Submit Search
Upload
114 Handy Formulae Quantitative Aptitude
•
1 like
•
169 views
AI-enhanced title
ABDULRAHIM RAFIQAHMED
Follow
General Aptitude
Read less
Read more
Education
Report
Share
Report
Share
1 of 12
Download now
Download to read offline
Recommended
Aptitude with handy-formulae
Aptitude with handy-formulae
IrudayaMinuPriya
Important formulaeforquantitativeaptitude
Important formulaeforquantitativeaptitude
Soban Mallesh
New Method for Finding an Optimal Solution of Generalized Fuzzy Transportatio...
New Method for Finding an Optimal Solution of Generalized Fuzzy Transportatio...
BRNSS Publication Hub
Matrix chain multiplication by MHM
Matrix chain multiplication by MHM
Md Mosharof Hosen
Management Aptitude Test 6 December
Management Aptitude Test 6 December
Dr. Trilok Kumar Jain
Amazon_Logistic_Abbey_Chaver_Ben_LeRoy
Amazon_Logistic_Abbey_Chaver_Ben_LeRoy
Benjamin LeRoy
Greedy method
Greedy method
Dr Shashikant Athawale
Summery of Robust and Effective Metric Learning Using Capped Trace Norm
Summery of Robust and Effective Metric Learning Using Capped Trace Norm
ssuser42f2881
Recommended
Aptitude with handy-formulae
Aptitude with handy-formulae
IrudayaMinuPriya
Important formulaeforquantitativeaptitude
Important formulaeforquantitativeaptitude
Soban Mallesh
New Method for Finding an Optimal Solution of Generalized Fuzzy Transportatio...
New Method for Finding an Optimal Solution of Generalized Fuzzy Transportatio...
BRNSS Publication Hub
Matrix chain multiplication by MHM
Matrix chain multiplication by MHM
Md Mosharof Hosen
Management Aptitude Test 6 December
Management Aptitude Test 6 December
Dr. Trilok Kumar Jain
Amazon_Logistic_Abbey_Chaver_Ben_LeRoy
Amazon_Logistic_Abbey_Chaver_Ben_LeRoy
Benjamin LeRoy
Greedy method
Greedy method
Dr Shashikant Athawale
Summery of Robust and Effective Metric Learning Using Capped Trace Norm
Summery of Robust and Effective Metric Learning Using Capped Trace Norm
ssuser42f2881
quantitative aptitude/ objective arithmetic
quantitative aptitude/ objective arithmetic
teddy bear
Quantitative Aptitude Test (QAT)-Tips & Tricks
Quantitative Aptitude Test (QAT)-Tips & Tricks
cocubes_learningcalendar
Cat quantitative-reasoning math-
Cat quantitative-reasoning math-
Naveen Anbalagan
RS Agarwal Quantitative Aptitude - 2 chap
RS Agarwal Quantitative Aptitude - 2 chap
Vinoth Kumar.K
Cat quant myths
Cat quant myths
sakshij91
Quantitative aptitude : Time & Work concept
Quantitative aptitude : Time & Work concept
JSS ACADEMY OF TECHNICAL EDUCATION,NOIDA
Critical reasoning
Critical reasoning
Prasanth Kumar RAGUPATHY
RS Agarwal Quantitative Aptitude - 6 chap
RS Agarwal Quantitative Aptitude - 6 chap
Vinoth Kumar.K
My bankexam quant flash cards
My bankexam quant flash cards
abhishek kumar
Quantitative Aptitude
Quantitative Aptitude
Siva Shankar
Grammar rules
Grammar rules
David Hoang
100 golden rules of english
100 golden rules of english
gr8 dreamz
Quantitative Aptitude Shortcut tricks
Quantitative Aptitude Shortcut tricks
BankExamsToday.com
48266497 101-shortcut-maths
48266497 101-shortcut-maths
srhaider
Questions Of Reasoning And Puzzles For Competitive Examinations
Questions Of Reasoning And Puzzles For Competitive Examinations
Dr. Trilok Kumar Jain
Mathematical shortcuts- DOWNLOAD ENABLED
Mathematical shortcuts- DOWNLOAD ENABLED
Veeraragavan Subramaniam
ias exam notes
ias exam notes
Zenitheducation
UPSC ANCIENT Indian history Topper Notes 2013 2014 General knowledge
UPSC ANCIENT Indian history Topper Notes 2013 2014 General knowledge
Prabh Jeet
Math tricks
Math tricks
faisal2106
#4 exam helper knowledge booster (for government job) 4th new edition
#4 exam helper knowledge booster (for government job) 4th new edition
Exam Affairs!
