Downloadmela.com Handy Formulae for Quantitative Aptitude Problems

114 Handy Formulae for Quantitative Aptitude Problemswww.downloadmela.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 Stocks & Shares ℵ True Discount w w ℵ Copyright Notice w ℵ Banker’s Discount .d ow ℵ Volume & Surface Area nl o ad m el a. Page 1 of 12 visit www.downloadmela.com co m for more papers Tn Sum of first ‘n’ terms Sn = [a(1 . Page 2 of 12 visit www.b)(a2 + ab + b2) Dividend = Quotient × Divisor + Remainder 15. if the number formed by its last two digits is divisible by 4 4. if the sum of its digits is divisible by 3 3.114 Handy Formulae for Quantitative Aptitude Problems Numbers 1. 4. A number is divisible by 2. A number is divisible by 8. Results on Division: ad m el a. Sn = n/2 (First Term + Last Term) 16.2ab + b2 .d ow nl o 14. or 8 2. if the number formed by its last three digits is divisible by 8 5. (1 + 2 + 3 + … … … + n) 18. (a2 – b2) 12. A number is divisible by 11.b)2 = a2 . P. (a3 + b3) 13.downloadmela. Tn Sum of first ‘n’ terms. (Sum of its digits at the odd place) – (Sum of its digits at even place) is equal to 0 or 11x 7.downloadmela. … … …. if the sum of its digits is divisible by 9 6.b) = (a + b)(a2 . [(a + 2d)].) with first term ‘a’ and Common Ratio ‘r’ is given by: a. (a . if its unit’s place digit is 0.(a . A Geometric Progression (G. arn-1 = arn-1 nth term. ar3.com = a2 + 2ab + b2 9. [(a + d)]. A number is divisible by 4. An Arithmetic Progression (A. P. 2. A number is divisible by 9.1)d nth term. (a + b)2 .b)2 = 2(a2 + b2) 11.r] 17.) with first term ‘a’ and Common Difference ‘d’ is given by: [a]. ar2. (12 + 22 + 32 + … … … + n2) 19. starting from the RHS.ab + b2) = (a .b)2= 4ab 10. ar. [a + (n . (a3 – b3) = (a + b)(a . … … ….rn)] / [1 .com co m for more papers 8. (a + b) 2 www. if. (a + b)2 + (a . A number is divisible by 3. (13 + 23 + 33 + … … … + n3) = [n(n + 1)] / 2 = [n(n + 1)(2n + 1)] / 6 = [n2(n + 1)2] / 4 w w w .1)d] = a + (n . (a / b)m 25. am / an 23. To express a / b as a percent.downloadmela.n) = a mb m = an / bn =1 www. Page 3 of 12 = (a1/n)n =a visit www. If ‘A’ is R% more than ‘B’. M. )m = = = = / ow 32. If the population of a town is ‘P’ in a year. then ‘B’ is more than ‘A’ by OR If the price of a commodity decreases by R%.downloadmela.C. × Their L. am × an 22. 27. (ab)m 24. then the increase in consumption.C. If ‘A’ is R% less than ‘B’.114 Handy Formulae for Quantitative Aptitude Problems H.d {100R / [100 + R] } % nl o Percentage ad m el a. ( 31. To express x% as a fraction. F. = a(m + n) = a(m . C. we have a / b = (a / b × 100) % w . 30.R] } % 36.F & L. Surds & Indices 21. 29. we have x% = x / 100 34. then its population after ‘N’ years is P (1 + R/100) N w 33. then ‘B’ is less than ‘A’ by OR If the price of a commodity increases by R%.com 28. Product of two numbers = Their H.com co m for more papers = a1/n . then the reduction in consumption. C. a0 26.M of Numbers 20. not to increase the expenditure is {100R / [100 . not to increase the expenditure is w 35. d 45. which is called the componendo. If a : b = c : d. Also. If a / b = c / d. The compounded ratio of the ratios (a : b). d are in proportion. If a / b = c / d. In a proportion.com = [(100 . then its value after ‘N’ years at a depreciation of ‘R’ p.b) = (c + d) / (c . Mean proportion between a and b is 49.a is P (1 . The equality of two ratios is called a proportion. 50.p. then. (e : f) is (ace : bdf) nl o ad 41.R/100)N 39. which is called the dividendo. we say that x is inversely proportional to y if x = k / y for some constant k and we write x α 1 / y.c. If the population of a town is ‘P’ in a year.d) / d. 51.p.d). (a + b) / (a . a3 : b3 is a triplicate ratio of a : b w 46. Product of extremes = Product of means 43. the first and fourth terms are known as extremes. If a / b = c / d.downloadmela. Selling Price = [(100 + Gain%) × Cost Price] / 100 visit www. then its population ‘N’ years ago is P / [(1 + R/100)N] Profit & Loss 38. w 48. (a + b) / b = (c + d) / d.R/100)N] www.downloadmela.b) / b = (c . (a . we write a : b :: c : d and we say that a. a1/3 : b1/3 is a sub-triplicate ratio of a : b w 47. 