49. A rectangular area of lawn of  dimesnions x and y is surrounded by a pathway of width 2 meters. What is the toal area of the pathway?

50. The length, breadth, and height of a room are l, b, and h units respectively. What is the perimter of the ceiling expressed as a percentage of the total area of the four walls?

51. When three coins are tossed together, what is the probability of getting all coins of the same face up?

29:
I think the mule has 2 and the donkey has 3.

Ninja 101, your answer to #48 is correct!

#39
x is 342.
Can someone please help me out here btw. I have a hard time expressing what really going on in a particular sequence. I know what's happening, it's just putting it into words in a correct manner.

#40
First off, let's get the area of 1 side:

Now, let's get the length of the sides:

Therefore, the answer is:

#49
Let's start with the area of the path just next to the sides with lengths of

and

:

This leaves the area of the corners. If I understand the puzzle correctly, the width of the path is measured from the edge of the lawn, to the outer edge of the path. Therefore, these 'edges' must be evenly curved, forming a

of a circle with a radius of 2. And since there are 4 of these corners, the total area of the corners is:

Adding these two areas, gives us the total area of the path.
Let A be the area of the path:

#51
The number of different outcomes of a throw is:

which can also be written as (t: tales, h: heads)
t - t - t
t - t - h
t - h - h
t - h - t

h - h - h
h - h - t
h - t - t
h - t - h
(obviously I wouldn't do this normally, just showing it to the ones who might not be familiar with this)

This gives us 2 out of 8 posibilities where all the coins have the same face up, and they are ofc t - t - t, and h - h - h.
So the answer is

depending on how you want the answer :)


edit: There's actually a reason for why I'm not just writing the answer. I'm showing what I'm actually doing, which might help me explain things to other people(practice makes perfect), and at the same time, people can understand how to solve the problem, if they couldn't do it themselves.(My teacher would hate me for that sentence :P grammer is prolly messed up, and it's a bit long^^)

Last edited by Patrick (2006-04-04 04:14:20)

52. Out of three examinations with a total of 500 marks each, a student scored 45% and 55% in the first and second examinations. To have an average of 60% in all the three, how many marks should the student score in the third examination?

53. Two trains were procedding in the same direction on parallel tracks at 29 km/hour and 65 km/hour respectively. The driver of the first train noticed that it took exactly 16 seconds for the faster train to pass by him. What is the length of the faster train?

54. Fill in the blank.

4/9, 9/20, ___, 39/86

55. What is the value of X in the series:
5, 8, 13, X, 34, 55, 89.

Well done, Patrick!

***49. Area of pathway = (x+4)*(y+4) - xy = 4x + 4y + 16

56. The monthly income of Arthur and Richard are in the ratio 4:3 and their monthly expenses are in the ratio 3:2. If both of them save $600 a month, whats the total of their income?

57. What is the maximum number of pieces 5cm x 5 cm x 10cm that can be cut from a bigger piece 5cm x 30 cm x 30cm size?

58. If x=-2, what is the value of x³-x²-x-1?

59. A person start from a point A and travels 3 km eastwards to B and then turns left and travels thrice that distance to reach C. He again turns left and travels five times the distance he covered between A and B and reaches his destination D. What is the distance he travelled from his starting point A to his destination D?

60. A club has 108 members. Two-thirds of them are men and the rest are women. All members are married except for 9 women members. How many married women are there in the club?

61. A bag contains 20 balls, 8 of them green, 7 white and 5 red. What is the minimum number of balls that must be picked up from the bag blindfolded without replacing any of it to be assured of picking atleast one ball of each color?

62. In an examination, every candidate took Physics or Mathematics or both. 65.8% took Physics and 59.2% too Mathematics. If the total number of candidates was 2000, how many candidates took both Physics and Mathematics?

65. From the given equations, find the possible value of x+y.

66. A city has a population of 300,000 out of which 180,000 are males. 50% of the population is literate. If 70%of the males are literate, what is the number of literate females?

67. In a survey, it was found that 80% of those surveyed owned a car while 60% of those surveyed owned a mobile phone. If 55% owned botha car and a mobile phone, what percent of those surveyed owned a car or a mobile phone or both?

68. Water is filled in a container in such a manner that its volume doubles every five minutes. If it takes 30 minutes for the container to be full, in how much time would it be one-fourth full?

69. In 1930, a person's age was 8 times that of his son. In 1938, the father's age became 10 times that of his son's age at 1930. What would be the age of the father and the son in 1940?

80. A car travels the first one-third of a certain distance at a speed of 10 km/hour, the next one-third at 20 km/hour and the third one-third at 60 km/hour. What is the average speed of the car for the whole journey?

81. A walks around a circular field making one round per hour while B runs around it making six rounds in an hour. If both of them start from the same point in the same direction at 7.30 AM, when will B cross A the first time?

82. Four different candles which can last for 5 hours, 4 hours, 3 hours, and 2 hours of burning are lit in a room at the same instant and are allowed to burn till three candles in the room get extinguished. If the cost of burning each candle is 75 cents per hour, what is the total cost involved?

83. A two member committee comprising of one male and one female member is to be formed out of five males and three females. Amongst the females, Ms.A refuses to be a member of the committee in which Mr.B is taken as a member. In how many different ways can the committee be constituted?

84. Three flags, each of different color, are available for a military exercise. Using these flags different codes can be generated by waving
(i) a single flag of different colors, or
(ii) any two flags in a different sequence of colors, or
(iii) three flags in a different sequence of colors.
What is the maximum number of codes that can be generated?

85. Three bells toll at intervals of 9, 12, and 15 minutes respectively. All the three toll together at 8 AM. At what time would they first toll together again?

86. The total time taken by a person in going to a place by walking and returning on bicycle is 5 hours and 45 minutes. He would have gained 2 hours by riding the bicycle both ways. What would be the time taken by him to walk both ways?

96. Two cars X and Y start from two places A and B respectively which are 700 kilometers apart, at 9.00 AM. Both the cars run at a speed of 60 kilometers/hour. Car X stops at 10.00 AM and starts again at 11.00 AM. At what time do the cars cross each other?

97. A and B start from the same point and in the same direction at 7.00 AM to walk around a rectangular field 400 metres by 300 metres. A and B walk at the rate of 3 km/hour and 2.5 km/hour respectively. How many times would they cross each other if they continue to walk until 12.30 PM?

98. Nine different letters are to be dropped in three different letter boxes. In how many different ways can this be done?

99. How many three-digit even numbers are there such that 9 comes as a succeeding digit in any number only when 7 is the preceeding digit and 7 is the preceeding digit only when 9 is the succeeding digit?

100. In how many different ways can six players be arranged in a line in such a way that two of them, David and Ian, are never together?

111. A train started from a station with a certain number of passengers. At the first halt, half of the passengers alighted and 120 new passengers got into the train. At the second halt, half of the passengers alighted and then the train left for its destination with 360 passengers. How many passengers were in the train when it started from the first station?

112. What is the LCM of

113. A number when divided by 765 leaves a remainder 42. What would be the remainder if the number is divided by 17?

114. If an angle of a triangle remains unchanged but each of its two including sides is doubled, by what factor would the area get multiplied?

115. If m and n are natural numbers such that

what is the value of m?