Algebra
Algebra
Mang Oha
Data sufficiency-formulae
Data sufficiency-formulae
techie_govind
More Related Content
Viewers also liked
quantitative aptitude/ objective arithmetic
quantitative aptitude/ objective arithmetic
teddy bear
Quantitative Aptitude Test (QAT)-Tips & Tricks
Quantitative Aptitude Test (QAT)-Tips & Tricks
cocubes_learningcalendar
Cat quantitative-reasoning math-
Cat quantitative-reasoning math-
Naveen Anbalagan
RS Agarwal Quantitative Aptitude - 2 chap
RS Agarwal Quantitative Aptitude - 2 chap
Vinoth Kumar.K
Cat quant myths
Cat quant myths
sakshij91
Quantitative aptitude : Time & Work concept
Quantitative aptitude : Time & Work concept
JSS ACADEMY OF TECHNICAL EDUCATION,NOIDA
Critical reasoning
Critical reasoning
Prasanth Kumar RAGUPATHY
RS Agarwal Quantitative Aptitude - 6 chap
RS Agarwal Quantitative Aptitude - 6 chap
Vinoth Kumar.K
My bankexam quant flash cards
My bankexam quant flash cards
abhishek kumar
Quantitative Aptitude
Quantitative Aptitude
Siva Shankar
Grammar rules
Grammar rules
David Hoang
100 golden rules of english
100 golden rules of english
gr8 dreamz
Quantitative Aptitude Shortcut tricks
Quantitative Aptitude Shortcut tricks
BankExamsToday.com
48266497 101-shortcut-maths
48266497 101-shortcut-maths
srhaider
Questions Of Reasoning And Puzzles For Competitive Examinations
Questions Of Reasoning And Puzzles For Competitive Examinations
Dr. Trilok Kumar Jain
Mathematical shortcuts- DOWNLOAD ENABLED
Mathematical shortcuts- DOWNLOAD ENABLED
Veeraragavan Subramaniam
ias exam notes
ias exam notes
Zenitheducation
UPSC ANCIENT Indian history Topper Notes 2013 2014 General knowledge
UPSC ANCIENT Indian history Topper Notes 2013 2014 General knowledge
Prabh Jeet
Math tricks
Math tricks
faisal2106
Viewers also liked
(19)
quantitative aptitude/ objective arithmetic
quantitative aptitude/ objective arithmetic
Quantitative Aptitude Test (QAT)-Tips & Tricks
Quantitative Aptitude Test (QAT)-Tips & Tricks
Cat quantitative-reasoning math-
Cat quantitative-reasoning math-
RS Agarwal Quantitative Aptitude - 2 chap
RS Agarwal Quantitative Aptitude - 2 chap
Cat quant myths
Cat quant myths
Quantitative aptitude : Time & Work concept
Quantitative aptitude : Time & Work concept
Critical reasoning
Critical reasoning
RS Agarwal Quantitative Aptitude - 6 chap
RS Agarwal Quantitative Aptitude - 6 chap
My bankexam quant flash cards
My bankexam quant flash cards
Quantitative Aptitude
Quantitative Aptitude
Grammar rules
Grammar rules
100 golden rules of english
100 golden rules of english
Quantitative Aptitude Shortcut tricks
Quantitative Aptitude Shortcut tricks
48266497 101-shortcut-maths
48266497 101-shortcut-maths
Questions Of Reasoning And Puzzles For Competitive Examinations
Questions Of Reasoning And Puzzles For Competitive Examinations
Mathematical shortcuts- DOWNLOAD ENABLED
Mathematical shortcuts- DOWNLOAD ENABLED
ias exam notes
ias exam notes
UPSC ANCIENT Indian history Topper Notes 2013 2014 General knowledge
UPSC ANCIENT Indian history Topper Notes 2013 2014 General knowledge
Math tricks
Math tricks
Similar to 114 Handy Formulae Quantitative Aptitude
#4 exam helper knowledge booster (for government job) 4th new edition
#4 exam helper knowledge booster (for government job) 4th new edition
Exam Affairs!
