SSC_MATHEMATICS_Chapterwise_and_T.pdf

 r a n’s Ki MATHEMATICS CHAPTERWISE COMPILATION OF PREVIOUS YEARS’ SOLVED PAPERS OF EXAMS CONDUCTED BY SSC SSC Graduate Level Exams— Combined Graduate Level Pre. Exams, CPO Sub-Inspector, Section Officer (Audit), Tax Assiatant (Income Tax & Central Excise), Section Officer (...

 r a n’s Ki MATHEMATICS CHAPTERWISE COMPILATION OF PREVIOUS YEARS’ SOLVED PAPERS OF EXAMS CONDUCTED BY SSC SSC Graduate Level Exams— Combined Graduate Level Pre. Exams, CPO Sub-Inspector, Section Officer (Audit), Tax Assiatant (Income Tax & Central Excise), Section Officer (Commercial Audit), Statistical Investigators, Combined Graduate Level Tier-I, Tier-II, SAS, CISF ASI, CPO ASI & Intelligence officer, FCI, Delhi Police SI Exams etc. SSC 10+2 Level Exams— Data Entry Operator & LDC and PA / SA Exam. SSC Combined Matric Level Exam — Combined With Tricky Solutions Matric Level Pre-Exam, Multitasking (Non-Technical) Staff, CISF Constable (GD), Constable (GD) & Riflemen (GD) and Other Competitive Exams. FOR FRANCHISEE CONTACT : RU-67, PITAMPURA, DELHI-110034, Ph : 27345258, 27342249, Fax : 27345258  Delhi : RU-67, For the Opposite Power House, books & magazines Pitampura, Delhi-110034, of Kiran Prakashan Ph. : 011-27342249, contact your nearest 47521267, booksellers. Fax : 011-27345258 For detailed information Email : [email protected] log on our website : www.kiranprakashan.com www.kiranprakashan.com © KIRAN INSTITUTE OF CAREER EXCELLENCE PVT. LTD. (KICX) NEW EDITION The copyright of this book is entirely with the Kiran Institute of Career Excellence Pvt. Ltd. The reproduction of this book or a part of this will be punishable under the Copyright Act. All disputes subject to Delhi jurisdiction. Every possible effort has been made to ensure that the information contained in this book is accurate at the time of going to press, and the publishers and authors cannot accept responsibility for any errors or omissions, however caused. No responsibility for loss or damage occasioned to any person acting, or refraining from action, as a result of the material in this publication can be accepted by the editor, the publisher or any of the authors. Compiled by : Think Tank of PRATIYOGITA KIRAN, KIRAN PRAKASHAN & KICX Assistance : Govind Pd. Singh Ratnesh Kumar Singh Sanket Sah Achal Gupta Design & Layout by : KICX COMPUTER SECTION, New Delhi. Printed at : MAA LAXMI PRINTER, Plot No. 2-A, Khasra No. 20/20, Begumpur Extn. Delhi-110086 Must Read USEFUL FOR ALL Buy Today COMPETITIVE EXAMS About the Book...... The significance of past never diminishes, either in effect or substance. To forget this moot point becomes suicidal sometimes. A minute observation of the past and accumulated experiences help us in shaping our present. The positive and compendious conclusions drawn from the past become our pioneer in charting new ways and teach us to rectify our remedies. Our present is, thus, beautified. Where there is beauty, attraction cannot be negated. It is in this way that the foundation of a concrete future is further solidified. Aspirations turn into realities. This is a realistic reflection. If the past is forgotten by marginalizing this realism, the truth of past surfaces as a path strewn with pebbles. If we preserve and cherish these pebbles of the past and make correct use of them, they become the linchpin of an edifice called success. Thus, the intricacies of our path become effortless and our destination gets more and more intelligible. Kiran Prakashan Pvt. Ltd., which has been at your service for decades and helping you with the multitude of relevant offerings, has made a meaningful effort to put together these invaluable and very useful pebbles in the form of a book, titled Kiran’s SSC Mathematics Chapterwise Solved Papers. It is an undeniable truth that the continuous motion of the past gives birth to change. Change gets inevitability. These changes bring coherence to the changed circumstances and fulfil the exact needs of the present. We reach our destinations only by striking coordination with these changes, lest we should find ourselves at the last row in this age of competition. The destination will be left as something impertinent. Our esteemed readers must be well aware of the changes introduced by the Staff Selection Commission (SSC) in the selection process for different posts. Kiran Prakashan has been keeping you updated with all the relevant information related to these very changes. According to Students, Teachers and Coaching Directors’ demand this book has been changed and arranged by Topicwise/Typewise. The latest edition of Kiran’s SSC Mathematics Chapterwise Solved Papers which is revised, enlarged and updated is another example of our sincere commitment to our readers, imparting completeness in their search for a better and secure future. We have updated each chapter with concise study material and tricky solutions have been provided wherever needed. The book before you, Kiran’s SSC Mathematics Chapterwise Solved Papers, has been based on the questions of Quantitative Aptitude/ Numerical ability that have been asked in the various competitive examinations at the CGL (Tier I & II), CHSL (10+2) and Matric levels. This book has been conceived as a holistic treatment and single solution to all the difficulties that a candidate encounters while appearing for the SSC exams. The Think-Tank of Kiran Prakashan has taken into account the needs and difficulties of candidates and made an attempt to simplify the subject matter by de-constructing every thread and each pattern. The questions asked in the different examinations conducted by the SSC have been not only compiled at one place, but also compartmentalized topicwise/typewise to grasp and digest easily with the help of comprehensive explanations and tricky solutions. This is a rare collection of more than 8900 questions and their respective explanations. It wouldn’t be bragging if we say, do master these questions and their explanations, you will automatically find yourself at ease with most of what surfaces in form of examination questions. In other words, master this book sincerely; success will itself become the mistress.  