1. Blue Lotus A ptitude - TCS

2. Problems on Numbers A car is filled with 4 ¼ gallons of oil for full round trip. Fuel is taken 1/4 gallon more while going down than coming up. What is the fuel consumed in coming up?

3. Problems on Numbers Let ‘X’ be the quantity of fuel consumed for the trip in one direction The fuel consumed while going = X + ¼ The fuel consumed while coming = X Therefore, the fuel consumed for the trip = (X + ¼) + X = 4 ½ 2X + ¼ = 4 ½ => 2X = 4 ½ - ¼ => 2X = 4 ¼ => X= 2 gallons approx

4. Problems on Numbers A box of 150 packets consists of 1kg packets and 2kg packets. Total weight of box is 264kg. How many 2kg packets are there?

5. Problem on Numbers 114

6. 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)

7. 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.

8. 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)

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

10. Puzzle In 80 coins one coin is counterfiet. What is the minimum number of weighings to find out counterfiet coin? (TCS)

11. Puzzle SIX

12. Puzzle In a well of 20feet depth, a frog jumps 5feet up in the morning and comes 4feet down in the evening,on which day the frog gets out of the well.

13. Puzzle Sixteen

14. Number System The number 362 in decimal system is given by (1362)x in the X system of numbers. find the value of X.

15. Number System In which of the system, decimal number 184 is equal to 1234?

16. Number System 5

17. Find the value of the 678 to the base 7.

18. Number System 1656

19. Number System The base 5 representation of the decimal number 2048 is _____.

20. Odd Man Out a)LINUX b) WINDOWS 98 c)SOLARIS d) SMTP a)JAVA b) LISP c) Smaltalk d) Eiffle

21. Odd Man Out 1.HTTP 2.ARP 3.SNMP 4.SAP 1.Linux 2.windows NT 3.sql server 4.Unix

22. 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)

23. 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

24. 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)

25. 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

26. 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)

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

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

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

30. 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? Alligation or Mixture

31. Solution: 7 17 10 (17-10) (10-7) 7 : 3 The ratio is 7:3 The quantity of 2nd kind = 3/10 of 100kg = 30kg Alligation or Mixture

32. A 3-gallon mixture contains one part of S and two parts of R. In order to change it to mixture containing 25% S how much R should be added? (TCS) Alligation or Mixture

33. Answer: R:S 2:1 75%:25% 3:1 1 gallon of R should be added. Alligation or Mixture

34. In two varieties of tea, one costing Rs. 25/kg. and the other costing RS. 30/kg are blended to produce blended variety of tea in ratio 2:3. find the cost price of the mixture ? Alligation or Mixture

35. Solution: 25 30 x (30- 28) (28-25) 2 : 3 Let mixed price be x If you subtract 28 from 30 you will get 2 and if you subtract 25 from 28 you will get 3. Alligation or Mixture

36. Chain Rule Direct Proportion : A B Indirect Proportion: A B

37. Chain Rule A can copy 50 papers in 10 hours while both A & B can copy 70 papers in 10 hours. Then how many hours are required for B to copy 26 papers? (TCS)

38. Chain Rule A stationary engine has enough fuel to run 12 hours when its tank is 4/5 full. How long will it run when the tank is 1/3 full? TCS Question

39. Chain Rule Answer: Tank hours 4/5 12 1/3 x 4/5 x = 12 * 1/3 It will run for 5 hours

40. Types: A invested Rs.x and B invested Rs.y then A:B = x : y A invested Rs. x and after 3 months B invested Rs. y then the share is A:B = x * 12 : y * 9 Partnership

41. A sum of money is divided among A, B, C such that for each rupee A gets, B gets 65 paise and c gets 35 paise if c’s share is Rs. 560. what is the sum? TCS Share

