![When interest is calculated annually
CI = P {[1 + (R/100)]N
– 1}
Amount = P [1 + (R/100)]N
P – Principal
N – Time period
R – Rate of interest
CI – Compound interest
COMPOUND INTEREST
CI = P {[1 + ((R/4)/100)]4N
– 1}
Amount = P [1 + ((R/4)/100)]4N
CI = P {[1 + ((R/2)/100)]2N
– 1}
Amount = P [1 + ((R/2)/100)]2N
CareersCloud
L E A R N T O L E A D
When interest is calculated half−yearly
Difference between SI and CI for 2 years
Difference = P (R/100)²
Difference between SI and CI for 3 years
Difference = P (R/100)² * [(300+R)/100]
When interest is calculated quarterly](https://image.slidesharecdn.com/basicsofarithmetic-20221-241121160529-09540564/85/Arithmetic-Basics-for-banking-aspirants-in-quants-15-320.jpg)
Arithmetic Basics for banking aspirants in quants
- 1. CRACK C A R E E R S C L O U D B A S I C S O F ARITHMETIC L E A R N T O L E A D Banking GUIDE TO
- 2. In recent days, the banking exams are getting more tougher so, the aspirants are very confused to follow a certain set of ideas for each exam. This course will be helpful for the beginners who are preparing for the banking exam. The aspirants need some guidance for cracking the bank exams. So we have launched a course titled a “Guide to Crack- Banking''. This course is completely FREE OF COST, consisting of shortcuts in quantitative aptitude and reasoning ability along with the set of rules for English language. You can download the important contents from the PDF and take printouts of them to stick in your study room. This course is available on our website www.careerscloud.in and in Careerscloud android Mobile application. P R E F A C E CareersCloud Team Regards,
- 3. PA R T N E R S H I P A G E S R AT I O A N D P R O P O R T I O N P E R C E N TA G E S AV E R A G E P R O F I T A N D L O S S S I M P L E I N T E R E S T C O M P O U N D I N T E R E S T T I M E A N D D I S TA N C E T R A I N S B O AT S A N D S T R E A M T I M E A N D W O R K P E R M U TAT I O N & C O M B I N AT I O N P R O B A B I L I T Y M I X T U R E A N D A L L I G AT I O N Q U A D R AT I C E Q U AT I O N N U M B E R S Y S T E M P I P E S A N D C I S T E R N 1 2 3 4 5 6 7 8 9 10 12 13 14 15 16 17 18 M E N S U R AT I O N 19 11 BASICS OF ARITHMETIC
- 4. CareersCloud L E A R N T O L E A D SQUARE NUMBER FROM 1 – 50 NUMBER 12 SQUARE VALUE SQUARE VALUE 1 NUMBER 152 22 4 162 32 9 172 25 16 182 NUMBER SQUARE VALUE SQUARE VALUE NUMBER 42 36 192 52 49 64 81 100 144 121 169 196 225 256 289 324 400 361 441 484 529 576 625 729 676 784 841 900 961 1024 1089 1225 1156 2116 2209 2304 2500 2401 1296 1369 1444 1521 1600 1764 1681 1849 1936 2025 202 62 212 72 222 82 232 92 242 102 252 112 262 122 272 132 282 142 292 302 312 322 332 342 352 362 372 382 392 402 412 422 432 442 452 462 472 482 492 502
- 5. CareersCloud L E A R N T O L E A D CUBE NUMBER FROM 1 - 30 NUMBER 13 SQUARE VALUE SQUARE VALUE 1 NUMBER 153 23 8 163 33 27 173 125 64 183 43 216 193 53 343 512 729 1000 1728 1331 2197 2744 3375 4096 4913 5832 8000 6859 9261 10648 12167 13824 15625 19683 17576 21952 24389 27000 203 63 213 73 223 83 233 93 243 103 253 113 263 123 273 133 283 143 293 303
- 6. CareersCloud L E A R N T O L E A D FRACTION TO PERCENTAGE: FRACTION 1/1 100% 50% 25% 20% 10% PERCENTAGE PERCENTAGE FRACTION 1/2 1/3 33.33% or 33 (1/3)% 16.66% or 16 (2/3)% 1/4 1/5 1/6 1/7 1/8 1/9 1/10 1/11 1/12 1/13 1/14 1/15 1/16 1/17 1/18 1/19 1/20 5% 14.28% or 14 (2/7)% 12.5% or 12 (1/2)% 11.11% or 11 (1/9)% 9.09% or 9 (1/11)% 8.33% 8 (1/3)% 7.69% or 7 (9/13)% 7.14% or 7 (1/7)% 6.66% or 6 (2/3)% 6.25% or 6 (1/4)% 5.88% or 5 (15/17)% 5.55% or 5 (5/9)% 5.26% or 5 (5/19)%