This edition of Kiran’s SSC Mathematics Chapterwise Solved Papers has been parceled out into 22 chapters, each dealing with study materials, Topicwise and comprising bulk of questions and explanations. The chapters are : Number System, LCM and HCF, Simplification, Power, Indices and Surds, Average, Ratio and Proportion, Percentage, Profit and Loss, Discount, Simple Interest, Compound Interest, Time and Work, Pipe and Cistern, Time and Distance, Boat and Streams, Sequence and Series, Algebra, Trigonometry, Geometry, Mensuration, Statistics and Data Interpretation and Miscellaneous. Explanations to the questions serve in some way as highly directed study material. We have ensured not to bombard you with bulky study materials which sometimes prove futile if a candidate is facing severe crunch of time. Johann Wolfgang von Goethe, considered the supreme genius of modern German literature, said once: “What is not started today is never finished tomorrow.” Relating to what Goethe had to say, we are proud to have made the beginning of a start. And, that start is Kiran’s SSC Mathematics Chapterwise Solved Papers, where facts have been consolidated and refined and presented in the easy-to-digest objective question format which have actually been already asked in the different levels and formats of competitive examinations. Scientifically it has been proved that you tend to remember anything for long if that has been asked from you and you found yourself in a testing situation. So, this book has been scientifically weaved on the principle of ‘Test to Prepare and Success.’ As our experience suggests, SSC, to a great extent, follows the pattern of questions asked in previous examinations. But the scope has been enlarged now. Earlier syllabus was of Arithmetic alone, now it is syllabus of Mathematics. New syllabus has some new topics such as, Trigonometry, Geometry and Algebra with Co-ordinate Geometry. The new syllabus has been given in the introduction. Last, but not the least, there is no shortcut to success. Only hard work and perseverance pays rich dividends in the long term. So, it is desirable on your part to make the best out of this unique offering before you. Let us remind you that the questions you find in this book will not only help you prepare for the SSC examinations, they will equip you with the much required knowledge and insight in ‘cracking’ other examinations as well. Hugh Nibley, the famous American author and Mormon apologist said: “Only if you reach the boundary will the boundary recede before you. And if you don’t, if you confine your efforts, the boundary will shrink to accommodate itself to your efforts. And you can only expand your capacities by working to the very limit.” Our researchers have taken painstaking efforts in the direction of accommodating and expanding to the limit. The guiding principle has been to have an eye on whatever is significant, and when you do have such a microscopic eye, there is little that can be expected to have been ignored. So, here is our new, novel and unique offering to you, Kiran’s SSC Mathematics Chapterwise Solved Papers. You will find a CD and scratch card for online test. This will help you prepare for the SSC online exam pattern. Read this book with pen and paper and digest it thoroughly to reach the limits of life. Have a serious glance to know what it is all about. With the Best Wishes (Publisher) Satyanarayan Prasad Email : [email protected]  SOME NOTABLE FACTS SSC (Staff Selection Commission) Combined Graduate Combined Higher Matric Level Level(CGL) Secondary Level (CHSL) CGL Tier–I, Tier–II, Tier–III LDC & DEO Multi Tasking Staff & Tier–IV, CAPFs SI & Delhi and and Constable (GD) Police SI and FCI etc. Stenographer 'C' & 'D' Ø Staff Selection Commission Conducts examinatiion for Graduate Level, Higher Secondary Level and Matric Level on all India basis. Ø Till now SSC conducted Combined Graduation level Examination used to be held in two parts i.e. Tier-I and Tier-II. But from now onwards this examination will be held in four parts i.e. Tier-I, Tier-II, Tier-III and Tier-IV. Ø Earlier in SSC conducted Tier-I Exam used to have 50 questions on Mathematics out of 200 questions, while in Tier-II a candidate had to answer 100 questions. But from 2016 onwards in Tier-I out of 100 questions, 25 questions will be on Mathematics, while a candidate has to answer 100 questions in Tier-II. Ø SSC Conducts Tier-I examination for CHSL of 100 questions out of which Mathematics carries a weightage of 25 questions. Ø Matric Level exams are conducted for Multi Tasking Staff in which out of 150, 25 questions are from Mathematics and in Constable GD exam weightage of Mathematics is 25 questions out of 100. Ø The Changing nature of Mathematics questions in recent exams conducted by SSC make this subject very important and deciding factor in success or failure. TOP 5 IMPORTANT CHAPTERS 10 9 No. of Questions 8 7 6 5 4 Matric Level Matric Level Matric Level 3 CHSL CHSL CHSL CHSL CGL CGL CGL CGL CGL CHSL 2 Matric Matric Level Level 1 0 Algebra Geometry Trigonometry Mensuration Statistics & Data Name of Chapter Interpretation Ø Combination of Algebra, Geometry, Trigonometry, Mensuration and Statistics & Data Inter- pretation in recent Exams (2011-2017) ion y e tr Mensurat on % om 11% Ge 8% 9 %r et acs & n 7 t io om i rp t g t e a t is et i A lg Tr ebr ry In S t 7% a Others  WE DO WORRY ABOUT YOUR CAREER That is why TO INCULCATE CONFIDENCE IN YOU We do publish almost all competitive books and monthly magazines INDISPENSABLE FOR ALL THE COMPETITIVE EXAMS Releasing shortly a very useful and com- prehensive book on Reasoning catering to the needs of every student preparing for competitive examinations. SPECIAL FEATURES : ➥ This Book is Unique in the sense that it follows easy methods in solving difficult questions. Step -by- step explanations have been given for easy understand- ing. ➥ Concept has been discussed citing questions asked in various competitive examinations. ➥ Step-by-step method has been followed, so that book becomes helpful for all aspirants. For beginners, Price : simple and easy questions have been discussed to give them conceptual clarity and standard of ques- 595 tions has gradually been raised so that they can mas- ter the subject. ➥ This book will stand out from other books available in market as not only the chapters have been discussed in detail;large number of questions have also been included in each chapter. ➥ We have tried to compile questions asked in various exams (Bank PO, Clerk, SSC, Railway, Insurance, RBI, Air Force, by UPSC such as IAS CSAT, CDS, CAPF, NDA , Police, Postal Assistant, Teachers Recruitment Exams and various State Public Service Commission etc; CAT, MAT,XAT etc.). These examples have been solved by conventional methods as well as by short-cut methods. ➥ If you go through this book, you will get acquainted with all types and standards of ques- tions.This will increase your level of preparation and ultimately the chances of your success. ➥ Latest questions i.e.