42. Solution A : B : C 100 : 65 : 35 20 : 13 : 7 Total = 20+13+7 = 40 C’ share = 560 7/40 *X =560 X= 3200 Partnership

43. Share If Rs. 1260 is divided among A, B, C in the ratio 2 : 3 : 4 what is C’s share? TCS

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

45. If A can do a piece of work in n days, then A’s 1 day’s work = 1/n If A is thrice as B, then: Ratio of work done by A and B = 3:1 Time and Work

46. Pipes and Cisterns P 1 fills in x hrs. Then part filled in 1 hr is 1/x P 2 empties in y hrs. Then part emptied in 1 hr is 1/y

47. P 1 and P 2 both working simultaneously which fills in x hrs and empties in y hrs resp ( y>x) then net part filled is 1/x – 1/y P 1 can fill a tank in X hours and P2 can empty the full tank in y hours( where x>y), then on opening both pipes, the net part empties in hour 1/y -1/x Pipes and Cisterns

48. One fast typist types same matter in 2 hours and another slow typist types the same matter in 3 hours. If both do combine in how much time will they finish? TCS Question Time and Work

49. Solution: Fast typist = 1/2 ; slow typist = 1/3 ; Together: = 1/2 + 1/3 = 5/6 so 6/5 hrs The work will be completed in 6/5 Hrs. Time and Work

50. A and B can finish a piece of work in 30 days, B and C in 40 days, while C and A in 60 days.In how many days A, B and C together can finish the work ? Time and Work

51. Solution: A + B = 30 days = 1/30 B + C = 40 days = 1/40 C +A = 60 days = 1/60 All work together A+B+C+B+C+A = 1/30 +1/40 +1/60 2(A+B+C) = 1/30+1/40+1/60 = (4+3+2) /120 = 9/120*2 = 9/240 = 3/80 = 26 2/3 A, B and C can finish the work in 26 2/3 days Time and Work

52. 10 men can complete a piece of work in 15 days and 15 women can complete the same work in 12 days. If all the 10 men and 15 women work together, In how many days will the work get completed ? Time and Work

53. Solution: 10 men = 15 days means 1day work = 1/15 15 men = 12 days means 1 day work = 1/12 10 men + 15 women = 1/15 + 1/12 = 4+5/60 = 9/60 = 3/20 20/3 days = 6 2/3 days The work will be completed in 6 2/3 days. Time and Work

54. A work done by two people in 24 minutes. One of them can do this work alone in 40 minutes. How much time is required to do the same work by the second person? TCS Question

55. Time and Work Solution : A and B together = 1/24; A = 1/40; B = ? = 1/24 – 1/40 = 2/120 = 1/60 The second person will complete in 60 minutes.

56. A cistern has two taps which fill it in 12 minutes and 15 minutes respectively. There is also a waste pipe in the cistern. When all the pipes are opened, the empty cistern is filled in 20 minutes. How long will a waste pipe take to empty a full cistern ? Time and Work (Pipes)

57. Solution: This problem is based on 2nd method. All the tap work together = 1/12 + 1/15 - 1/20 = 5/60 + 4/60 – 3/60 = 6/60 = 1/10 The waste pipe can empty the cistern in 10 minutes. Time and Work (Pipes)

58. A tap can fill a cistern in 8 hours and another can empty it in 16 hours. If both the taps are opened simultaneously, Find the time ( in hours) to fill the cistern Time and Work (Pipes)

59. Solution: Tap 1 = 1/8 (fill); Tap 2 = 1/16 (empty) = 1/8 – 1/16 = 1 / 16 Total time taken to fill the cistern = 16 hours Time and Work (Pipes)

60. A water tank is 2/5 th full. Pipe A can fill the tank in 10 minutes and the pipe B can empty it in 6 minutes. If both the pipes are open, how long will it take to empty or fill the tank completely?