Algebra
Algebra
Mang Oha
Data sufficiency-formulae
Data sufficiency-formulae
techie_govind
Quant formulae
Quant formulae
Singh Satyajeet Kumar
50 keys to cat from test funda (1)
50 keys to cat from test funda (1)
Shivangi Agrawal
50 useful quant formula
50 useful quant formula
Chintan Leo
Chapter 5
Chapter 5
jennytuazon01630
Aptitude .docx
Aptitude .docx
GokrishVenkat1
Aptitude .docx
Aptitude .docx
GokrishVenkat1
Handa ka funda math formulas 5.0
Handa ka funda math formulas 5.0
Chandan Kumar
Aptitude .pdf
Aptitude .pdf
GokrishVenkat1
Chapter 3 : Balagurusamy Programming ANSI in C
Chapter 3 : Balagurusamy Programming ANSI in C
BUBT
Algebra
Algebra
Christian Bation
50 keys to cat from test funda (1)
50 keys to cat from test funda (1)
Shivangi Agrawal
50 keys to cat from test funda
50 keys to cat from test funda
arpitnigam01
50 keys to cat from test funda
50 keys to cat from test funda
pallavisingla1
50 keys to cat from test funda
50 keys to cat from test funda
jesusisgood
Properties of Addition & Multiplication
Properties of Addition & Multiplication
itutor
Chapteronesectionone
Chapteronesectionone
Cathy Hager
Algebra chap1section1
Algebra chap1section1
Cathy Hager
Similar to 114 Handy Formulae Quantitative Aptitude
(20)
#4 exam helper knowledge booster (for government job) 4th new edition
#4 exam helper knowledge booster (for government job) 4th new edition
Algebra
Algebra
Data sufficiency-formulae
Data sufficiency-formulae
Quant formulae
Quant formulae
50 keys to cat from test funda (1)
50 keys to cat from test funda (1)
50 useful quant formula
50 useful quant formula
Chapter 5
Chapter 5
Aptitude .docx
Aptitude .docx
Aptitude .docx
Aptitude .docx
Handa ka funda math formulas 5.0
Handa ka funda math formulas 5.0
Aptitude .pdf
Aptitude .pdf
Chapter 3 : Balagurusamy Programming ANSI in C
Chapter 3 : Balagurusamy Programming ANSI in C
Algebra
Algebra
50 keys to cat from test funda (1)
50 keys to cat from test funda (1)
50 keys to cat from test funda
50 keys to cat from test funda
50 keys to cat from test funda
50 keys to cat from test funda
50 keys to cat from test funda
50 keys to cat from test funda
Properties of Addition & Multiplication
Properties of Addition & Multiplication
Chapteronesectionone
Chapteronesectionone
Algebra chap1section1
Algebra chap1section1
Recently uploaded
The Most Excellent Way | 1 Corinthians 13
The Most Excellent Way | 1 Corinthians 13
Steve Thomason
Enzyme, Pharmaceutical Aids, Miscellaneous Last Part of Chapter no 5th.pdf
Enzyme, Pharmaceutical Aids, Miscellaneous Last Part of Chapter no 5th.pdf
Sumit Tiwari
Solving Puzzles Benefits Everyone (English).pptx
Solving Puzzles Benefits Everyone (English).pptx
OH TEIK BIN
Presiding Officer Training module 2024 lok sabha elections
Presiding Officer Training module 2024 lok sabha elections
anshu789521
Employee wellbeing at the workplace.pptx
Employee wellbeing at the workplace.pptx
NirmalaLoungPoorunde1
Painted Grey Ware.pptx, PGW Culture of India
Painted Grey Ware.pptx, PGW Culture of India
Virag Sontakke
How to Make a Pirate ship Primary Education.pptx
How to Make a Pirate ship Primary Education.pptx
manuelaromero2013
CARE OF CHILD IN INCUBATOR..........pptx
CARE OF CHILD IN INCUBATOR..........pptx
GaneshChakor2
18-04-UA_REPORT_MEDIALITERAСY_INDEX-DM_23-1-final-eng.pdf
18-04-UA_REPORT_MEDIALITERAСY_INDEX-DM_23-1-final-eng.pdf
ssuser54595a
“Oh GOSH! Reflecting on Hackteria's Collaborative Practices in a Global Do-It...
“Oh GOSH! Reflecting on Hackteria's Collaborative Practices in a Global Do-It...