53. while the second and third are known as means. x α y. m el a. a2 : b2 is a duplicate ratio of a : b ow 44. (c : d). c. then. If the value of a machine is ‘P’ in a year. b. : is a sub-duplicate ration of a : b .a is P / [(1 . Variation: We say that x is directly proportional to y if x = ky for some constant k and we write. then. then its value ‘N’ years ago at a depreciation of ‘R’ p.c. co m Page 4 of 12 40.Loss%) × Cost Price] / 100 Ratio & Proportion 42.com for more papers .114 Handy Formulae for Quantitative Aptitude Problem 37. which is called the componendo & dividendo. 52. If the value of a machine is ‘P’ in a year. If A is thrice as good a workman as B. If A’s 1 day’s work = 1/n. moving at ‘u’ kmph and ‘v’ kmph (where. visit www. Pipes & Cisterns 62. The work done is directly proportional to the number of men working at it. then A can finish the work in n days.v)] hrs 65. Page 5 of 12 60. then average speed during his whole journey is w . ow nl o Time And Distance ad m 61.downloadmela. then on opening both the pipes. Lengths of trains are ‘x’ km and ‘y’ km.com 59. www. 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. Time taken to cover a distance is inversely proportional to the speed of the car. then the time taken y the over-taker train to cross the slower train is [(x + y) / (u . Time taken to cross each other is [(x + y) / (u + v)] hrs 66.downloadmela. If a number of partners have invested in a business and it has a profit. Suppose a man covers a distance at ‘x’ kmph and an equal distance at ‘y’ kmph. the net part of the tank filled in 1 hour is (1/x – 1/y) w w 63. then Share Of Partner = (Total_Profit × Part_Share / Total_Share) Chain Rule 55. Ratio of times taken by A & B to finish a work = 1 : 3 el a. 58. The cost of articles is directly proportional to the number of articles. The time (number of days) required to complete a job is inversely proportional to the number of hours per day allocated to the job. u > v) in the same direction. If a pipe can fill a tank in ‘x’ hours and another pipe can empty the full tank in ‘y’ hours (where y > x). 57. then A’s 1 day’s work = 1/n. If A can do a piece of work in n days. 56.d [2xy / (x + y)] kmph Trains 64.114 Handy Formulae for Quantitative Aptitude Problems Partnership 54. then: Ratio of work done by A and B = 3 : 1.com co m for more papers Time & Work . = ( 100 × S. then: el a.com 72. Then.b) km/hr. a. 75.: (Cheaper quantity) : (Dearer quantity) = (d .114 Handy Formulae for Quantitative Aptitude Problems Then. = ( 100 × S. c. 70. then: Speed in still water = ½ (a + b) km/hr. 71. then: Speed downstream = (u + v) km/hr.d ow 74. b. If the speed downstream is a km/hr and the speed upstream is b km/hr. ) / ( P × T ). Boats & Streams 69.downloadmela. P R T = ( P × R × T ) / 100 = ( 100 × S. www. y metres/sec = (y × 18/5) km/hr. Alligation or Mixture : ).m) : (m .I. Rule of Alligation: If two ingredients are mixed. Rate = R% per annum and Time = T years. d.I. We represent the above formula as under: nl o ad m 73. 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.c) Simple Interest 76. w w w .downloadmela. If the speed of a boat in still water is u km/hr and the speed of the stream is v hm/hr. Let Principle = P. Mean Price: The cost price of a quantity of the mixture is called the mean price. A’s speed : B’s speed = ( 67.I.I.com for more papers . S. Speed upstream = (u . x kmph = (x × 5/18) m/sec. 68. co m Page 6 of 12 visit www. . ) / ( R × T ). Rate of stream = ½ (a . ) / ( P × R ).v) km/hr. Let Principle = P. loga (xy) b. Amount = P (1 + R/100)N II.com 80. When interest is compounded Half-yearly: Amount = P (1 + R/2/100)2N III. it is taken as 10 i. loga x h. When interest is compounded Quarterly: Amount = P (1 + R/4/100)4N 78. loga 1 e.d ow = loga x + loga y = loga x . 