61. Time and Work (Pipes) Answer : A = 1/10; B = 1/6 = 1/10 -1/6 = - 1/15 Empty in 15 minutes To empty 2/5 of the tank 2/5 * 15 = 6 Time taken (empty)= 6 minutes

62. Area and Volume Cube: Let each edge of the cube be of length a. then, Volume = a 3 cubic units Surface area= 6a 2 sq.units. Diagonal = √3 a units.

63. Cylinder: Let each of base = r and height ( or length) = h. Volume = πr 2 h Surface area = 2 πr h sq. units Total Surface Area = 2 πr ( h+ r) units. Area and Volume

64. Cone: Let radius of base = r and height=h, then Slant height, l = √h 2 +r 2 units Volume = 1/3 πr 2 h cubic units Curved surface area = πrl sq.units Total surface area = πr (l +r) Area and Volume

65. Sphere: Let the radius of the sphere be r. then, Volume = 4/3 πr 3 Surface area = 4 π r 2 sq.units Area and Volume

66. Circle: A= π r 2 Circumference = 2 π r Square: A= a 2 Perimeter = 4a Rectangle: A= l x b Perimeter= 2( l + b) Area and Volume

67. Triangle: A = ½*base*height Equilateral = √3/4*(side) 2 Area of the Scalene Triangle S = (a+b+c)/ 2 A = √ s*(s-a) * (s-b)* (s-c) Area and Volume

68. One rectangular plate with length 8inches,breadth 11 inches and 2 inches thickness is there. What is the length of the circular rod with diameter 8 inches and equal to volume of rectangular plate? Area and Volume

70. If the length of a rectangle is increased by 30% and the width is decreased by 20%, then the area is increased by what Percentage? Area and Volume

71. 4% Area and Volume

72. The length of a rectangle is increased by 60%. By what % would the width have to be decreased to maintain the same area? Area and Volume

73. 37.5% Area and Volume

74. Probability: P(E) = n(E) / n(S) Addition theorem on probability: n(AUB) = n(A) + n(B) - n(A  B) Mutually Exclusive: P(AUB) = P(A) + P(B) Independent Events: P(A  B) = P(A) * P(B) Probability

75. There are 19 red balls and One black ball. Ten balls are placed in one jar and remaining in one jar. What is probability of getting black ball in right jar ? (Infosys -2008) Probability

76. Answer: Probability is 1/2. Probability

77. There are 5 red shoes 4 green shoes. If one draws randomly a shoe what is the probability of getting a red shoe? CTS Question Probability

78. Answer: The probability is 5/9 Probability

79. A bag contains 2 red, 3 green and 2 blue balls are to be drawn randomly. Two balls are drawn at random. What is the probability that the balls drawn contain only blue balls ? Probability

80. Answer : The probability is 1/21 Probability

81. Sam and Jessica are invited to a dance party. If there are 7 men and 7 women in total at the dance and 1 woman and 1 man are chosen to lead the dance, what is the probability that Sam and Jessica will not chosen to lead the dance ?

82. Probability Answer: The Probability of Selecting = 1/7*7 = 1/49 The Probability of not Selecting = 1-1/49 = 48/49

83. Probability The letters of the word SOCIETY are placed in a row. What is the probability that the three vowels come together?

84. Probability Answer: Required Probability = (5!*3! )/7! = 1/7

85. Average Average is a simple way of representing an entire group in a single value. “Average” of a group is defined as: X = (Sum of items) / (No of items)

86. Average Gavaskar’s average in first 50 innings was 50. After the 51 st innings his average was 51. How many runs did he make in the 51 st innings?

87. Average Hansie made the following amounts in seven games of cricket in India: Rs.10, Rs.15, Rs.21, Rs.12, Rs.18, Rs.19 and Rs.17 (all figures in crores). Find his average earnings.

88. Average Average of 5 number is -10 and sum of 3 numbers is 16. What is the average of other two numbers?

89. Average Average of 5 number is -10 and sum of 3 numbers is 16. What is the average of other two numbers?

90. Permutations and Combinations Factorial Notation: n! = n(n-1)(n-2)….3.2.1 Number of Permutations: n!/(n-r)! Combinations: n!/r!(n –r)!