Marc Dusseiller Dusjagr
Introduction to ArtificiaI Intelligence in Higher Education
Introduction to ArtificiaI Intelligence in Higher Education
pboyjonauth
Class 11 Legal Studies Ch-1 Concept of State .pdf
Class 11 Legal Studies Ch-1 Concept of State .pdf
akmcokerachita
Model Call Girl in Bikash Puri Delhi reach out to us at 🔝9953056974🔝
Model Call Girl in Bikash Puri Delhi reach out to us at 🔝9953056974🔝
9953056974 Low Rate Call Girls In Saket, Delhi NCR
A Critique of the Proposed National Education Policy Reform
A Critique of the Proposed National Education Policy Reform
Chameera Dedduwage
EPANDING THE CONTENT OF AN OUTLINE using notes.pptx
EPANDING THE CONTENT OF AN OUTLINE using notes.pptx
RaymartEstabillo3
Call Girls in Dwarka Mor Delhi Contact Us 9654467111
Call Girls in Dwarka Mor Delhi Contact Us 9654467111
Sapana Sha
Organic Name Reactions for the students and aspirants of Chemistry12th.pptx
Organic Name Reactions for the students and aspirants of Chemistry12th.pptx
VS Mahajan Coaching Centre
Paris 2024 Olympic Geographies - an activity
Paris 2024 Olympic Geographies - an activity
GeoBlogs
Alper Gobel In Media Res Media Component
Alper Gobel In Media Res Media Component
InMediaRes1
9953330565 Low Rate Call Girls In Rohini Delhi NCR
9953330565 Low Rate Call Girls In Rohini Delhi NCR
9953056974 Low Rate Call Girls In Saket, Delhi NCR
Recently uploaded
(20)
The Most Excellent Way | 1 Corinthians 13
The Most Excellent Way | 1 Corinthians 13
Enzyme, Pharmaceutical Aids, Miscellaneous Last Part of Chapter no 5th.pdf
Enzyme, Pharmaceutical Aids, Miscellaneous Last Part of Chapter no 5th.pdf
Solving Puzzles Benefits Everyone (English).pptx
Solving Puzzles Benefits Everyone (English).pptx
Presiding Officer Training module 2024 lok sabha elections
Presiding Officer Training module 2024 lok sabha elections
Employee wellbeing at the workplace.pptx
Employee wellbeing at the workplace.pptx
Painted Grey Ware.pptx, PGW Culture of India
Painted Grey Ware.pptx, PGW Culture of India
How to Make a Pirate ship Primary Education.pptx
How to Make a Pirate ship Primary Education.pptx
CARE OF CHILD IN INCUBATOR..........pptx
CARE OF CHILD IN INCUBATOR..........pptx
18-04-UA_REPORT_MEDIALITERAСY_INDEX-DM_23-1-final-eng.pdf
18-04-UA_REPORT_MEDIALITERAСY_INDEX-DM_23-1-final-eng.pdf
“Oh GOSH! Reflecting on Hackteria's Collaborative Practices in a Global Do-It...
“Oh GOSH! Reflecting on Hackteria's Collaborative Practices in a Global Do-It...
Introduction to ArtificiaI Intelligence in Higher Education
Introduction to ArtificiaI Intelligence in Higher Education
Class 11 Legal Studies Ch-1 Concept of State .pdf
Class 11 Legal Studies Ch-1 Concept of State .pdf
Model Call Girl in Bikash Puri Delhi reach out to us at 🔝9953056974🔝
Model Call Girl in Bikash Puri Delhi reach out to us at 🔝9953056974🔝
A Critique of the Proposed National Education Policy Reform
A Critique of the Proposed National Education Policy Reform
EPANDING THE CONTENT OF AN OUTLINE using notes.pptx
EPANDING THE CONTENT OF AN OUTLINE using notes.pptx
Call Girls in Dwarka Mor Delhi Contact Us 9654467111
Call Girls in Dwarka Mor Delhi Contact Us 9654467111
Organic Name Reactions for the students and aspirants of Chemistry12th.pptx
Organic Name Reactions for the students and aspirants of Chemistry12th.pptx
Paris 2024 Olympic Geographies - an activity
Paris 2024 Olympic Geographies - an activity
Alper Gobel In Media Res Media Component
Alper Gobel In Media Res Media Component
9953330565 Low Rate Call Girls In Rohini Delhi NCR
9953330565 Low Rate Call Girls In Rohini Delhi NCR
114 Handy Formulae Quantitative Aptitude
1.