2nd. Present worth of Rs. Amount = P (1 + R/100)3 × (1 + ⅞R/100) www. When interest is compounded Annually. I. Then. R2%. say 3⅞ years. The logarithm of a number contains two parts.downloadmela. 82. 79. Properties of Logarithms: a. and 3rd year respectively. When base is not mentioned. loga (xp) f. R3% for 1st. Then.com for more papers . When Rates are different for different years. Amount = P (1 + R1/100) (1 + R2/100) (1 + R3/100) co m Page 7 of 12 visit www.e. but the time is in fraction.e. Logarithms to the base 10 are known as common logarithms j. When interest is compounded Annually. Rate = R% per annum and Time = T years. Then. x due n years hence is given by: Present Worth = x / (1 + R/100)n Logarithms 81. namely characteristic and mantissa. loga x g. loga (x/y) w w w c. Logarithm: If a is a positive real number. Log of 1 to any base is 0) = p loga x = 1 / logx a = logb x / logb a = log x / log a (Change of base rule) nl o ad m el a.downloadmela. then we write m = loga x and say that the value of log x to the base a is m.114 Handy Formulae for Quantitative Aptitude Problems Compound Interest 77. say R1%. . The integral part is known as characteristic and the decimal part is known as mantissa. other than 1 and am = x. logx x d.loga y = 1 (i. Log of any number to its own base is 1) = 0 (i. Antilog: If log x = y.456 2. 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. Area of a parallelogram = Base × Height Page 8 of 12 visit www.d b.downloadmela. b.234 0. Radius of incircle of an equilateral triangle of side a = a / 2 e.g. the characteristic is one less than the number of digits in the left of decimal point in the given number. Area of a triangle = .com w 85. In this case. Area of 4 walls of a room = 2 (length + breadth) × height . Triangle: a. In this case. IV. for more papers co m . Case 1: When the number is greater than 1. Area of a triangle = ½ × base × height b. e. Perimeter of a rectangle = 2 (length + breadth) 84. www. Rectangle: el a. Case 2: When the number is less than 1. Square: w 86. then antilog y = x.com Characteristic 2 1 0 -1 -2 -3 For mantissa. we look through the log table. and a. II. Area of square = (side)2 nl o ad a. Area of an equilateral triangle = / 4 × (side)2 d.56 23.114 Handy Formulae for Quantitative Aptitude Problems I. Radius of circumcircle of an equilateral triangle of side a = a / 87. Area of a square = ½ (diagonal)2 ow a.0234 0. Number 234. Parallelogram/Rhombus/Trapezium: a. c are the sides of the triangle c. where w s = ½ (a + b + c). Area of a rectangle = (length × breadth) m 83.downloadmela.34 0. Area b.00234 III. units units ad a. Then. 90.com b. Area of a rhombus c. = a3 cu units = 6a2 sq. Then. for more papers co m d. el a. Volume w w b. Surface Area w . Area of a sector = ½ (arc × R) . units =( × a) units c. 92. Area of trapezium 88. Page 9 of 12 Total Surface Area = 2πr(r + h) sq. Circle/Arc/Sector.downloadmela. Then. Volume = (l × b × h) cu units m Let length = l.d Let each edge of a cube be of length a. Cylinder: Let radius of base = r & height (or length) = h. a. Surface Area = 2 (lb + bh + hl) sq.downloadmela. breadth = b & height = h units Then. units b. Cube: Diagonal = a. where R is the radius of the circle: a.114 Handy Formulae for Quantitative Aptitude Problems www. Volume = (πr2h) cu. Cone: Let radius of base = r & height = h.com ow nl o b. Cuboid: c. Diagonal 91. units c. = ½ × (Product of diagonals) The halves of diagonals and a side of a rhombus form a right angled triangle with side as the hypotenuse. units visit www. Length of an arc = Ө/360 × 2πR = Ө/360 × πR2 Volume & Surface Area 89. Curved Surface Area = (2πrh) sq. = ½ × (sum of parallel sides) × (distance between them) d. Area of a circle = πR2 b. Circumference of a circle = 2πR c. the payment of Rs. if S. When stock is purchased. above par (or at premium). if S. 100. 