91. A foot race will be held on Saturday. How many different arrangements of medal winners are possible if medals will be for first, second and third place, if there are 10 runners in the race … Permutations and Combinations

92. Solution: n = 10 r = 3 n P r = n!/(n-r)! = 10! / (10-3)! = 10! / 7! = 8*9*10 = 720 Number of ways is 720. Permutations and Combinations

93. To fill a number of vacancies, an Employer must hire 3 programmers from 6 applicants, and two managers from 4 applicants. What is total number of ways in which she can make her selection ? Permutations and Combinations

94. Solution: It is selection so use combination formula Programmers and managers = 6C 3 * 4C 2 = 20 * 6 = 120 Total number of ways = 120 ways. Permutations and Combinations

95. In how many ways can the letters of the word BALLOON be arranged so that two Ls do not come together? Permutations and Combinations

96. Solution: Total arrangement = 7! / 2!*2! (L and O occurred twice) =1260 Ls come together (BAOON) (LL) = 6! / 2! = 3* 4* 5*6* = 360 Ls not come together 1260 – 360 = 900 Number of ways = 900. Permutations and Combinations

97. A man has 7 friends. In how many ways can he invite one or more of them to a party?

98. Permutations and Combinations Solution: In this problem, the person is going to select his friends for party, he can select one or more person, so = 7C1 + 7C2+7C3 +7C4 +7C5 +7C6 +7C7 = 127 Number of ways is 127

99. Percentage By a certain Percent, we mean that many hundredths. Thus, x Percent means x hundredths, written as x%

100. Percentage After having spent 35% of the money on machinery, 40% on raw material, 10% on staff, a person is left with Rs.60,000. What is the total amount of money spent on machinery and the raw materials?

101. Percentage Solution: Let total salary =100% Spending: Machinery + Raw material + staff = 35%+40%+10% = 85% Remaining percentage = 100 %– 85% = 15% 15 % of X = 60000 X = 4, 00,000 In this 4, 00,000 75% for machinery and raw material = 4, 00,000* 75/100 = 3, 00,000

102. Percentage If the number is 20% more than the other, how much percent is the second number less than the first?

103. Percentage Solution: Let X =20 = X / (100+X) *100% = 20 /120 *100% =16 2/3% The percentage is 16 2/3%

104. Percentage Find the percentage increase in the area of a Rectangle whose length is increased by 20% and breadth is increased by 10%

105. Percentage Answer: Percentage of Area Change=( X +Y+ XY/100)% =20+10+20*10/100 =32%

106. Percentage If A’s income is 40% less than B’s income, then how much percent is B’s income more than A’s income?

107. Percentage Answer: Percentage = R*100%/(100-R) = (40*100)/ (100-40) =66 2/3%

108. Percentage One side of a square is increased by 30%. To maintain the same area by how much percentage the other side will have to be decreased?

109. Percentage Answer: Percentage = r*100%/(100+r) = (30*100) / 130 = 23 1/3%

110. Boats and streams Up stream – against the stream Down stream – along the stream u = speed of the boat in still water v = speed of stream Down stream speed (a)= u+v km / hr Up stream speed (b)=u-v km / hr u = ½(a+b) km/hr V = ½(a-b) km / hr

111. A man can row Upstream at 12 kmph and Downstream at 16 kmph. Find the man’s rate in still water and rate of the current? Boats and streams

112. Solution: Rate in still water = 1/2 (16 + 12) = 14 Kmph Rate of Current = 1/2 (16 – 12 ) = 2 Kmph Boats and streams

113. A Boat is rowed down a river 40 km in 5 hr and up a river 21 km in 7 hr. Find the speed of the boat and the river? Boats and streams