(lengthy questions & tricky questions) particularly in Problem Solving, Decision Making, Ranking and Arrangement, Statement-Argument, Statement-Conclusion/ Inferences have been collected and solved in easy way especially to make you tackle every type of question. ➥ Unique way of solutions to Input-Output Problems. You can also order the book by sending demand draft (D.D.) (Printed price of the book) + Rs. 25 in favour of Kiran Prakashan, payable at Delhi. Shop online at www.kiranprakashan.com  TOPICWISE DISTRIBUTION OF QUESTIONS OF SSC GRADUATE LEVEL (TIER-I, TIER-II, CPO, DPSI) EXAMS HELD DURING 2010–2017 QUANTITATIVE APTITUDE EXAMINATIONS 16.05.2010 (Ist Sitting) SSC CPO SI 12.12.2010 SSC CAPFs SI, CISF ASI * Average number SSC CISF 29.08.2010 & D.P. SI 21.06.2015 SSC CGL Tier-II (CBE) SSC CGL Tier-I (IInd Sitting) 27.10.2016 SSC CGL Tier-II SSC CGL Tier-I & ASI 28.08.2011 SSC CGL Tier-I SSC CGL Tier-I SSC CGL Tier-II of Questions SSC CGL Tier-II SSC CGL Tier-II SSC CGL Tier-II 29.09.2013 SSC CGL Tier-I SSC CGL Tier-I 21.04.2013 26.10.2014 21.09.2014 16.09.2012 SSC CPO SI 12.04.2015 TOPICS 26.06.2011 16.08.2015 25.10.2015 12.01.2017 S. No. 1. Number System 1 4 3 2 3 2 4 2 4 1 — 4 — 2 3 1 4 2. LCM and HCF 1 2 1 1 2 — 1 2 1 3 — — — 1 2 — 2 3. Simplification 1 5 7 6 7 — — 2 — 3 2 3 2 — 1 — 2 4. Power, Indices and Surds 2 6 3 7 4 4 1 3 1 1 3 3 3 1 4 — 1 5. Average 3 2 2 3 2 2 5 2 8 7 2 6 1 1 6 1 5 6. Ratio and Proportion 3 3 4 4 3 3 5 2 5 3 1 5 3 2 7 1 6 7. Percentage 2 2 5 4 4 2 5 2 4 5 1 3 2 1 4 1 6 8. Profit and Loss 3 3 4 4 5 5 6 3 6 6 — 7 3 2 5 1 7 9. Discount 2 2 2 2 3 — 4 1 4 4 4 5 1 1 4 1 3 10. Simple Interest 1 1 3 2 1 2 1 1 1 1 1 1 — — 2 1 — 11. Compound Interest 1 2 1 1 2 — 3 1 3 3 — 3 1 1 3 — 4 12. Time and Work 2 3 3 3 3 2 3 1 3 3 3 6 1 3 5 1 6 13. Pipe and Cistern 1 — 1 1 — 1 2 1 2 2 — 1 — — 2 — — 14. Time and Distance 2 3 2 2 1 1 3 1 3 2 2 2 2 3 4 1 4 15. Boat and Stream 1 — 1 1 1 1 1 1 1 1 — 2 — — 1 — — 16. Sequence and Series 1 2 2 3 — — 1 — 2 2 — — — — — — — 17. Algebra 4 3 — — — 5 9 5 8 10 4 8 5 8 10 4 9 18. Trigonomentry 4 — — — — 5 10 5 10 10 6 9 5 7 9 3 10 19. Geometry 4 — — — — 4 11 5 10 10 7 7 3 5 7 4 7 20. Mensuration 6 3 — 1 5 6 15 5 15 15 5 20 8 5 16 1 19 21. Statistics & Data Interpretation 4 3 3 3 4 5 5 5 6 5 7 5 9 7 5 4 5 22. Miscellaneous 1 1 — — — — 5 — 3 3 2 — 1 — — — — Total Number of Questions 50 50 50 50 50 50 100 50 100 100 50 100 50 50 100 25 100 * Average number of questions is based on the data available in the chart mentioned above (Considering 50 questions set) ARE YOU FOR THEAN AVAILABILITY ASPIRANT OF SSC TIER-I, OF TIER-II, THE FCI, 10+2 LDC & FOLLOWING DATA ENTRY OPERATOR AND MATRIC LEVEL EXAMS ? You do well know that in the recent exams conducted by SSC, 20–30 questions (out of 50) were asked from 1.ALGEBRA 2.TRIGONOMETRY 3.GEOMETRY 4.MENSURATION topics. The chart given below proves the importance of these topics. ALGEBRA TRIGONOMETRY GEOMETRY MENSURATION SSC CHSL (10+2) LDC, DEO & PA/SA Exam, 15.11.2015 (1st Sitting) 10 5 4 6 SSC CHSL (10+2) LDC, DEO & PA/SA Exam, 15.11.2015 (2nd Sitting) 6 6 5 4 SSC CGL Tier-II Exam, 25.10.2015 22 9 11 12 SSC CGL Tier-I Exam, 30.08.2015 11 7 8 3 SSC CGL Tier-I Exam, 19.08.2015 (2nd Sitting) 10 7 9 2 SSC Combined Graduate Level (CGL) Tier-I Exam, 21.04.2013 7 5 8 5 SSC FCI Assistant Grade-III Exam, 07.04.2013 5 5 5 6 SSC FCI Assistant Grade-III Exam, 11.11.2012 6 5 6 5 SSC 10+2 Higher Secondary Level Data Entry Operator & LDC Exam, 04.11.2012 4 6 4 4 CONTENTS MENSURATION v Chapter-18 : Area ALGEBRA and Perimeter ( Tri- v Chapter-01 : Indices and Surds angles, Rectangles, v Chapter-02 : Polynomials Squares, Quadrilaterals, v Chapter-03 : Factorisation of Quadratic Polynomials Rhombus, Circles) v Chapter-04 : Simplification of Fractions v Chapter-19 : Vo l - ume (Cubes, Spheres, Price : v Chapter-05 : Algebraic Identities Hemispheres, Cylinders, 295 v Chapter-06 : Solutions of Linear Equations Cones, Frustums, Prism, v Chapter-07 : Graphic Representation of Straight Pyramids) Pages: Lines v IMPORTANT POINTS 712 v Chapter-08 : Co-ordinate Geometry AT A GLANCE v Chapter-09 : Sequence and Series v IMPORTANT POINTS AT A GLANCE Indispensable Book for the Preparation of TRIGONOMETRY v Chapter-10 : Circular Measure of Angles l ALGEBRA v Chapter-11 : Trigonometric Ratios l TRIGONOMETRY v Chapter-12 : Trigonometric Identities l GEOMETRY v Chapter-13 : Heights and Distances l MENSURATION v IMPORTANT POINTS AT A GLANCE Useful for : SSC CGL GEOMETRY Tier-I Exam, SSC CGL v Chapter-14 : Lines and Angles Price : Tier-II Exam, SSC v Chapter-15 : Triangles : Similarity and Congru- 99 ence CAPFs Exam, SSC v Chapter-16 : Quadrilaterals 10+2 DEO/LDC/PA/SA v Chapter-17 : Circles : Chords and Tangents Exam and other SSC v IMPORTANT POINTS AT A GLANCE and Competitive Exams You can also order the book by sending demand draft (D.D.) (Printed price of the book) + Rs. 25 in favour of Kiran Prakashan, payable at Delhi. Shop online at www.kiranprakashan.com  TOPICWISE DISTRIBUTION OF QUESTIONS SSC 10+2 DEO & LDC AND MATRIC LEVEL EXAMS HELD ON DURING 2010–2017 QUANTITATIVE APTITUDE EXAMINATIONS * Average number 10.11.2013 (IInd Sitting) SSC CHSL (10+2) Tier-I SSC CHSL DEO & LDC SSC CHSL (10+2) Tier-I SSC CHSL DEO & LDC 20.12.2015 (Ist Sitting) SSC CHSL DEO & LDC 06.12.2015 (Ist Sitting) SSC CHSL DEO & LDC 15.11.2015 (Ist Sitting) 04.10.2015 (Ist Sitting) SSC