800. 156 after 4 years and the rate of interest is 14% per annum. Volume = (2/3 πr3) cu. Total Surface Area = (3πr2) sq. 97. units b.100) = (Sum due) – (P. we mean a stock whose face value is Rs. is more than Rs. c. is Rs. a. Suppose a man has to pay Rs. 156 due 4 years hence.P.downloadmela. Rs. 9% stock at 95’. units = (4πr2) sq. 95. Present Worth (P. units Stocks & Shares 95. Volume b. if S. Brokerage: The broker’s charge is called brokerage. l b. units c.) = Rs. 100 stock is said to be: . brokerage is added to the cost price.D. 800.d ow 96. 100 now will clear off the debt of Rs. Surface Area 94. We say that: Sum due = Rs. The selling price of a Rs. Page 10 of 12 visit www. at par.W. is less than Rs. Sphere: Let the radius of the sphere be r. Curved Surface Area = (2πr2) sq. By ‘a Rs. Then. (156 . 100. Total Surface Area = πr(r + l) sq. annual interest is 9% of the face value and the market price of a Rs. 99. 100.114 Handy Formulae for Quantitative Aptitude Problems www.downloadmela. b. 100 stock is Rs.) = Rs. Slant height. Hemi-sphere: Let the radius of the sphere be r. 156 in 4 years.com a. below par (or at discount). 100 exactly.) w a. units d. Clearly. nl o ad m el a. units 93. a. Volume c.P. Then. True Discount 100.P.com co m for more papers . 100 at 14% will amount to Rs. units Curved Surface Area = (πrl) sq. w w 98. = units = (⅓ πr2h) cu.W. 156 due 4 years hence. So. units = (4/3 πr3) cu. True Discount (T. When the stock is sold. brokerage is subtracted from the selling price. 113.downloadmela.D.) is the S.] × [T.D.D. Amount 114. then P.D.114 Handy Formulae for Quantitative Aptitude Problems 101.) for the unexpired time 107. = = (Amount × Rate × Time) / 100 = (Amount × Rate × Time) / (100 + [Rate × Time]) = (B.) / P. × T. When the sum is put at compound interest. and true discount is reckoned on the amount 104.I.d = (B.) – (T. T. grace days are not to be added 109. w 111. on the face value for the period from the date on which the bill was discounted and the legally due date.) / (B. Then.D. on T.I.W.I.D.D.D.W. = S. B.I.W.) = S.]) / ([S. c. Let rate = R% per annum & time = T years. P.G.I.D. on T. Amount = Interest on P.W. (S.) www. Interest is reckoned on R.com w 110. a.D.) / (R × T) = (P.) – (T.) + (T. 112. b.G.D.D. = (P.I.W. visit www. = Amount / (1 + R/100) T Banker’s Discount 106. B.D. T. 102.W.D.) = (B.) – (T. × 100) / (Rate × Time) ow 108. T.D. 2 = (T.D.G.I. T. on bill for unexpired time nl o ad m 105.D.) = (B. co m for more papers d. B. When the date of the bill is not given.) = S. w .D. – T. . Banker’s Gain (B.D.D.]) e.downloadmela.D. Sum = (100 × Amount) / (100 + [R × T]) = (100 × T. el a.D.com 103.W. Banker’s Discount (B.] – [T. T.) × R × T / 100 = ([Amount] × R × T) / (100 + [R × T]) = ([S.D.D. d ow nl o ad for more papers m el a. co m .www.downloadmela.com w w .com visit w www.downloadmela. com/videotutorials/ videotutorials.html .com/ebooks/ebookdisplay.com/previouspapers/previouspapers.downloadmela.downloadmela.Certification dumps at www.This Download is from www.Reasoning Questions.downloadmela.com/ magazines/magazines.html Download Various Kind of magazines at www.downloadmela.html Download Placement papers.com/companypapers/itpapers.html Download Video tutorials at www.Hr Questions.Puzzles.Technical Interview questions.html Download Previous papers of all exams and study materials and tips at www.downloadmela.Aptitude Questions.com Download e-books at www.downloadmela. 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