114. Solution: Speed of the Boat Downstream = 40/7 = 8 (a) Speed of the Boat Upstream = 21/7 = 3 (b) Speed of the Boat = 1/2 ( a + b ) = 1/2 ( 8+3 ) = 5.5 Kmph Speed of the River = 1/2 ( a – b ) = 1/2 (8 – 3) = 2.5 kmph Boats and streams

115. A boat’s crew rowed down a stream from A to B and up again in 7 ½ hours. If the stream flows at 3km/hr and speed of boat in still water is 5 km/hr. find the distance from A to B ? Boats and streams

116. Solution: Down Stream = Sp. of the boat + Sp. of the stream = 5 +3 =8 Up Stream = Sp. of the boat – Sp. of the stream = 5-3 = 2 Let distance be X Distance/Speed = Time X/8 + X/2 = 7 ½ X/8 +4X/8 = 15/2 5X / 8 = 15/2 5X = 15/2 * 8 5X = 60 X =12 Boats and streams

117. Boats and Streams A boat goes 40 km upstream in 8 hours and 36 km downstream in 6 hours. Find the speed of the boat in still water in km/hr?

118. Boats and Streams Solution: Speed of the boat in upstream = 40/8 = 5 km/hr Speed of the boat in downstream= 36/6 =6 km/hr Speed of the boat in still water = (5+6 ) / 2 = 5.5 km/hr

119. Boats and Streams A man rows to place 48 km distant and back in 14 hours. He finds that he can row 4 kmph with the stream in the same time as 3 Kmph against the stream. Find the rate of the stream?

120. Boats and Streams Solution: Down stream 4 km in x hours. Then, Speed Downstream = 4/x km/hr, Speed Upstream = 3/x km/hr 48/ (4/x) + 48/(3/x) = 14 x = 1/2 Speed of Downstream = 8, Speed of upstream = 6 Rate of the stream =1/2 (8-6) km/hr = 1 km/hr

121. Time and Distance Speed:- Distance covered per unit time is called speed. Speed = distance/time (or) Distance = speed*time (or) Time = distance/speed

122. Distance covered α Time (direct variation). Distance covered α speed (direct variation). Time α 1/speed (inverse variation). Time and Distance

123. Speed from km/hr to m/sec - (Multi by 5/18). Speed from m/sec to km/h, - (Multi by 18/5). Average Speed:- Average speed = Total distance traveled Total time taken Time and Distance

124. From height of 8 m a ball fell down and each time it bounces half the distance back. What will be the distance traveled? Sathyam Question Time and Distance

125. Solution: = 8 + 4 + 4+2+2+1+1+0.5+0.5 +….etc. The total distance traveled is 24 m Time and Distance

126. Two cars are 15 km apart. One is running at a speed of 50 kmph and the other at 40 kmph. How much time will it take for the two cars to meet? Sathyam Question Time and Distance

127. Solution: Time taken =Distance / (S1 – S2) = 15 / (50 – 40) = 15 / 10 = 1.5 It will take 1½ hours. Time and Distance

128. The center of a storm shifts 22.5 miles in 1 hour. At the same rate what time will it take to move 60 miles? TCS Question Time and Distance

129. Answer: For 22.5 miles it takes 1 hour It means for 60 miles T = D / S Time taken = 60 / 22.5 It will take 2 2/3 hours. Time and Distance

130. By walking at ¾ of his usual speed, a man reaches office 20 minutes later than usual. Find his usual time?

131. Time and Distance Solution: Usual time = Numerator * late time = 3*20 = 60

132. Time and Distance A man on motorcycle rides 110 miles in 330 minutes. What is his average speed in miles per hour? TCS Question

133. Time and Distance Answer: Speed = D / T =110*60 /330 The average speed = 20 miles/hour

134. Time and Distance (Trains) A train starts from Delhi to Madurai and at the same time another train starts from Madurai to Delhi after passing each other they complete their journeys in 9 and 16 hours, respectively. At what speed does second train travels if first train travels at 160 km/hr ?