- 7. · When two ratios are equal, they are said to be in proportion, for example, a: b : : c: d. From this, the product of extreme is equal to the product of mean can be obtained RATIO AND PROPORTION RATIO: PROPORTION: or Merging of ratios: If the ratio between the first and second quantities is a: b and the ratio between second and third quantities is c: d, then the ratio among the first, Second and third quantities is given by (ac: bc: bd) First Second Third Resultant ac : bc : bd a : b c : d means extremes a: b : : c: d a/b = c/d a * d = b* c CareersCloud L E A R N T O L E A D
- 8. AGES The most important terms in this topic are (Before/Ago, Present, After/Hence) Before/Ago A’s age (x - N) Years (x) Years (x + M) Years A’s age A’s age N years ago M years hence Present After/Hence CareersCloud L E A R N T O L E A D Here before/Ago denotes the past and After/Hence denotes the future
- 9. PARTNERSHIP The most important terms in this topic are Profit share = Investment * time period A's capital * A's Time period = B's capital * B's Time period A's profit share B's profit share CareersCloud L E A R N T O L E A D (1. Investment, 2. Time period, 3. Profit)
- 10. CareersCloud L E A R N T O L E A D PERCENTAGES A is what percentage of B = (A/B) * 100 A is what percent more than B = (A - B)/B * 100 A is what percent less than B = (B - A)/B * 100 If the value of a number is first increased by X% and later decreased by Y%, the net change is either an increase or decrease, then there is (X + Y + XY/100) % increase (X - Y - XY/100) % increase or decrease, If the value of a number is first decreased by X% and later decreased by Y%, the net change is always a decrease, then there is (- X - Y + XY/100) % decrease, according to the +ve or –ve sign respectively according to the –ve sign If the value of a number is first increased by X% and later increased by Y%, the net change is always an increase, then there is
- 11. AVERAGE Average = Sum of observations/ Number of observations Sum of observations = Average * Number of observations Number of observations = Sum of observations/ Average 1. Average of first ‘n’ natural numbers = (n +1)/2 2. Average of first ‘n’ even numbers = n +1 3. Average of first ‘n’ odd numbers = n 4. Average of first ‘n’ consecutive natural numbers = (First number + Last number)/2 5. Average of square of first ‘n’ natural numbers = ((n+1)(2n+1))/6 If the average of ‘n’ numbers is a and that of ‘m’ numbers is b, then the average of (n+m) numbers = (na + mb)/ n + m CareersCloud L E A R N T O L E A D
- 12. CareersCloud L E A R N T O L E A D L E A R N T O L E A D PROFIT AND LOSS Profit = Selling Price − Cost Price Loss = Cost Price − Selling Price Profit % = (Profit/CP) * 100 Loss % = (Loss/CP) * 100 Discount = MP – SP Discount % = (Discount/MP) * 100 Markup Price = Marked Price – Cost Price Markup % = (Markup price/ CP) * 100 Other important relations and formulas SP = MP * ((100 – D)/100) MP * ((100 – D)/100) = CP * (100+P)/100 or CP* (100-L)/100 Where, D = Discount% P = Profit % L = Loss % BASIC FORMULA The most important terms in this topic are (Cost Price - CP, Selling Price - SP, Marked Price - MP)
- 13. Shortcut If there is same successive Profit% and Loss% for a product (x%), then the resultant transaction will be always LOSS Loss % = (− x²/100) Dishonest dealer A dishonest dealer selling his goods at CP but uses false weight, then the profit of the dealer is Profit % = ((True weight – False weight)/False weight) * 100 CareersCloud L E A R N T O L E A D If there are two successive profit% or loss % applied for a product, it can be easily written as For successive profit = x + y + (xy/100) % For successive loss = – x – y + (xy/100)% Use ‘+’ for profit% and ‘−’ for loss%
