, DLL: Flow Control, DLL: Access Control, DLL: Error Control, Data Link Layer - Ethernet, Net Layer: IPv4 & Proto, Net Layer: IP Addressing, Transport Layer Services, TL: Congestion & UDP, Application Layer, Hardware basics, Network Access Technologies, Network Security, Society, Law & Ethics, Mobile Computing, Net Layer:Routing Protocol, Cyber Safety and Security
  9. Section B: Teaching Methodology: Child Development, Concept of Pedagogy, Theories, Inclusive Education, Experiential Pedagogy, Assessment & Evaluation, Curriculum Framework & Reforms, National Education Policy (NEP) 2020, Psychology, Teaching-Learning Process, Personality Development, Teaching Methods & Strategies, Learning and Motivation, Learners & Learning Process, Factors Affecting Teaching, Methods of Teaching, Nature, Objectives & Characteristics of Teaching, Teaching-Learning Aids & ICT Integration, Classroom Management & Communication, Evaluation, Assessment & Measurement, Curriculum & School Environment, Inclusive Education & Special Needs, Professional Development & Ethics
  10. Section B: Digital Electronics / Boolean Logic: Digital Systems & Boolean Basics, Logic Gates & Hardware, Boolean Expression, Boolean Minimization, Combinational Circuit, Sequential Circuits, Number System, Number Representation, Analog-Digital Conversion
  11. Section B: Operating Systems & Linux: Introduction to OS, Process Management, CPU Scheduling, Process Synchronization, Threads & Process Creation, Deadlock, Memory Management, Virtual Memory, File Management, Disc Scheduling, Unix OS, Linux OS, Distributed Systems, Windows OS
  12. Section B: Data Base Management System: Basics of DBMS, ER Diagram, Relational Model & Functional Dependencies, Keys & Integrity Constraints, Normalization (1NF - BCNF), Decomposition Properties & 4NF, Relational Algebra, SQL, File Organization & Indexing, Transaction Management, Concurrency Control, Database Security & Authorization, Database Recovery, Data Warehousing & Mining
  13. Section B: Internet & Web Technologies: Website, Browser & Services, Internet Fundamentals, Web Design & Development, Protocols & Services, Web Publishing & Hosting, Server Side & Security, HTML Basics, CSS, Emerging Technologies, JavaScript-Basics, .Net Programming, Electronic Data Interchange and E-Commerce, XML
  14. Section B: Computer Fundamentals, IT Basics & Architecture: Basics of COA, Cache Memory Organization, Input Output Organisation, Register Transfer and Microoperations, Control Unit Design, Programming the Basic Computer, Terms & Abbreviations, MS Office Applications, Instr Formats & Modes, Floating Point Rep
  15. Section B: Python Language: Introduction to Python, Tokens, Variables, Data Types, I/O, Operators & Expressions, Control Flow & Looping, Collections & Strings, Functions & Modules, File Handling & Data Analysis
  16. Section B: Software Engineering: Fundamentals of Software Engineering, Software Requirements and Quality Assurance, Software Design, Estimation and Metrics, Software Testing, Software Maintenance and Configuration Management, extras, Fundamentals of Systems and Information Systems
  17. Section B: Design & Analysis of Algorithms: Algorithm Analysis, Time Complexity Analysis, Sorting Algorithms, Greedy Algorithms, Dynamic Programming, Minimum Spanning Trees, Shortest Path Algos, Advanced Algorithms
  18. Section B: Mathematics: Linear Algebra, Calculus, Trigonometry, Vectors, Set Theory, Functions, Relations, Propositional and Predicate Logic, Research Process Steps, Graph Theory
  19. Section B: Computer Graphics, Multimedia & Mobile Computing: Basics of Computer Graphics, 2-D Geometrical Transforms and Viewing, 3-D Object Representation, Geometric Transformations and Viewing, Multimedia
  20. Section B: Emerging Trends: Emerging Tech Trends, Knowledge Representation, Natural Language Processing
  21. DSSSB Previous Year Paper:
  22. Business Studies and Management: Business Communication, Business Organization and Management, Financial Accounting, Business Economics, Management Information System (MIS), Knowledge Management & New Economy
AI summary & chapters

AI Summary

An AI-generated summary of this video lecture.

