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Blue Lotus

Blue Lotus. A ptitude Numerical Reasoning. Numerical Reasoning. Problems on Numbers Problems on Ages Ratio and Proportion Alligation or Mixture Chain Rule Partnership Venn Diagram. Numerical Reasoning. Area and Volume Probability Time and Work (Pipes) SI and CI Average

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Blue Lotus

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  1. Blue Lotus Aptitude Numerical Reasoning

  2. NumericalReasoning • Problems on Numbers • Problems on Ages • Ratio and Proportion • Alligation or Mixture • Chain Rule • Partnership • Venn Diagram

  3. Numerical Reasoning • Area and Volume • Probability • Time and Work (Pipes) • SI and CI • Average • Permutation and Combination • Percentage

  4. Numerical Reasoning • Boats and Streams • Time and Distance (Trains) • Data Sufficiency • Profit and Loss • Calendar • Clocks • Data Interpretation • Cubes

  5. Problems on Numbers Division Algorithm: Dividend = the number to be divided. Divisor = the number by which it is divided. Dividend / Divisor = Quotient. Quotient * Divisor = Dividend. Quotient * Divisor + Remainder = Dividend.

  6. Problems on Numbers Arithmetic Progression: The nth term of A.P. is given by Tn = a + (n – 1)d; Sum of n terms of A.P Sn = n/2 *(a + L) or n/2 *[2a+(n-1)d)] a = 1st term, n = number of term, d= difference, Tn = nth term Geometrical Progression: Tn = arn – 1. Sn = a(rn – 1)/(r-1); Where a = 1st term , r = 1st term / 2nd term

  7. Basic Formulae 1. ( a+b)2 = a2 + b2 + 2ab 2. (a-b)2 = a2 +b2 -2ab 3. ( a+b)2 -(a – b)2 = 4ab 4. (a+b)2 + (a – b)2 = 2 (a2 +b2) 5. (a2 – b2) = (a+b) (a-b) 6. (a+b+c)2 =a2 +b2 +c2 + 2(ab +bc+ca) 7. (a3 +b3) = ( a+b) (a2 +ab +b2) 8. (a3 –b3) = (a-b) (a2 - ab + b2)

  8. Problems on Numbers Three numbers are in the ratio 3:4:5. the sum of the largest and the smallest equal to the sum of the third and 52. Find the smallest number ?

  9. Problems on Numbers Solution: Let the numbers be 3x, 4x and 5x Then 5x+3x = 4x +52 8x – 4x = 52 4x = 52 x = 52/4 x = 13 The smallest number = 3x = 3*13 = 39.

  10. Problems on Numbers What is one half of two third of three fourths of four fifths of five sixth of six sevenths of seven eights of eight ninth of nine tenths of thirty?

  11. Problems on Numbers Solution: = ½ * 2/3 *3/4 * 4/5 * 5/6*6/7*7/8*8/9*9/10 *30 = 3

  12. Problem on Numbers If the operation ^ is defined by the equator x ^ y = 2x + y what is the value of a in 2 ^ a = a ^ 3? (Sathyam)

  13. Problem on Numbers Solution: 2(2) = a ^ 3 4 + a = 2a + 3 a = 1

  14. Problem on Numbers There are 150 weight some are 1 kg weight and some are 2 kg weights. The sum of the weights is 260. what is the number of 1 kg weight. (TCS)

  15. Problem on Numbers Solution: X + 2Y = 260 X + Y = 150 On Solving Two Equations Y = 110 X + Y = 150 X = 150 – 110 = 40 Kg

  16. Problem on Numbers The cost of 1 pencil, 2 pens and 4 erasers is Rs. 22, while the cost of five pencils, four pens and two eraser is 32. how much will 3 pencils, 3 pens and 3 eraser? (TCS)

  17. Problem on Numbers Solution: Let Pencil be x, Pens be y, Erasers be z x + 2y + 4z = 22 5x + 4y + 2z = 32 Adding we get 6x+6y+6z = 54 3x + 3y + 3z = 27 3 Pencil, 3 Pens and 3 Eraser is Rs. 27.

  18. Problem on Numbers If the numerator of a fraction is increased by 25% and denominator decrease by 20%, the new value is 5/4. what is the original value? (TCS)

  19. Problem on Numbers Solution: ( x + 25x/100) / (y – 20y/100) = 5/4 125x / 80y = 5/4 x/y = 5/4 * 80/ 125 = 4/5

  20. Problem on Numbers The difference between two numbers is 1/7 of the sum of these two numbers. What is the ratio of the two numbers? (Wipro)

  21. Problem on Numbers (x- y ) = 1/7 (x+y) 7( x- y) =( x + y) 7x – 7y = x + y 6x = 8y x/y = 3 / 4

  22. Problem on Numbers A fraction has a denominator greater than its numerator by 4. but if you add 10 to the denominator, the value of the fraction would then become 1/8, what is the fraction? (Caritor)

  23. Problem on Numbers Solution: x/(x+4+10) = 1/8 x/(x+14) = 1/8 8x =( x + 14) 7x = 14; hence x = 2 x/(x+4 )= 2/(2+4 )= 2/6

  24. Problems on Ages The ages of two persons differ by 10 years. If 5 years ago, the elder one be 2 times as old as the younger one, find their present ages.