114 Handy Formulae
for Quantitative Aptitude Problems Author: Sagar Sonker Page 1 of 12 Copyright © 2006 www.sonker.com Table of Contents ℵ Numbers ℵ H.C.F & L.C.M of Numbers ℵ Surds & Indices ℵ Percentage ℵ Profit & Loss ℵ Ratio & Proportion ℵ Partnership ℵ Chain Rule ℵ Time & Work ℵ Pipes & Cisterns ℵ Time And Distance ℵ Trains ℵ Boats & Streams ℵ Alligation or Mixture ℵ Simple Interest ℵ Compound Interest ℵ Logarithms ℵ Area ℵ Volume & Surface Area ℵ Stocks & Shares ℵ True Discount ℵ Banker’s Discount ℵ Copyright Notice
2.
114 Handy Formulae
for Quantitative Aptitude Problems Author: Sagar Sonker Page 2 of 12 Copyright © 2006 www.sonker.com Numbers 1. A number is divisible by 2, if its unit’s place digit is 0, 2, 4, or 8 2. A number is divisible by 3, if the sum of its digits is divisible by 3 3. A number is divisible by 4, if the number formed by its last two digits is divisible by 4 4. A number is divisible by 8, if the number formed by its last three digits is divisible by 8 5. A number is divisible by 9, if the sum of its digits is divisible by 9 6. A number is divisible by 11, if, starting from the RHS, (Sum of its digits at the odd place) – (Sum of its digits at even place) is equal to 0 or 11x 7. (a + b)2 = a2 + 2ab + b2 8. (a - b)2 = a2 - 2ab + b2 9. (a + b)2 - (a - b)2 = 4ab 10. (a + b)2 + (a - b)2 = 2(a2 + b2 ) 11. (a2 – b2 ) = (a + b)(a - b) 12. (a3 + b3 ) = (a + b)(a2 - ab + b2 ) 13. (a3 – b3 ) = (a - b)(a2 + ab + b2 ) 14. Results on Division: Dividend = Quotient × Divisor + Remainder 15. An Arithmetic Progression (A. P.) with first term ‘a’ and Common Difference ‘d’ is given by: [a], [(a + d)], [(a + 2d)], … … …, [a + (n - 1)d] nth term, Tn = a + (n - 1)d Sum of first ‘n’ terms, Sn = n/2 (First Term + Last Term) 16. A Geometric Progression (G. P.) with first term ‘a’ and Common Ratio ‘r’ is given by: a, ar, ar2 , ar3 , … … …, arn-1 nth term, Tn = arn-1 Sum of first ‘n’ terms Sn = [a(1 - rn )] / [1 - r] 17. (1 + 2 + 3 + … … … + n) = [n(n + 1)] / 2 18. (12 + 22 + 32 + … … … + n2 ) = [n(n + 1)(2n + 1)] / 6 19. (13 + 23 + 33 + … … … + n3 ) = [n2 (n + 1)2 ] / 4
3.
114 Handy Formulae
for Quantitative Aptitude Problems Author: Sagar Sonker Page 3 of 12 Copyright © 2006 www.sonker.com H.C.F & L.C.M of Numbers 20. Product of two numbers = Their H. C. F. × Their L. C. M. Surds & Indices 21. am × an = a(m + n) 22. am / an = a(m - n) 23. (ab)m = am bm 24. (a / b)m = an / bn 25. a0 = 1 26. = a1/n 27. = (a1/n )n = a 28. = 29. = / 30. ( )m = 31. = Percentage 32. To express x% as a fraction, we have x% = x / 100 33. To express a / b as a percent, we have a / b = (a / b × 100) % 34. If ‘A’ is R% more than ‘B’, then ‘B’ is less than ‘A’ by OR If the price of a commodity increases by R%, then the reduction in consumption, not to increase the expenditure is {100R / [100 + R] } % 35. If ‘A’ is R% less than ‘B’, then ‘B’ is more than ‘A’ by OR If the price of a commodity decreases by R%, then the increase in consumption, not to increase the expenditure is {100R / [100 - R] } % 36. If the population of a town is ‘P’ in a year, then its population after ‘N’ years is P (1 + R/100)N
4.