- 14. SI = PNR/100 Amount = Principal + Simple Interest P – Principal N – Time period R – Rate of interest SI – Simple interest The annual payment discharging for a debt of Rs. A due in t years at the rate of interest r% per annum is = 100 * A / (100 * t + (r * t (t - 1)/2)) SIMPLE INTEREST CareersCloud L E A R N T O L E A D
- 15. When interest is calculated annually CI = P {[1 + (R/100)]N – 1} Amount = P [1 + (R/100)]N P – Principal N – Time period R – Rate of interest CI – Compound interest COMPOUND INTEREST CI = P {[1 + ((R/4)/100)]4N – 1} Amount = P [1 + ((R/4)/100)]4N CI = P {[1 + ((R/2)/100)]2N – 1} Amount = P [1 + ((R/2)/100)]2N CareersCloud L E A R N T O L E A D When interest is calculated half−yearly Difference between SI and CI for 2 years Difference = P (R/100)² Difference between SI and CI for 3 years Difference = P (R/100)² * [(300+R)/100] When interest is calculated quarterly
- 16. (A₁) (1/T1) = (A₂) (1/T2) Important shortcuts: When two rate of interest is given as R1 and R2 in Compound Interest, then it can combine into a single rate of interest using this formula R = {R₁ + R₂ + (R₁ *R₂)/100} -> Effective percentage method If the sum of money placed at CI amounts to A1 times itself in T1 years and to A2 times itself in T2 years, then The annual payment discharging for a debt of Rs. P due in N years at the rate of interest r% per annum CI is P = X/ (1+ r/100)N + X/ (1+ r/100) N-1 …………………….. X/(1+ r/100)² + X/ (1+ r/100) Where X is the installment CareersCloud L E A R N T O L E A D Note: Simple interest and compound interest for the 1st year will always be equal
- 17. In general, Distance = (Speed * Time) km or meter Speed = (Distance/ Time) km/hr or m/s Time = (Distance/ Speed) hour or seconds TIME AND DISTANCE Conversion: Average speed: From km/hr to m/s Multiply by 5/18 From m/s to km/hr Multiply by 18/5 Conversion from hour to minutes or minutes to seconds, Multiply by 60 Conversion from seconds to minutes or minutes to hours, divide by 60 Average speed = Total distance travelled/ Total time taken Average speed = (2xy)/ (x + y) When the distance covered is the same Average speed = (x + y)/2 Where x and y are speeds of moving objects when the CareersCloud L E A R N T O L E A D time taken is constant
- 18. Relative speed Where x and y are speeds of moving objects, Relative speed is calculated when two objects with speeds of x km/hr and y km/hr was traveling in the opposite direction or in the same direction - Relative speed = x + y When in the opposite direction - Relative speed = x – y When in the same direction CareersCloud L E A R N T O L E A D
- 19. TRAINS Time taken by the train to cross a standing pole/stone/man standing on the platform or stationary train. Time = (LT/ST) Here, LT – Length of the train ST – Speed of the train CareersCloud L E A R N T O L E A D LT sT Pole Time taken by a train to cross a platform/Tunnel/Bridge Time = (LT + LP)/ ST Here, LT – Length of the train LP – Length of the platform ST – Speed of the train LT LP sT Platform