  25. Problems on Ages Solution: x - y = 10; x = 10 + y x - 5 = 2(y-5) y + 10 -5 = 2y -10 y+5 = 2y -10 2y- y = 15 y=15 and x = 25 Their present ages are 15 years and 25 years.

  26. Problems on Ages The present ages of three persons are in the proportion of 4:7:9. Eight years ago, the sum of their ages was 56. Find their present ages ?

  27. Problems on Ages Solution: Three person’s ratio = 4:7:9 Total = 4+7+9 = 20 Sum of their age = 56, after 8 years their sum = 56 +24 = 80 A’s age = 4/20 *80 = 16 B’s age = 7/20 *80 = 28 C’s age = 9/20 *80 = 36 Their present ages are 16, 28 and 36.

  28. Problems on Ages Father’s age is 5 times his son's age.4 years back the father was 9 times older than his son. Find the father's present age? (TCS)

  29. Problems on Ages Solution: F = 5S F – 4 = 9(S-4) F – 5s = 0 F – 9S = -36 + 4 = -32 4S = 32 S = 8 Father age = 40 years

  30. Problems on Ages One year ago Pandit was three times his sister’s age. Next year he will be only twice her age. How old will Pandit be after five years? (TCS)

  31. Problems on Ages Solution: (P-1) = 3(S -1) P + 1 = 2( s+1) P – 3S = -3 + 2 = -2 P – 2S = 2-1 = 1 S = 3 P – 3(3) = -2 P – 9 = -2 P = -2 + 9 = 7 After 5 years = 12

  32. Problems on Ages A father is 30 years older than his son, however he will be only thrice as old as his son after 5 years what is father’s present age?

  33. Problems on Ages Solution: F = S + 30 F + 5 = 3(S+5) S+30 + 5 = 3S + 15 2S = 20 S= 10 F = 10 + 30 = 40

  34. Problems on Ages A father is three times as old as his son after 15 years the father will be twice as old as his son’s age at that time. What is the father’s present age ? (TCS)

  35. Problems on Ages Solution: F = 3S F + 15 = 2(S +15) Father’s age = 45, Son’s age = 15

  36. Ratio and Proportion • Ratio: The Relationship between two variables is ratio. • Proportion: The relationship between two ratios is proportion.

  37. Ratio and Proportion The two ratios are a : b and the sum nos. is x ax bx -------- and ------- a + b a + b Similarly for 3 numbers a : b : c

  38. Ratio and Proportion If Rs. 1260 is divided among A, B, C in the ratio 2 : 3 : 4 what is C’s share?

  39. Ratio and Proportion Solution: C’s Share = 4/9*1260 C’s share = Rs. 560

  40. Ratio and Proportion To 15 liters of water containing 20% alcohol, we add 5 liters of pure water. What is the % of alcohol?

  41. Ratio and Proportion Solution: 15 lit 20 % 20 lit (15+5) x by solving we get = 15% 15% alcohol

  42. Ratio and Proportion What number should be added or subtracted from each term of the ratio 17 : 24 so that it becomes equal to 1 : 2

  43. Ratio and Proportion Solution: Let the number be x. 17 + x/24 + x = 1/2 Solving the above equation, The number to be subtracted is 10.

  44. Ratio and Proportion The ratio of white balls and black balls is 1:2. If 9 gray balls are added it becomes 2:4:3. Then what is the number of black balls ?

  45. Ratio and Proportion Solution: Ratio of all the three balls = 2:4:3 Ratio of two balls before adding gray = 1:2 9 gray ratio =3 3 parts = 9 balls 1 part = 9/3 4 parts =? = 9*4/3 =12 Number of black balls is 12

  46. Ratio and Proportion Rs. 770 was divided among A, B and C such that A receives 2/ 9th of what B and C together receive. Find A’s share?

  47. Ratio and Proportion Solution: A = 2/9 (B+C) B+C =9A/2 A+B+C = 770 A + 9A/2 = 770 11A = 770*2 A = 140

  48. Alligation or Mixture • (Quantity of cheaper / Quantity of costlier) (C.P. of costlier) – (Mean price) = -------------------------------------- (Mean price) – (C.P. of cheaper)

  49. Alligation or Mixture Cost of Cheaper Cost of costlier c d Cost of Mixture m d-m m-c (Cheaper quantity) : (Costlier quantity) = (d – m) : (m – c)

  50. Alligation or Mixture A merchant has 100 kg of salt, part of which he sells at 7% profit and the rest at 17% profit. He gains 10% on the whole. Find the quantity sold at 17% profit?

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