135. Time and Distance (Trains) Solution: Let x be the speed of the second train S1 / S2 = √T2/T1 160/x = √16/9 160/x = 4/3 x = 120 The speed of second train is 120km/hr.

136. Time and Distance (Trains) Two hours after a freight train leaves Delhi a passenger train leaves the same station traveling in the same direction at an average speed of 16 km/hr. After traveling 4 hours the passenger train overtakes the freight train. What was the average speed of the freight train?Wipro Question

137. Time and Distance (Trains) Solution : Speed of Passenger train = 16 kmph Distance = 16*4 = 64 Speed of freight train = Distance / ( S1 + S2 ) = 64 / (4+2) = 64/6 = 10.6 km/hr The average speed = 10.6 km/hr

138. Time and Distance (Trains) There are 20 poles with a constant distance between each pole. A train takes 24 sec to reach the 12 pole. How much time will it take to reach the last pole ?

139. Time and Distance (Trains) Solution: To cross 11 poles it is taking 24 sec To cross 19 poles it will take x time Poles time 11 24 19 x 11x = 19 * 24 x = 19* 24 /11 x = 41.45 sec It reaches the last pole in 41.45sec

140. Time and Distance (Trains) 120 m long train crosses the pole after 2½ sec. Find how much time it takes to cross 140 m long platform? Caritor Question

141. Time and Distance (Trains) Solution: To cross 120 m it is taking 2 ½ sec. (5/2sec) To cross (120 +140)=260 m it will take x sec 120x = 260*5/2 (apply chain rule) = 5 5/12 It takes 5 5/12 seconds.

142. Time and Distance (Trains) A train X speeding with 120 kmph crossed another train Y, running in the same direction, in 2 minutes. If the lengths of the trains X and Y be 100 m and 200m respectively, what is the speed of train Y?

143. Time and Distance (Trains) Solution: Let the speed of train Y be x km/hr Relative Speed of X to Y = (120 –x) km/hr = [(120 –x)*5/18] m/sec =( 600 – 5x) / 18 m/sec T = D / Rel. Speed 300 / (600 – 5x /18) = 120 ( 2 Minutes ) 5400 = 120 (600 -5x) x = 111 m/sec.

144. Calendar Odd days: 0 = Sunday 1 = Monday 2 = Tuesday 3 = Wednesday 4 = Thursday 5 = Friday 6 = Saturday

145. Calendar Month code: Ordinary year J = 0 F = 3 M = 3 A = 6 M = 1 J = 4 J = 6 A = 2 S = 5 O = 0 N = 3 D = 5 Month code for leap year after Feb. add 1.

146. Calendar Ordinary year = (A + B + C + D )-2 -----------------------take remainder 7 Leap year = (A + B + C + D) – 3 ------------------------- take remainder 7

147. What is the day of the week on 30/09/2007? Calendar

148. Solution: A = 2007 / 7 = 5 B = 2007 / 4 = 501 / 7 = 4 C = 30 / 7 = 2 D = 5 ( A + B + C + D )-2 = ----------------------- 7 = ( 5 + 4 + 2 + 5) -2 ----------------------- = 14/7 = 0 = Sunday 7 Calendar

149. What was the day of the week on 13 th May, 1984? Calendar

150. Clock: In every Hour, the minute hand gains 55 minutes on the hour hand In every hour both the hands coincide once.  = (11m/2) – 30h (hour hand to min hand)  = 30h – (11m/2) (min hand to hour hand) If you get answer in minus, you have to subtract your answer with 360 o Clocks