114 Handy Formulae
for Quantitative Aptitude Problems Author: Sagar Sonker Page 4 of 12 Copyright © 2006 www.sonker.com 37. If the population of a town is ‘P’ in a year, then its population ‘N’ years ago is P / [(1 + R/100)N ] Profit & Loss 38. If the value of a machine is ‘P’ in a year, then its value after ‘N’ years at a depreciation of ‘R’ p.c.p.a is P (1 - R/100)N 39. If the value of a machine is ‘P’ in a year, then its value ‘N’ years ago at a depreciation of ‘R’ p.c.p.a is P / [(1 - R/100)N ] 40. Selling Price = [(100 + Gain%) × Cost Price] / 100 = [(100 - Loss%) × Cost Price] / 100 Ratio & Proportion 41. The equality of two ratios is called a proportion. If a : b = c : d, we write a : b :: c : d and we say that a, b, c, d are in proportion. In a proportion, the first and fourth terms are known as extremes, while the second and third are known as means. 42. Product of extremes = Product of means 43. Mean proportion between a and b is 44. The compounded ratio of the ratios (a : b), (c : d), (e : f) is (ace : bdf) 45. a2 : b2 is a duplicate ratio of a : b 46. : is a sub-duplicate ration of a : b 47. a3 : b3 is a triplicate ratio of a : b 48. a1/3 : b1/3 is a sub-triplicate ratio of a : b 49. If a / b = c / d, then, (a + b) / b = (c + d) / d, which is called the componendo. 50. If a / b = c / d, then, (a - b) / b = (c - d) / d, which is called the dividendo. 51. If a / b = c / d, then, (a + b) / (a - b) = (c + d) / (c - d), which is called the componendo & dividendo. 52. Variation: We say that x is directly proportional to y if x = ky for some constant k and we write, x α y. 53. Also, we say that x is inversely proportional to y if x = k / y for some constant k and we write x α 1 / y.
5.
114 Handy Formulae
for Quantitative Aptitude Problems Author: Sagar Sonker Page 5 of 12 Copyright © 2006 www.sonker.com Partnership 54. If a number of partners have invested in a business and it has a profit, then Share Of Partner = (Total_Profit × Part_Share / Total_Share) Chain Rule 55. The cost of articles is directly proportional to the number of articles. 56. The work done is directly proportional to the number of men working at it. 57. The time (number of days) required to complete a job is inversely proportional to the number of hours per day allocated to the job. 58. Time taken to cover a distance is inversely proportional to the speed of the car. Time & Work 59. If A can do a piece of work in n days, then A’s 1 day’s work = 1/n. 60. If A’s 1 day’s work = 1/n, then A can finish the work in n days. 61. If A is thrice as good a workman as B, then: Ratio of work done by A and B = 3 : 1, Ratio of times taken by A & B to finish a work = 1 : 3 Pipes & Cisterns 62. If a pipe can fill a tank in ‘x’ hours and another pipe can empty the full tank in ‘y’ hours (where y > x), then on opening both the pipes, the net part of the tank filled in 1 hour is (1/x – 1/y) Time And Distance 63. Suppose a man covers a distance at ‘x’ kmph and an equal distance at ‘y’ kmph, then average speed during his whole journey is [2xy / (x + y)] kmph Trains 64. Lengths of trains are ‘x’ km and ‘y’ km, moving at ‘u’ kmph and ‘v’ kmph (where, u > v) in the same direction, then the time taken y the over-taker train to cross the slower train is [(x + y) / (u - v)] hrs 65. Time taken to cross each other is [(x + y) / (u + v)] hrs 66. If two trains start at the same time from two points A and B towards each other and after crossing they take a and b hours in reaching B and A respectively.
6.
114 Handy Formulae
for Quantitative Aptitude Problems Author: Sagar Sonker Page 6 of 12 Copyright © 2006 www.sonker.com Then, A’s speed : B’s speed = ( : ). 67. x kmph = (x × 5/18) m/sec. 68. y metres/sec = (y × 18/5) km/hr. Boats & Streams 69. If the speed of a boat in still water is u km/hr and the speed of the stream is v hm/hr, then: Speed downstream = (u + v) km/hr. Speed upstream = (u - v) km/hr. 70. If the speed downstream is a km/hr and the speed upstream is b km/hr, then: Speed in still water = ½ (a + b) km/hr. Rate of stream = ½ (a - b) km/hr. Alligation or Mixture 71. Alligation: It is the rule that enables us to find the ratio in which two or more ingredients at the given price must be mixed to produce a mixture at a given price. 72. Mean Price: The cost price of a quantity of the mixture is called the mean price. 73. Rule of Alligation: If two ingredients are mixed, then: 74. We represent the above formula as under: 75. .: (Cheaper quantity) : (Dearer quantity) = (d - m) : (m - c) Simple Interest 76. Let Principle = P, Rate = R% per annum and Time = T years. Then, a. S.I. = ( P × R × T ) / 100 b. P = ( 100 × S.I. ) / ( R × T ), c. R = ( 100 × S.I. ) / ( P × T ), d. T = ( 100 × S.I. ) / ( P × R ).