This video is a lecture on solving average-related problems, presented by an instructor in a virtual classroom setting. The lecture begins with a problem about Yuvraj Singh's cricket innings, where the average of 40 innings is 50, and the difference between the highest and lowest runs is 172. The average of the remaining 38 innings is 48. The instructor uses the formula for average (Sum = Average × Number) to find the total sum of runs for 40 innings (2000) and for 38 innings (1824). By subtracting these, the sum of the highest and lowest runs is found to be 176. This is combined with the given difference of 172 to form a system of equations: x + y = 176 and x - y = 172, where x is the highest run and y is the lowest. Solving this system yields x = 174 and y = 2, making the highest run 174. The video then transitions to a second problem about the average age of an Indian cricket team. It states that Hardik Pandya is 25, KL Rahul is 3 years older (28), and the average age of the remaining 9 players is x. The total sum of ages is 11x + 25 + 28 = 11x + 53. When Hardik and Rahul are removed, the average of the remaining 9 players is x-1, so their total sum is 9(x-1) = 9x - 9. The equation 11x + 53 = 9x - 9 is solved to find x = -31, which is an impossible age, indicating a data inconsistency. The final problem involves 8 observations with an average of 20, so the total sum is 160. The average of the first two is 15.5, so their sum is 31. The average of the next three is 21.3, so their sum is 64. The sixth observation is 4 less than the seventh, and the seventh is 7 less than the eighth. The instructor sets up the equation 31 + 64 + (x-4) + x + (x+7) = 160, which simplifies to 3x + 98 = 160, leading to 3x = 62 and x = 20.67. The last observation is x+7 = 27.67. The video concludes with a 'Thanks for Watching' screen.

Chapters

  1. 0:00 – 2:00 00:00-02:00

    The video opens with a title card displaying the word 'AVERAGE' in a futuristic, glowing green font against a dark, digital background. This transitions to a lecture screen where the first problem is presented. The problem states: 'The average runs of 40 innings of Yuvraj Singh is 50. The difference between the highest and lowest runs scored by him in any innings is 172. If the average run of the remaining 38 innings is 48. What is the highest run scored by Yuvraj in any inning?'. The options are (a) 172, (b) 174, (c) 176, (d) Data Insufficient. The instructor begins to solve the problem by writing the formula 'Avg = Sum / n' on the blackboard. He calculates the total sum of runs for 40 innings as 40 * 50 = 2000.

  2. 2:00 – 5:00 02:00-05:00

    The instructor continues solving the first problem. He calculates the total sum of runs for the 38 remaining innings as 38 * 48 = 1824. He then subtracts this from the total sum of 40 innings to find the sum of the highest and lowest runs: 2000 - 1824 = 176. He writes the equation 'x + y = 176' on the board, where x is the highest run and y is the lowest. He then uses the given difference, 'x - y = 172'. He adds the two equations: (x + y) + (x - y) = 176 + 172, which simplifies to 2x = 348. He solves for x, getting x = 174. He concludes that the highest run scored is 174, which corresponds to option (b). The instructor then moves to the next problem.

  3. 5:00 – 10:00 05:00-10:00

    The second problem is presented: 'In Indian Cricket team, the age of Hardik Pandya is 25 years. Wicket Keeper KL Rahul is 3 years older than him. If we leave these two from the team, then the average age of the remaining team is decreased by 1 year from the average age of the whole Indian team. What is the average age of the whole team?'. The options are (a) 19, (b) 20, (c) 21, (d) 22. The instructor sets up the problem by letting the average age of the remaining 9 players be 'x'. The total sum of ages for the 11 players is 11x + 25 + 28 = 11x + 53. The sum of the ages of the remaining 9 players is 9(x-1) = 9x - 9. He sets up the equation 11x + 53 = 9x - 9. He simplifies this to 2x = -62, which gives x = -31. He notes that this is an impossible age, indicating a data inconsistency. He then moves to the third problem.

  4. 10:00 – 10:24 10:00-10:24

    The third problem is presented: 'The average of 8 observations is 20. The average of first two and next three observations is 15 1/2 and 21 1/3. If the 6th observation is 4 less than the 7th and 7th is 7 less than 8th observation, then find the last observation?'. The options are (a) 25, (b) 30, (c) 27, (d) Data Insufficient. The instructor calculates the total sum of 8 observations as 8 * 20 = 160. The sum of the first two observations is 2 * 15.5 = 31. The sum of the next three is 3 * 21.333... = 64. He lets the 7th observation be 'x'. Then the 6th is 'x-4' and the 8th is 'x+7'. He sets up the equation: 31 + 64 + (x-4) + x + (x+7) = 160. He simplifies this to 3x + 98 = 160, which gives 3x = 62 and x = 20.67. The last observation is x+7 = 27.67. The video ends with a 'Thanks for Watching' screen.

The video presents a structured lesson on solving average problems, progressing from a straightforward calculation to more complex scenarios involving systems of equations. The core concept is the fundamental formula for average, Sum = Average × Number, which is applied to find total sums and then used to set up equations. The first problem demonstrates how to find the sum of two unknown values (highest and lowest runs) by subtracting the sum of the remaining values from the total sum. This is then combined with a difference to form a system of two linear equations, which is solved to find the individual values. The second problem introduces a logical inconsistency, where the data leads to an impossible negative age, highlighting the importance of checking the validity of solutions. The third problem uses a similar approach, setting up a system of equations based on relationships between variables (observations) to find a specific value. The overall teaching method is to break down each problem into clear, logical steps, using the blackboard to show the derivation process.

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