- 20. CareersCloud L E A R N T O L E A D L2 Y L1 X L2 Y L1 X When two trains move in the same direction, then the time for both trains to overtake one another is calculated by Time = (L1 + L2)/ (X − Y) Here, L1 - Length of the train 1 L2 – Length of the train 2 X – Speed of the train 1 Y – Speed of the train 2 When two trains moving in the opposite direction, the time for both trains to cross each other is calculated by Time = (L1 + L2)/ (X + Y) Here, L1 - Length of the train 1 L2 – Length of the train 2 X – Speed of the train 1 Y – Speed of the train 2 Same direction Opposite direction
- 21. CareersCloud L E A R N T O L E A D LT X Y When a man and a train move in the same direction, then the time by the train (X) to overtake the man (Y) is calculated by Time = LT/ (X − Y) Here, LT – Length of the train X – Speed of the train Y – Speed of the man L2 S2 L1 LT X Y When a man and a train move in the opposite direction, then the time by both to cross each other is calculated by Time = LT/ (X + Y) Here, LT – Length of the train X – Speed of the train Y – Speed of the man Where L1 and L2 are the lengths of the two trains and S1 and S2 are the speeds of the two trains When the starting time of two trains is same from station x and y and it travels towards each other. After crossing each other, they took time t1 and t2 in reaching stations y and x respectively, then the ratio between the speed of the two trains S1 /S2 = √t2 : √t1 Kmph S1 Kmph
- 22. CareersCloud L E A R N T O L E A D BOATS AND STREAM The most important terms in this topic are SB – Speed of the boat or Speed of the boat in still water Sw – Speed of water or Speed of stream or Rate of stream or Speed of Current DWs – Downstream speed of the boat UPs – Upstream speed of the boat Downstream speed = SB + Sw (km/hr) Upstream speed = SB – Sw (km/hr) Speed of the boat in still water = 1/2( DWs+ UPs) Speed of the stream = 1/2(DWs − UPs) Sw SB Downstream Upstream Sw SB
- 23. CareersCloud L E A R N T O L E A D TIME AND WORK Total work = Efficiency * time taken Efficiency = Total work / Number of days Efficiency = Amount of work done by a person in 1 hour or 1 day If the person constructing a building, there will be positive efficiency and if the person is destroying the building the efficiency will be negative Fraction method: If a person completes a piece of work in ‘n’ days, then the part of the work done by the person in one day = (1/n)
- 24. Wages is proportional to the amount of work done by the workers If A and B together take ‘x’ days to complete a job If A alone takes ‘a’ days more than A and B working together to do a job and B alone takes ‘b’ days more than A and B working together to do a job, then x = √(a*b) days Wages Other important formula CareersCloud L E A R N T O L E A D Chain rule (M₁ * T₁ * D₁)/W₁ = (M₂ * T₂ * D₂)/W₂ Here, M – Number of Men T – Number of Hours D – Number of Days W – Amount of work done
- 25. PIPES AND CISTERN If pipes P₁ can fill the tank in ‘x’ hours and P₂ can fill the tank in ‘y’ hours and both are opened together, then part of the tank is filled in 1 hour = (1/x) + (1/y) If pipes P₁ can fill the tank in ‘x’ hours and P₂ can empty the tank in ‘y’ hours and both are opened together, then part of the tank filled in 1 hour = (1/x) – (1/y) Note: Pipes that empty the tank will have negative efficiency Hours CareersCloud L E A R N T O L E A D P1 X Hours Y P2 Hours P2 Y Hours P1 X
- 26. CareersCloud L E A R N T O L E A D 1) If clockwise and anti−clockwise orders are different, then the number of ways to arrange ‘n’ number of distinct object = (n − 1)! 2) If clockwise and anti−clockwise orders are same, then the number of ways to arrange ‘n’ number of distinct object = (n − 1)! / 2 Circular permutation Note 1) 2) 3) n Pn n P0 = n! = 1 0! = 1 PERMUTATION AND COMBINATION Permutation Permutation means an arrangement of numbers or alphabets in order nPr = n! / (n − r)! where 0 ≤ r ≤ n n – Total number of elements in a set; r – Number of elements to be arranged