7.
114 Handy Formulae
for Quantitative Aptitude Problems Author: Sagar Sonker Page 7 of 12 Copyright © 2006 www.sonker.com Compound Interest 77. Let Principle = P, Rate = R% per annum and Time = T years. Then, I. When interest is compounded Annually, Amount = P (1 + R/100)N II. When interest is compounded Half-yearly: Amount = P (1 + R/2/100)2N III. When interest is compounded Quarterly: Amount = P (1 + R/4/100)4N 78. When interest is compounded Annually, but the time is in fraction, say 3⅞ years. Then, Amount = P (1 + R/100)3 × (1 + ⅞R/100) 79. When Rates are different for different years, say R1%, R2%, R3% for 1st , 2nd , and 3rd year respectively, Then, Amount = P (1 + R1/100) (1 + R2/100) (1 + R3/100) 80. Present worth of Rs. x due n years hence is given by: Present Worth = x / (1 + R/100)n Logarithms 81. Logarithm: If a is a positive real number, other than 1 and am = x, then we write m = loga x and say that the value of log x to the base a is m. 82. Properties of Logarithms: a. loga (xy) = loga x + loga y b. loga (x/y) = loga x - loga y c. logx x = 1 (i.e. Log of any number to its own base is 1) d. loga 1 = 0 (i.e. Log of 1 to any base is 0) e. loga (xp ) = p loga x f. loga x = 1 / logx a g. loga x = logb x / logb a = log x / log a (Change of base rule) h. When base is not mentioned, it is taken as 10 i. Logarithms to the base 10 are known as common logarithms j. The logarithm of a number contains two parts, namely characteristic and mantissa. The integral part is known as characteristic and the decimal part is known as mantissa.
8.
114 Handy Formulae
for Quantitative Aptitude Problems Author: Sagar Sonker Page 8 of 12 Copyright © 2006 www.sonker.com I. Case 1: When the number is greater than 1. In this case, the characteristic is one less than the number of digits in the left of decimal point in the given number. II. Case 2: When the number is less than 1. In this case, the characteristic is one more than the number of zeroes between the decimal point and the first significant digit of the number and it is negative. e.g. Number Characteristic 234.56 2 23.456 1 2.34 0 0.234 -1 0.0234 -2 0.00234 -3 III. For mantissa, we look through the log table. IV. Antilog: If log x = y, then antilog y = x. Area 83. Rectangle: a. Area of a rectangle = (length × breadth) b. Perimeter of a rectangle= 2 (length + breadth) 84. Square: a. Area of square = (side)2 b. Area of a square = ½ (diagonal)2 85. Area of 4 walls of a room = 2 (length + breadth) × height 86. Triangle: a. Area of a triangle = ½ × base × height b. Area of a triangle = , where s = ½ (a + b + c), and a, b, c are the sides of the triangle c. Area of an equilateral triangle = / 4 × (side)2 d. Radius of incircle of an equilateral triangle of side a = a / 2 e. Radius of circumcircle of an equilateral triangle of side a = a / 87. Parallelogram/Rhombus/Trapezium: a. Area of a parallelogram = Base × Height
9.
114 Handy Formulae
for Quantitative Aptitude Problems Author: Sagar Sonker Page 9 of 12 Copyright © 2006 www.sonker.com b. Area of a rhombus = ½ × (Product of diagonals) c. The halves of diagonals and a side of a rhombus form a right angled triangle with side as the hypotenuse. d. Area of trapezium = ½ × (sum of parallel sides) × (distance between them) 88. Circle/Arc/Sector, where R is the radius of the circle: a. Area of a circle = πR2 b. Circumference of a circle = 2πR c. Length of an arc = Ө/360 × 2πR d. Area of a sector = ½ (arc × R) = Ө/360 × πR2 Volume & Surface Area 89. Cuboid: Let length = l, breadth = b & height = h units Then, a. Volume = (l × b × h) cu units b. Surface Area = 2 (lb + bh + hl) sq. units c. Diagonal = units 90. Cube: Let each edge of a cube be of length a. Then, a. Volume = a3 cu units b. Surface Area = 6a2 sq. units c. Diagonal = ( × a) units 91. Cylinder: Let radius of base = r & height (or length) = h. Then, a. Volume = (πr2 h) cu. units b. Curved Surface Area = (2πrh) sq. units c. Total Surface Area = 2πr(r + h) sq. units 92. Cone: Let radius of base = r & height = h. Then,
10.