Multitasking Staff SSC Constable (GD) SSC Constable (GD) of Questions TOPICS (CBE) 08.09.2016 (CBE) 16.01.2017 SSC Multi-Tasking SSC DEO & LDC SSC DEO & LDC 22.04.2012 (Ist S) SSC DEO & LDC SSC DEO & LDC SSC DEO & LDC SSC Cons. (GD) & Riflemen (GD) 16.11.2014 27.11.2010 (IInd Sitting) 11.12.2012 20.02.2011 (Ist Sitting) 04.12.2011 27.02.2011 05.06.2011 17.03.2013 S. No. 1. Number System 1 4 2 3 6 2 3 3 2 3 — 2 3 — 1 — 2 2. LCM and HCF 1 2 — 1 2 1 1 1 1 1 — — — — 1 — — 3. Simplification 2 5 — 7 5 6 — — 1 — 1 1 1 2 — — — 4. Power, Indices and Surds 3 6 10 6 5 7 1 1 1 3 1 — 2 1 1 3 — 5. Average 2 2 3 2 1 3 2 2 2 2 2 3 1 3 2 1 1 6. Ratio and Proportion 3 3 5 4 2 4 2 2 2 — 2 1 1 2 2 1 1 7. Percentage 3 2 4 5 2 4 2 2 2 1 2 2 2 1 2 1 1 8. Profit and Loss 3 3 3 4 3 5 2 2 3 3 2 2 3 4 3 1 — 9. Discount 2 2 3 2 3 2 2 2 2 2 2 4 2 2 2 1 2 10. Simple Interest 1 1 2 3 1 2 — — 1 1 — 2 — 1 2 1 — 11. Compound Interest 1 2 1 1 1 1 1 1 1 1 1 — 2 1 — — 1 12. Time and Work 2 3 2 3 2 3 2 2 2 1 1 2 2 2 2 1 1 13. Pipe and Cistern 1 — 1 1 1 1 — — 1 — 1 — — — — — — 14. Time and Distance 2 3 3 2 4 2 — — 1 1 1 2 2 1 2 1 1 15. Boat and Stream 1 — — 1 — 1 1 1 — 1 — — — 1 — — — 16. Sequence and Series 1 2 — 2 1 3 — — — — 3 — — 1 — — — 17. Algebra 3 3 — — 1 — 5 5 — 5 5 — 5 3 5 2 5 18. Trigonomentry 3 — — — — — 5 5 — 5 5 — 4 5 5 3 4 19. Geometry 4 — — — — — 6 6 — 6 7 — 5 6 6 4 1 20. Mensuration 5 3 5 — 4 1 6 6 1 8 5 2 6 5 5 1 1 21. Statistics & Data Interpretation 5 3 5 3 3 3 9 9 2 4 9 2 9 9 9 4 4 22. Miscellaneous 1 1 1 — — — 5 5 — 2 — — — — — — — Total Number of Questions 50 50 50 50 50 50 25 25 25 50 50 25 50 50 50 25 25 * Average number of questions is based on the data available in the chart mentioned above (Considering 50 questions set)  6th REVISED AND ENLARGED EDITION SALIENT HIGHLIGHTS : F Comprehensive Coverage of Syllabi of almost all Competitive Exams. F Revised Edition based on analysis of the trend of latest questions of various exams. F Fundamental concepts dealt in detail with illustrative examples. F Derivation of Short-cut methods and tricks from fundamentals and their applications. F Problem-solving by Traditional as well as Tricky/short-cut methods. F Wide variety of questions covered on each topic. F Inclusion of questions based on the latest pattern of examinations. F Exhaustive solved problems in each chapter. F Caution notes on grey areas prone to common error. F Wide coverage of previous years’ solved problems. F Frequently used Rules and Formulae marked in boxes. F A unique approach to Data Sufficiency and Data Analysis & Data Inter- Price : pretation. 555 CHAPTERS 1. Numbers 2. Binary Number System 3. Addition and Subtraction 4. Vedic Mathematics 5. Multiplication 6. Division 7. Divisibility 8. LCM and HCF 9. Decimal & Fraction 10. Power and Roots – Square, Cube - Indices, Surds 11. Algebra 12. Simplification 13. Percentage 14. Profit and Loss 15. Average 16. Ratio and Proportion 17. Alligation or Mixture 18. Partnership 19. Problems Based on Ages 20. Simple Interest 21. Compound Interest 22. Time and Work 23. Work and Wages 24. Pipes and Cistern 25. Time and Distance 26. Trains 27. Boats and Streams 28. Races and Games 29. Geometry : Lines, Angles 30. Triangles 31. Quadrilaterals 32. Circles 33. Area and Perimeter 34. Volume and Surface Areas (3-Dimensional Figures) 35. Trigonometry 36. Height and Distance 37. Series 38. Progression and Sequence 39. Permutation and Combination 40. Probability 41. Logarithms 42. Calendar 43. Clocks 44. Data Analysis 45. Data Sufficiency 46. Data Interpretation A NEW INTRODUCTION ON HIGH DEMAND Kiran’s Quickest Mathematics Practice Work Book F It is truly said, “ Practice makes a man Perfect” and there can be no better example than Mathematics to suffice this golden rule. F Keeping alive this spirit, we consciously and cautiously and cautiously decided to have a separate but synergised publica- tion, “Kiran’s Practice Work Book on Quickest Mathematics” that serves the very objective of readers elegantly. F It provides ample opportunity to the Readers of Quickest Math- ematics as well other aspirants to hone their skills and apply the Tricky methods. F It can also work as a tool to review and rate your preparation. Price : F In this book Answers and Explanations have been provided 325 separately - to make you feel the essence of real exam. F It will certainly help you identify your Strength and Weak- nesses and take remedial steps. You can also order the book by sending demand draft (D.D.) (Printed price of the book) + Rs. 25 in favour of Kiran Prakashan, payable at Delhi. Shop online at www.kiranprakashan.com  CONTENTS CHAPTERS........................................ PAGES CHAPTERS........................................ PAGES 1. Number System TYPE–IV : Questions based on ratio of the (No. of Questions 447)........ SME–21-72 numbers...................................... SME–79 TYPE–I : Questions based on Smallest TYPE–V : Questions based on addition, and Largest fraction etc............... SME–25 subtraction, multiplication and division of the numbers............................. SME–79 TYPE–II : Questions based on TYPE–VI : Miscellaneous Questions Division Multiplication, Addition and.................................................... SME–81 Subtraction.................................. SME–26 EXPLANATIONS TYPE–III : Questions based on the Fraction of numbers.................. SME–33 TYPE–I........................................ SME–82 TYPE–IV : Questions based on finding TYPE–II....................................... SME–83 the ascending & descending order of TYPE–III...................................... SME–86 numbers etc................................ SME–39 TYPE–IV...................................... SME–88 TYPE–V : Questions based on finding TYPE–V....................................... SME–89 the unit place of a number.......... SME–39 TYPE–VI...................................... SME–91 TYPE–VI : Questions based on the TEST YOURSELF........................ SME–92 sum of Consecutive numbers 3. Simplification (No. of Questions 334) (Odd, even, etc.)........................... SME–40............................................ SME–95-136 TYPE–VII : Miscellaneous Questions TYPE–I : Questions based on continued.................................................... SME–41 fraction........................................ SME–97 EXPLANATIONS TYPE–II : Questions based on TYPE–I....................................... SME–48 BODMAS..................................... SME–99 TYPE–II...................................... SME–49 TYPE–III : Questions based on TYPE–III..................................... SME–56 square and square root...............SME–104 TYPE–IV..................................... SME–62 TYPE–IV : Questions based on cube & cube root........................SME–111 TYPE–V...................................... SME–62 TYPE–V : Miscellaneous TYPE–VI..................................... SME–63 Questions...................................SME–113 TYPE–VII.................................... SME–65 EXPLANATIONS TEST YOURSELF....................... SME–71 TYPE–I.......................................SME–113 2. LCM and HCF (No. of Questions 177) TYPE–II......................................SME–116............................................. SME–73-94 TYPE–III.....................................SME–122 TYPE–I : Questions based on the TYPE–IV.....................................SME–130 formula (LCM × HCF = First Number TYPE–V......................................SME–132 × Second Number)........................ SME–74 TEST YOURSELF.......................SME–133 TYPE–II : Questions based on only 4. Power, Indices and Surds finding the LCM of the numbers.. SME–75 (No. of Questions 353).... SME–137-192 TYPE–III : Questions based on only TYPE–I : Questions based on finding the HCF of the numbers.. SME–77 Simplification.............................SME–138 CHAPTERS........................................ PAGES CHAPTERS........................................ PAGES TYPE–II : Questions based on finding the TYPE-VI : Question where correct largest and smallest value etc....SME–145 average have to be find out as earlier TYPE–III : Simplifying when root some mistake was done..............SME–203 values are given If TYPE-VII : Questions based on cricket x = a is given...................................................SME–205 (where x = 1, 2, 3 and ‘a’ is the correct TYPE-VIII : Questions where missing value of x )...............................SME–147 number has to be find one as there has TYPE–IV : Questions based on been some change in given average. rationalising or prime factor.......SME–148...................................................SME–207 TYPE–V : Questions based on positive TYPE–IX : Questions based on and negative exponent...............SME–148 determining the average age.......SME–208 TYPE–VI : Questions of type TYPE-X : Miscellaneous Questions...................................................SME–213 EXPLANATIONS x + x + x +....... and x x x x....... TYPE–I......................................SME–217...................................................SME–150 TYPE–II.....................................SME–220 TYPE–VII : Miscellaneous Questions TYPE–III....................................SME–222...................................................SME–151 TYPE–IV....................................SME–223 EXPLANATIONS TYPE–V.....................................SME–224 TYPE–I......................................SME–154 TYPE–VI....................................SME–227 TYPE–II.....................................SME–167 TYPE–VII...................................SME–230 TYPE–III....................................SME–169 TYPE–VIII..................................SME–231 TYPE–IV....................................SME–171 TYPE–IX....................................SME–232 TYPE–V.....................................SME–171 TYPE–X.....................................SME–236 TYPE–VI....................................SME–174 TEST YOURSELF......................SME–240 TYPE–VII...................................SME–175 6. Ratio and Proportion TEST YOURSELF......................SME–179 (No. of Questions 443).... SME–242-312 5. Average (No. of Questions 388) TYPE–I : Questions based on the basic...................................... SME–193-241 concept of Ratio & Proportion......SME–247 TYPE-I : Basic Average Questions TYPE–II : Questions based on Fractions...................................................SME–195...................................................SME–251 TYPE-II : To find nth number when TYPE–III : Questions based on Percentage average of first ‘p’ and last ‘q’ numbers...................................................SME–252 are given....................................SME–198 TYPE–IV : Questions based on Age TYPE-III : average of consecutive even,...................................................SME–252 odd and prime numbers etc........SME–200 TYPE–V : Questions based on addition, TYPE-IV : If the monthly income of difference and product...............SME–254 factors (x, y or z) are given, then TYPE–VI : Questions based on L.C.M. finding the monthly income of ‘x’ & H.C.F.......................................SME–256 or ‘y’ or ‘z’ or ‘x+y’ or ‘‘x–y’ etc......SME–201 TYPE–VII : Finding the sum/difference/ TYPE-V : Questions based on twice, thrice, product of numbers where some change one-third etc. of numbers.............SME–202 has been done in given ratio.......SME–256 CHAPTERS........................................ PAGES CHAPTERS........................................ PAGES TYPE–VIII : Questions based on TYPE–VIII : Questions based on Allegation or Mixtures..................SME–257 tricks Net increase or Decrease % TYPE–IX : Questions based on xy Income or Expenditure.................SME–263 x+y+ 100 TYPE–X : Questions based on -x - y + xy Coins and Rupees......................SME–264 100 TYPE–XI : Questions based on xy Shares and Partners...................SME–265 x-y- 100 TYPE–XII : Miscellaneous Questions xy.........SME–330 -x + y -...................................................SME–268 100 EXPLANATIONS TYPE–IX : Questions based on Voters TYPE–I......................................SME–272 in an Election.............................SME–332 TYPE–II.....................................SME–278 TYPE–X : Questions based on TYPE–III....................................SME–279 Depreciation & Population increase...................................................SME–333 TYPE–IV....................................SME–279 TYPE–XI : Questions based on TYPE–V.....................................SME–282 reducing & exceeding prices........SME–334 TYPE–VI....................................SME–285 TYPE–XII............................................. : TYPE–VII...................................SME–285 Miscellaneous Questions.......................... TYPE–VIII..................................SME–288...................................................SME–335 TYPE–IX....................................SME–296 EXPLANATIONS TYPE–X.....................................SME–299 TYPE–I......................................SME–340 TYPE–XI....................................SME–300 TYPE–II.....................................SME–344 TYPE–XII...................................SME–304 TYPE–III....................................SME–345 TEST YOURSELF......................SME–307 TYPE–IV....................................SME–350 7. Percentage (No. of Questions 485) TYPE–V.....................................SME–352......................................... SME–313-376 TYPE–VI....................................SME–354 TYPE–I : Questions based on the basic concept of percentage................SME–315 TYPE–VII...................................SME–355 TYPE–II : If 'x' is less/more than 'y' TYPE–VIII..................................SME–360 by 'm %’ then 'y' exceed/less TYPE–IX....................................SME–362 than 'x'.......................................SME–319 TYPE–X.....................................SME–364 TYPE–III : Questions based on Income, TYPE–XI....................................SME–366 expenditure, Salary and Wages...SME–320 TYPE–XII...................................SME–369 TYPE–IV : Questions based on Ratio...................................................SME–323 TEST YOURSELF......................SME–373 TYPE–V : Questions based on 8. Profit and Loss (No. of Questions 541) Alligation & Mixture...................SME–325......................................... SME–377-453 TYPE–VI : Questions based on TYPE–I : Questions based on the consumption and expenditure....SME–326 basic concept of C.P. & S.P. and TYPE–VII : Questions based profit & loss................................SME–378 on examination and marks TYPE–II : Questions based on obtained.....................................SME–327 gain & loss percent.....................SME–380 CHAPTERS........................................ PAGES CHAPTERS........................................ PAGES TYPE–III : Questions based on TYPE–VIII..................................SME–429 sold & bought.............................SME–383 TYPE–IX....................................SME–430 TYPE–IV : Questions based on TYPE–X.....................................SME–434 ratio & partnership....................SME–386 TYPE–XI....................................SME–436 TYPE–V : Questions based on tricks TYPE–XII...................................SME–438 xy xy TYPE–XIII.................................SME–439 x+y+ -x - y + 100 100 TYPE–XIV..................................SME–440 xy xy TEST YOURSELF......................SME–447 -x + y - x-y-..SME–389 100 100 9. Discount (No. of Questions 346) TYPE–VI : Questions based On......................................... SME–454-506 selling an article and interchanging TYPE-I : Questions based on its values....................................SME–390 Successive Discount...................SME–455 TYPE–VII : Questions based on TYPE-II : Questions where The Market marked price..............................SME–391 Price is x% higher of cost price. A discount TYPE–VIII : Loss/gain percent is of y% is given on the market Price. Find equals to the C.P./S.P...................SME–393 the Loss/gain percent................SME–459 TYPE–IX : Finding the cost of article TYPE-III : A shopkeeper earns a profit where a man sold an article at a loss of x% after allowing a discount of y% of x%. If he had sold it for 'y' more than on the printed price....................SME–463 he would have gained/loss m%.... SME–394 TYPE-IV : Mixed problems of TYPE–X : Questions where articles marked price..............................SME–466 are sold in a circular chain........SME–396 TYPE-V : Miscellaneous Questions TYPE–XI : A person bought two articles...................................................SME–469 for x. He sold A at m% profit/loss EXPLANATIONS and B at n% loss/profit. Then gain/ TYPE–I......................................SME–474 loss p% on his outlay. Find the c.p. TYPE–II.....................................SME–483 of A/B/A+B etc...........................SME–396 TYPE–III....................................SME–490 TYPE–XII : Difference between TYPE–IV....................................SME–495 selling price and Cost Price........SME–399 TYPE–V.....................................SME–501 TYPE–XIII : Find the reduced/increased price of an article.......................SME–399 TEST YOURSELF......................SME–506 TYPE–XIV : Miscellaneous Questions 10. Simple Interest (No. of Questions 186)...................................................SME–400...................................... SME–507-538 TYPE–I : Questions based on the basic EXPLANATIONS P´R´T TYPE–I......................................SME–407 formula of Simple Interest S.I. = 100 TYPE–II.....................................SME–410...................................................SME–508 TYPE–III....................................SME–415 TYPE–II : The sum of money becomes TYPE–IV....................................SME–420 'n' times of itself in 't' years at a certain rate of Simple Interest....SME–511 TYPE–V.....................................SME–424 TYPE–III : If simple interest on a TYPE–VI....................................SME–425 certain sum for ‘n’ years if x/y of TYPE–VII...................................SME–427 the sum find the rate..................SME–512 CHAPTERS........................................ PAGES CHAPTERS........................................ PAGES TYPE–IV : Questions based on the TYPE–IV....................................SME–566 difference and equality of Simple TYPE–V.....................................SME–568 Interest rate and years................SME–512 TYPE–VI....................................SME–571 TYPE–V : Questions based on ratios TYPE–VII...................................SME–572...................................................SME–514 TEST YOURSELF......................SME–575 TYPE–VI : Questions based on Increase/ decrease in rate of Interest.........SME–515 12. Time and Work (No. of Questions 383)...................................... SME–578-650 TYPE–VII : Miscellaneous Questions...................................................SME–515 TYPE-I : Questions Based on the basic EXPLANATIONS concept of time and work............SME–580 TYPE–I......................................SME–518 TYPE-II : Questions where worker leaves or joins............................SME–585 TYPE–II.....................................SME–522 TYPE-III : Questions based on ‘M’ man, TYPE–III....................................SME–525 ‘W’ women and ‘B’ boys...............SME–589 TYPE–IV....................................SME–527 TYPE-IV : Questions based on fraction TYPE–V.....................................SME–530 of the work.................................SME–591 TYPE–VI....................................SME–530 TYPE-V : Questions based on TYPE–VII...................................SME–532 efficiency of worker.....................SME–594 TEST YOURSELF......................SME–535 TYPE-VI : Questions based on the 11. Compound Interest (No. of Questions 204) formulae M1D1W1 = M2D2W2 and its...................................... SME–539-577 interchange................................SME–596 TYPE–I : Questions based on the basic TYPE-VII : Questions based on formula of compound Interest.....SME–540 Work and Wages.........................SME–598 TYPE–II : Questions based on both TYPE-VIII: Miscellaneous Questions compound and simple interest...SME–543...................................................SME–600 TYPE–III : Difference between compound EXPLANATIONS and simple interest.................................. TYPE–I......................................SME–603...................................................SME–544 TYPE–II.....................................SME–614 TYPE–IV : If the amount becomes TYPE–III....................................SME–622 'n' times of the sum after 't' years at compound interest.................SME–547 TYPE–IV....................................SME–627 TYPE–V : A sum of money amounts TYPE–V.....................................SME–632 to x1 in t1 years and to x2 in TYPE–VI....................................SME–636 t2 years at compound interest.....SME–547 TYPE–VII...................................SME–639 TYPE–VI : Questions based on TYPE–VIII..................................SME–641 Installments...............................SME–548 TEST YOURSELF......................SME–645 TYPE–VII : Miscellaneous Questions 13. Pipe and Cistern (No. of Questions 83)...................................................SME–549...................................... SME–651-665 EXPLANATIONS TYPE–I : Questions based on the concept TYPE–I......................................SME–550 of pipe and cistern......................SME–652 TYPE–II.....................................SME–557 TYPE–II : Questions based on fractions/ TYPE–III....................................SME–562 part of filled tank........................SME–653 CHAPTERS........................................ PAGES CHAPTERS........................................ PAGES TYPE–III : Questions based on taps TYPE–XII : Miscellaneous Questions are opened alternatively or a leak...................................................SME–686 in a tank....................................SME–654 EXPLANATIONS TYPE–IV : Miscellaneous Questions TYPE–I......................................SME–690...................................................SME–655 TYPE–II.....................................SME–695 EXPLANATIONS TYPE–III....................................SME–698 TYPE–I......................................SME–656 TYPE–IV....................................SME–700 TYPE–II.....................................SME–659 TYPE–V.....................................SME–703 TYPE–III....................................SME–660 TYPE–VI....................................SME–705 TYPE–IV....................................SME–662 TYPE–VII...................................SME–708 TEST YOURSELF......................SME–664 TYPE–VIII..................................SME–709 14. Time and Distance (No. of Questions 401) TYPE–IX....................................SME–712...................................... SME–666-736 TYPE–X.....................................SME–714 TYPE–I : Questions based on the basic concept of time and distance......SME–669 TYPE–XI....................................SME–716 TYPE–II : Questions based on Rail TYPE–XII...................................SME–717 and Platform/Bridge...................SME–672 TEST YOURSELF......................SME–721 TYPE–III : Questions based on Rail 15. Boat and Stream (No. of Questions 61) and a man/pole/signal..............SME–673...................................... SME–737-748 TYPE–IV : Questions based on two TYPE–I : Questions based on upstream Rails cross each other in opposite and downstream.........................SME–738 direction.....................................SME–675 TYPE–II : Questions based on a TYPE–V : Questions based on a car travels boat/a man takes 'n' times as much n time in going the same distance in with of its usual speed...........SME–677 opposite direction.......................SME–740 y TYPE–III : Miscellaneous Questions TYPE–VI : Questions based on...................................................SME–740 average speed.............................SME–678 EXPLANATIONS TYPE–VII : Questions based TYPE–I......................................SME–741 on Ratios....................................SME–680 TYPE–II.....................................SME–745 TYPE–VIII : Questions based on two train travel in same direction at TYPE–III....................................SME–746 different speed or thief/ constable TEST YOURSELF......................SME–748 overtake.....................................SME–681 16. Sequence and Series TYPE–IX : Questions based on a train (No. of Questions 143).... SME–749-765 (transport system)/a man changes his TYPE–I : Questions based on finding speed, then he arrives at its destination the next number/missing number/ before/later................................SME–683 wrong number............................SME–751 TYPE–X : Questions based on any train TYPE–II : Questions based on 'xth' crosses both platform and a man/a term & sum of 'n' terms..............SME–753 pole at same time.......................SME–684 TYPE–III : Questions based on Simple TYPE–XI : Question based on races calculation.................................SME–755...................................................SME–685 CHAPTERS........................................ PAGES CHAPTERS........................................ PAGES TYPE–IV : Questions based on square/ TYPE–III : Questions based on cube of natural/odd/even/prime angle of elevation........................SME–907 numbers etc...............................SME–755 TYPE–IV : Questions based on EXPLANATIONS angle of depression.....................SME–914 TYPE–I......................................SME–756 TYPE–V : Miscellaneous Questions TYPE–II.....................................SME–758...................................................SME–916 TYPE–III....................................SME–762 EXPLANATIONS TYPE–IV....................................SME–763 TYPE–I......................................SME–918 TEST YOURSELF......................SME–764 TYPE–II.....................................SME–919 17. Algebra (No. of Questions 759) TYPE–III....................................SME–955...................................... SME–766-878 TYPE–IV....................................SME–973 TYPE–I : Questions based on the basic TYPE–V.....................................SME–979 algebraic concept/calculation....SME–771 TEST YOURSELF......................SME–980 TYPE–II : Questions based on polynomial 19. Geometry (No. of Questions 608) and algebraic identity.................SME–787.................................... SME–991-1104 TYPE–III : Questions based on graphs TYPE–I : Equilateral Triangles. SME–1008 of linear equations and co-ordinate TYPE–II : Isosceles Triangles....SME–1009 Geometry....................................SME–801 TYPE–III : Scalene triangles, Acute & TYPE–IV : Questions based on ratios obtuse angles triangles and others...................................................SME–804 triangles................................... SME–1011 TYPE–V : Questions based on TYPE–IV : Right angle Permutation and Combination and Triangles.................................. SME–1018 Binomial Therom........................SME–805 TYPE–V : Similar Triangles...... SME–1020 TYPE–VI : Miscellaneous Questions...................................................SME–805 TYPE–VI : Rectangle................. SME–1021 EXPLANATIONS TYPE–VII : Square................... SME–1021 TYPE–I......................................SME–808 TYPE–VIII : Polygon.................. SME–1021 TYPE–II.....................................SME–834 TYPE–IX : Parallelogram.......... SME–1023 TYPE–III....................................SME–859 TYPE–X : Cyclic and others Quadrilateral........................... SME–1023 TYPE–IV....................................SME–864 TYPE–XI : Trapezium/Rhombus..SME–1024 TYPE–V.....................................SME–866 TYPE–XII : Simple Circle.......... SME–1025 TEST YOURSELF......................SME–868 TYPE–XIII : Tangents to Circle. SME–1030 18. Trigonometry (No. of Questions 626)...................................... SME–879-990 TYPE–XIV : Incentre/Circumcentre and Incircle Circumcircle......... SME–1034 TYPE–I : Questions based on Circular Measure of angles (Radian & Degree TYPE–XV : Miscellaneous Questions Measure)....................................SME–884................................................. SME–1036 TYPE–II : Questions based on EXPLANATIONS Trigonometric Ratios & Identities, TYPE–I.................................... SME–1040 Function, Projection, Law of TYPE–II................................... SME–1043 Tangents etc...............................SME–884 TYPE–III.................................. SME–1045 CHAPTERS........................................ PAGES CHAPTERS........................................ PAGES TYPE–IV.................................. SME–1060 TYPE–IV : Horizontal and Divide TYPE–V................................... SME–1065 Bar Diagram............................. SME–1296 TYPE–VI.................................. SME–1068 TYPE–V : Multi Bar Diagram.... SME–1300 TYPE–VII................................. SME–1068 TYPE–VI : Histogram................ SME–1319 TYPE–VIII................................ SME–1068 TYPE–VII : Table...................... SME–1323 TYPE–VIII : Miscellaneous Questions TYPE–IX.................................. SME–1071................................................ SME–1331 TYPE–X................................... SME–1071 EXPLANATIONS TYPE–XI.................................. SME–1073 TYPE–I................................... SME–1333 TYPE–XII................................. SME–1075 TYPE–II................................... SME–1344 TYPE–XIII............................... SME–1086 TYPE–III.................................. SME–1346 TYPE–XIV................................ SME–1092 TYPE–IV.................................. SME–1350 TYPE–XV................................. SME–1096 TYPE–V................................... SME–1352 TEST YOURSELF.................... SME–1101 TYPE–VI.................................. SME–1361 20. Mensuration (No. of Questions 946) TYPE–VII................................. SME–1362.................................. SME–1105-1256 TYPE–VIII................................ SME–1367 TYPE–I : (2-D : Area)................. SME–1114 TEST YOURSELF.................... SME–1368 TYPE–II : (2-D : Perimeter)........ SME–1132 22. Miscellaneous (No. of Questions 50) TYPE–III : (2-D : Percentage/Cost/.................................. SME–1370-1376 Quantity).................................. SME–1137 TYPE–IV : (3-D