- 27. Relation between permutation and combination n Cr = n Pr / r! (or) n Pr = r! * nCr Some important factorial values to be memorized for faster calculation: Combination means selection of objects from the given sets n Cr = n! / ((n − r)! * r!) where 0 ≤ r ≤ n n – Total number of objects; r – Number of objects to be selected Combination 1) 2) 3) 4) 5) Note 0! = 1 1! = 1 2! = 2 3! = 6 4! = 24 5! = 120 6! = 720 7! = 5040 8! = 40320 9! = 362880 CareersCloud L E A R N T O L E A D n Cn n C0 n Cr n C(n-r) n Cr + n Cr-1 (n+1) Cr = 1 = 1 = = 0! = 1
- 28. CareersCloud L E A R N T O L E A D PROBABILITY Probability = Number of favorable outcomes/ Total number of outcomes P(E) = n(E)/n(S) The value of probability lies between 0 to 1 Sample space means the total number of outcomes for an event The sample space for coins or dice can be found using the formula xy Where, x= number of faces y= number of coins/dice 1) Sample space of 2 coins tossed together {HH, HT, TH, TT} = 4 2) Sample space of 3 coins tossed together {HHH, HHT, HTH, THH, HTT, THT, TTH, TTT} = 8 SAMPLE SPACE FOR COINS
- 29. CareersCloud L E A R N T O L E A D 1) Throwing a dice, we can have 6 outcomes. So the sample space will be, S = {1, 2, 3, 4, 5, 6}. 2) Sample space of 2 dice thrown together = 36 Throwing a die twice and throwing two dice simultaneously are treated as the same experiment. Sample space = {(1,1), (1,2), (1,3), (1,4), (1,5), (1,6) (2,1), (2,2), (2,3), (2,4), (2,5), (2,6) (3,1), (3,2), (3,3), (3,4), (3,5), (3,6) (4,1), (4,2), (4,3), (4,4), (4,5), (4,6) (5,1), (5,2), (5,3), (5,4), (5,5), (5,6) (6,1), (6,2), (6,3), (6,4), (6,5), (6,6)} SAMPLE SPACE FOR DICE
- 30. MIXTURE AND ALLIGATION (Mean price – CP of cheaper quantity)/ (CP of dearer quantity – Mean price) = (m - c)/ (d - m) Repeated dilution: If a container contains ‘x’ litres of a liquid out of the total capacity and it is replaced by ‘y’ liters of other liquid for ‘n’ number of times, then the final quantity of liquid ‘x’ in the container is, Final quantity of liquid ‘x’ = x (1 – (y/c)n ) x – Initial quantity of the liquid y – Replaced quantity at a time n – Number of times replaced c - Capacity of Container Cost Price = CP CP of cheaper quantity(c) (d − m) (m − c) CP of dearer quantity(d) Mean price(m) CareersCloud L E A R N T O L E A D
- 31. QUADRATIC EQUATION Quadratic equation is in the form of ax² + bx + c = 0 Sign of ‘b’ + + - + - - + - Sign of ‘c’ Signs of smaller value root, Signs of larger value root CareersCloud L E A R N T O L E A D -,- +,+ -,+ +,-
- 32. Number System CareersCloud L E A R N T O L E A D 1. Sum of first n natural numbers = n(n+1)/2 E.g. Sum of first 5 natural numbers = 1+2+3+4+5=5(5+1)/2=15 2. Sum of squares of first n natural numbers = n(n+1)(2n+1)/6 E.g. Sum of squares of first 6 natural numbers = 1²+2²+3²+4²+5²+6² = 6(6+1)(2*6+1)/6 = 91 3. Sum of cubes of first n natural numbers = (n(n+1)/2)² E.g. Sum of cubes of first 4 natural numbers = 1³+2³+3³+4³= (4(4+1)/2)² = 100 4. Sum of first n even natural numbers = n(n+1) E.g. Sum of first 4 even natural numbers = 2+4+6+8 = 4(5) = 20 5. Sum of first n odd natural numbers = n² E.g. Sum of first 3 odd natural numbers = 1+3+5 = n² = 9 6. Sum of n number of terms of a natural number series in which the difference between any two consecutive terms is same = n/2 (first term + last term) E.g. Sum of all 3 term in the series 3, 6, 9 = 3/2(3+9) = 18 Important formulas:
- 33. CareersCloud L E A R N T O L E A D 2D Formulas Name Figure Perimeter Area Rectangle Square Scalene Triangle Right Triangle 2 * (l + b) s = {a + b + c}/2 S = Semi-perimeter b + h + d 1/2 * b * h √ {s (s - a) (s - b) (s - c)} 4 * a a a h d b c b a a a b l a2 l * b Diagonal of Rectangle d² = l² + b² Diagonal of square = d = a * √2 Note:
- 34. CareersCloud L E A R N T O L E A D 2D Formulas Name Figure Perimeter Area Equilateral triangle Isosceles Triangle Parallelogram Rhombus 3 * a 4 * a 2a + b 2 * (a + b) b * h 1/2 * d1 * d2 a a b b a a a h h h b a a 1/2 * b * h or 1/4 x b * √(4a²-b²) 1/2 * a * h (or) √3/4 * a² a a a a d1 d2
- 35. CareersCloud L E A R N T O L E A D Name Figure Perimeter/Circumference Area Trapezium Circle Semicircle Ring (Shaded Region) Sector of a Cirlce a + b + c + d 2 * π * r π * r + 2 * r Outer Radius - R Outer Circumference = 2πR Inner Circumference = 2πr Inner Radius - r L + 2 * r Here L = segment ϴ/360⁰ * (π * r²) Area = π * (R² - r²) b a c d h o r π * r² 1/2 * (a + b) * h o r r r R B L A C r 1/2 * π * r²
- 36. CareersCloud L E A R N T O L E A D Name Figure Perimeter/Circumference Area Pathways running across the middle of a rectangle Outer Pathways Inner Pathways ( l + b - w ) w w w b l w w w w Inner = 2 ( l + b) Outer = 2 ( l + b) Inner = 2 ( l + b - 4 w) Outer = 2 (l + b + 4 w) (l + b + 2 w) * 2 w (l + b - 2 w) * 2 w 2( l + b - 2 * w) b l w w b l
- 37. Lateral surface area = 2 * (l + b) * h Total surface area = 2 * (lb + bh + hl) Lateral surface area = 4a² Total surface area = 6a² Diagonal of cube = d = a * √3 Face diagonal of the cube = a * √2 Curved surface area = 2 * π * r * h Total surface area = 2 * π * r (h + r) Curved surface = π * r * l Total surface area = π * r (l + r) π * r² * h 1/3 * π * r² * h a³ l * b * h Diagonal of Cuboid d² = l² + b² + h² Cuboid Cube Right circular Cylinder Right Circlular Cone CareersCloud L E A R N T O L E A D 3D Formulas Name Figure Surface Area Volume b a h l h r r a a l h
- 38. Frustum of a Right Circular Cone Sphere Hemisphere CareersCloud L E A R N T O L E A D 3D Formulas Name Figure Surface Area Total Area Curved surface area = π * (R + r) * l Total surface area = π * (R + r) * l + π * (R² + r²) 1/3 * π * (R² + r² + R * r) * h Curved surface area = 4 * π * r² Total surface area = 4 * π * r² Curved surface area = 2 * π * r² Total surface area = 3 * π * r² 4/3 * π * r³ 2/3 * π * r³ r r r R h
- 39. Paid Paid Subscribers Subscribers Daily Daily Gets 200 Question Daily 200 Questions 200 Questions 200 Questions Subject Course Title Hindu Editorial Vocabulary 10 - 15 5 : 00 AM 120 40 270 140 2150 1775 2150 6 : 00 AM 7 : 00 AM 8 : 00 AM 10 : 00 AM | 10:15 AM 10 : 00 AM | 10:45 AM 11 : 00 AM | 11:15 AM 5 - 7 10 10 10 10 Crack - Reading Comprehension Prelims General English Mains General English Mains Data Interpretation Mains Puzzle & Seating Prelims Data Interpretation Mains Arithmetic Prelims Arithmetic Mains Quantitative Aptitude Prelims Quantitative Aptitude Mains Logical Reasoning Prelims Logical Reasoning Crack - Current Affairs Other CA Topic-Wise Quiz Quiz timing Total Questions No.of Questions Total Prelims Puzzle & Seating 10 10 10 10 10 10 10 10 15 - 30 30 180 - 200 11 : 30 AM | 11:45 AM 12 : 00 PM 12 : 30 PM 4 : 30 PM 5 : 00 PM 6 : 00 PM 6 : 00 PM 6 : 00 AM 6 : 00 PM Never Fails Daily Efforts 1825 950 1000 2050 1500 1950 900 1500 Note : The given total questions count are upto February 2022