114 Handy Formulae
for Quantitative Aptitude Problems Author: Sagar Sonker Page 10 of 12 Copyright © 2006 www.sonker.com a. Slant height, l = units b. Volume = (⅓ πr2 h) cu. units c. Curved Surface Area = (πrl) sq. units d. Total Surface Area = πr(r + l) sq. units 93. Sphere: Let the radius of the sphere be r. Then, a. Volume = (4/3 πr3 ) cu. units b. Surface Area = (4πr2 ) sq. units 94. Hemi-sphere: Let the radius of the sphere be r. Then, a. Volume = (2/3 πr3 ) cu. units b. Curved Surface Area = (2πr2 ) sq. units c. Total Surface Area = (3πr2 ) sq. units Stocks & Shares 95. Brokerage: The broker’s charge is called brokerage. 96. When stock is purchased, brokerage is added to the cost price. 97. When the stock is sold, brokerage is subtracted from the selling price. 98. The selling price of a Rs. 100 stock is said to be: a. at par, if S.P. is Rs. 100 exactly; b. above par (or at premium), if S.P. is more than Rs. 100; c. below par (or at discount), if S.P. is less than Rs. 100. 99. By ‘a Rs. 800, 9% stock at 95’, we mean a stock whose face value is Rs. 800, annual interest is 9% of the face value and the market price of a Rs. 100 stock is Rs. 95. True Discount 100. Suppose a man has to pay Rs. 156 after 4 years and the rate of interest is 14% per annum. Clearly, Rs. 100 at 14% will amount to Rs. 156 in 4 years. So, the payment of Rs. 100 now will clear off the debt of Rs. 156 due 4 years hence. We say that: Sum due = Rs. 156 due 4 years hence; Present Worth (P.W.) = Rs. 100; True Discount (T.D.) = Rs. (156 - 100) = (Sum due) – (P.W.)
11.
114 Handy Formulae
for Quantitative Aptitude Problems Author: Sagar Sonker Page 11 of 12 Copyright © 2006 www.sonker.com 101. T.D. = Interest on P.W. 102. Amount = (P.W.) + (T.D.) 103. Interest is reckoned on R.W. and true discount is reckoned on the amount 104. Let rate = R% per annum & time = T years. Then, a. P.W. = (100 × Amount) / (100 + [R × T]) = (100 × T.D.) / (R × T) b. T.D. = (P.W.) × R × T / 100 = ([Amount] × R × T) / (100 + [R × T]) c. Sum = ([S.I.] × [T.D.]) / ([S.I.] – [T.D.]) d. (S.I.) – (T.D.) = S.I. on T.D. e. When the sum is put at compound interest, then P.W. = Amount / (1 + R/100)T Banker’s Discount 105. Banker’s Discount (B.D.) is the S.I. on the face value for the period from the date on which the bill was discounted and the legally due date. 106. Banker’s Gain (B.G.) = (B.D.) – (T.D.) for the unexpired time 107. When the date of the bill is not given, grace days are not to be added 108. B.D. = S.I. on bill for unexpired time 109. B.G. = (B.D.) – (T.D.) = S.I. on T.D. = (T.D.)2 / P.W. 110. T.D. = 111. B.D. = (Amount × Rate × Time) / 100 112. T.D. = (Amount × Rate × Time) / (100 + [Rate × Time]) 113. Amount = (B.D. × T.D.) / (B.D. – T.D.) 114. T.D. = (B.G. × 100) / (Rate × Time) Copyright Notice: Feel free to share, print, copy, distribute this document for free. Make sure to preserve this copyright notice alongwith the header and footer with the copyright note of www.sonker.com. Be sure to read the copyright information and terms of use of the documents at http://www.sonker.com/sagar/Copyright.htm before you share, print, copy, distribute this document.
12.
114 Handy Formulae
for Quantitative Aptitude Problems Author: Sagar Sonker Page 12 of 12 Copyright © 2006 www.sonker.com Illegal reproduction of this document without the prior permission of the author and/or removal of this copyright notice and/or the header/footer gives www.sonker.com the full authority to take a legal action. Do you have any more information to add to this document? Write to me at sagar@sonker.com or submit your feedback at www.sonker.com/sagar.
Download now