151. Find the angle between the minute hand and hour hand of a clock when the time is 7:20.

152. Solution:  = 30h – (11m/2) = 30 (7) – 11 20/2 = 210 – 110 = 100 Angle between 7: 20 is 100 o Clocks

153. At what time between 7 and 8 o’clock will the hands of a clock be in the same straight line but, not together?

154. Clocks Solution:h = 7  = 30h – 11m/2 180 = 30 * 7 – 11 m/2 On simplifying we get, 5 5/11 min past 7

155. In interpretation of data, a chart or a graph is given. Some questions are given below this chart or graph with some probable answers. The candidate has to choose the correct answer from the given probable answers. Data Interpretation

156. 1. The following table gives the distribution of students according to professional courses: __________________________________________________________________ Courses Faculty ___________________________________ Commerce Science Total Boys girls Boys girls ___________________________________________________________ Part time management 30 10 50 10 100 C. A. only 150 8 16 6 180 Costing only 90 10 37 3 140 C. A. and Costing 70 2 7 1 80 __________________________________________________________________ On the basis of the above table, answer the following questions:

157. The percentage of all science students over Commerce students in all courses is approximately: (a) 20.5 (b) 49.4 (c) 61.3 (d) 35.1 Data Interpretation

158. Answer: Percentage of science students over commerce students in all courses = 35.1% Data Interpretation

159. What is the average number of girls in all courses ? (a) 15 (b) 12.5 (c) 16 (d) 11 Data Interpretation

160. Answer: Average number of girls in all courses = 50 / 4 = 12.5 Data Interpretation

161. What is the percentage of boys in all courses over the total students? (a) 90 (b) 80 (c) 70 (d) 76 Data Interpretation

162. Answer: Percentage of boys over all students = (450 x 100) / 500 = 90% Data Interpretation

163. Venn Diagram If X and Y are two sets such that X u Y has 18 elements, X has 8 elements, and Y has 15 elements, how many element does X n Y have?

164. Venn Diagram Solution: We are given n (X uY) = 18, n (X) = 8, n (Y) =15. using the formula. n( X n Y) = n (X) + n (Y) - n ( X u Y) n( X n Y) = 8 + 15 – 18 n( X n Y) = 5

165. Venn Diagram If S and T are two sets such that S has 21elemnets, T has 32 elements, and S n T has 11 elements, how many element elements does S u T have?

166. Venn Diagram Answer: n (s) = 21, n (T) = 32, n ( S n T) = 11, n (S u T) = ? n (S u T) = n (S) + n( T) – n (S n T) = 21 + 32 – 11 = 42

167. Venn Diagram If A and B are two sets such that A has 40 elements, A u B has 60 elements and A n B has 10 elements, how many element elements does B have?

168. Venn Diagram Answer: n ( A) = 40, n ( n B) = 60 and n ( A n B) = 10, n ( A u B) = n ( A) + n (B) – n ( A n B) 60 = 40 + n (B) – 10 n (B) = 30

169. Venn Diagram In a group of 1000 people, there are 750 people who can speak Hindi and 400 who can speak English. How many can Speak Hindi only?

170. Answer: n( H u E) = 1000, n (H) = 750, n (E) = 400, n( H u E) = n (H) + n (E) – n( H n E) 1000 = 750 +400 – n ( H n E) n ( H n E) = 1150 – 100 = 150 No. of people can speak Hindi only _ = n ( H n E) = n ( H) – n( H n E) = 750 – 150 = 600

171. Venn Diagram In a class of 100 students, the number of students passed in English only is 46, in maths only is 46, in commerce only is 58. the number who passes in English and Maths is 16, Maths and commerce is 24 and English and commerce is 26, and the number who passed in all the subject is 7. find the number of the students who failed in all the subjects.

172. Venn Diagram Solution: No. of students who passed in one or more subjects = 11+ 9 + 13 + 17 + 15 + 19 + 7 = 91 No of students who failed in all the subjects = 100 -91 = 9

173. Venn Diagram In a group of 15, 7 have studied Latin, 8 have studied Greek, and 3 have not studied either. How many of these studied both Latin and Greek?

174. Venn Diagram Answer: 3 of them studied both Latin and Greek.