60. A gentleman bought a horse, a chaise, and harness, for £60; the horse cost twice as much as the chaise, and the harness half as much as the horse.

What was the cost of each?
Horse, £30.

Ans. Chaise, £15.

61. Divide $1000 among 3 men, in such often as the first has $3, the second shall third $8.

Harness, £15.

a manner that as have $5, and the 1st, $187.50.

Ans. 2d, $312.50. 3d, $500.00.

62. A. can do a piece of work in 10 days; D. can do the same in 13 days. In what time will

do the same work?

both working together Ans. 51 days.

63. If 6 lbs. of pepper be worth 13 lbs. of ginger, and 19 lbs. of ginger be worth 43 lbs. of cloves, and 10 lbs. of cloves be worth 63 lbs. of sugar, at 10 cents per pound, what is the value of 1 cwt. of pepper? Ans. $38.22.

64. A tradesman increased his estate annually one third, less $960, which he spent in his family. At the end of 3 years he found that his estate amounted to $30284. What had he at first? Ans. $13551.75.

65. A person wants a cylindrical vessel, 3 feet deep, which shall hold twice as much as another 28 inches deep, and 46 inches in diameter. What must be the diameter of the required vessel ? Ans. 57.373 inches.

66. How long must be the tether of a horse which will allow him to graze quite round an acre of ground?

Ans. 20.

Ans. 391 yards. 67. What number is that which, being increased by its,, and 5 more, the number will be doubled? 68. A man, after having spent and of his money, had £26 left. How much had he at first? Ans. £160.

69. A vessel has 3 pipes; the first will fill it in of an hour, the second in of an hour, and the third in of an hour. In what time will all running together fill it?

Ans. of an hour.

70. A. and B. employed equal sums in trade. A. gained a sum equal to of his stock; B. lost $225; then A.'s money was double that of B's. What was each man's stock?

Ans. $600.

71. There is a certain number, of which exceeds by 6. What is that number? Ans. 80.

72. If $60 be divided between 4 men in such a proportion that the first shall have, the second, the third, and the fourth, what will each receive?

1st, $21. Ans. 2d, 1515. 3d, 1212 19. 4th, 101.

73. A., B., C., and D. spent 35 shillings at a reckoning, and being a little dipped, agreed that A. should pay, B., C., and D. 1. What does each pay, in this proportion?

Ans.

A. 13s. 4d.
B. 108.

C. 6s. 8d.

D. 58.

74. The wheels of a chaise, each 4 feet high, in turning within a ring, moved so that the outer wheel made two turns while the inner made one, and their distance from one another was 5 feet. What were the circumferences of the tracks described by them? Outer, 62.8318 feet. Inner, 31.4159 feet.

Ans.

75. A., B., and C. traded in company, and gained £350, of which A. took a certain sum; B. took 4 times as much as A., and C. 8 times as much as B. shares of the gain?

Ans.

What were their respective

A.'s gain, £9 98. 2d. 137gr.
B.'s gain, £37 16s. 9d. 012qr.
C.'s gain, £302 14s. Od. 222qrs.

C.'s

76. A gentleman divided his fortune among his sons, giving A. £9 as often as B. £5, and C. £3 as often as B. £7. dividend was £1537%. To what did the whole estate amount? Ans. £11583 8s. 10d. 77. If of of of a ship be worth of of 13 of the cargo, valued at £1000, what was the value of both ship and cargo? Ans. £1837 12s. 177157d. 78. Three men purchase a lot of land in company. A. paid , B. of the whole, and C. paid £256. How much did A. and B. pay, and what part of the land had C.?

(A. paid £597 6s. 8d.

Ans. B. paid £640.

C.'s share, 6

35.

79. A gay fellow soon got the better of of his fortune. He then gave £1500 for a commission, and his profusion con

tinued until he had but £450 left, which he found to be just of his money, after purchasing his commission. What was his fortune at first? Ans. £3780.

80. A. and B. are on opposite sides of a circular field, 268 rods in circumference. They start both at the same time to go round it, and go the same way. A. goes 22 rods in 2 minutes; B. goes 34 rods in 3 minutes. How many times will B. go round the field before he will overtake A.?

Ans. 17 times. 81. How high above the earth must a man be raised to see of its surface ?* Ans. One diameter high. outside of the hoop is 22 What is the true girt of Ans. 155. minute hand of a watch are exactly toWhen are they next together?

82. The girt of a vessel round the inches, and the hoop is 1 inch thick. the vessel?

83. The hour and gether at 12 o'clock.

Ans. 1 h. 5 m. 27 s. 84. Three men trade in company till they gain £120. The sums put in were in such proportion, that as often as A. had £5 of the gain, B. had £7; and as often as B. had £4, C. had £6. What was each man's share of the gain?

A.'s, £26 13s. 4d. Ans. B.'s, £37 6s. 8d.

C.'s, £56.

85. A. and B. cleared by an adventure at sea 45 guineas, which was £35 per cent. upon money adventured. With this gain they agreed to purchase a genteel horse and carriage, which they were to use in proportion to their sums adventured, which was found to be 11 to A. as often as 8 to B. What money did each adventure?

Ans.

{

A. £104 4s. 210d.
B. £75 15s. 9d.

86. A military officer drew up his soldiers in rank and file, having the number in rank and file equal. On being reinforced with three times his first number of men, he placed them all in the same form, and then the number in rank and in file was just double what it was at first. He was again reinforced with three times his whole number of men; and, after placing the whole in the same form as at first, his number in rank and in file was 40 men each. How many men had he at first?

Ans. 100 men.

* This question is for the student in Geometry.

87. A general disposing his army into a square battalion, found he had 231 over and above, but increasing each side with one soldier, he wanted 44 to fill up the square. Of how many men did his army consist?

Ans. 19000.

7

88. There are 3 horses belonging to different men, employed to draw a load of salt from Boston to Lowell for $9.50. A.'s and B.'s horses are supposed to do of the work, A.'s and C.'s 12, B.'s and C.'s. They are to be paid proportionally. What is each man's share of the gain? A.'s, $3.2881. Ans. B.'s, 4.3848 13.

C.'s, 1.82613.

89. A., B., and C. are to share £100, in the proportion of ,,and, respectively; but C. dying, it is required to divide the whole sum properly between the other two.

Ans. {

SA.'s share, £57 28. 101d.
B.'s share, £42 17s. 15d.

90. There is an island 50 miles in circumference, and 3 men start together to travel the same way round it. A. travels 7 miles a day, B. 8, and C. 9. When will they all come together again, and how far will each travel?

91. A man died leaving $1000 to be divided between his two sons, one 14 and the other 18 years of age, in such a manner that the share of each being let, at 6 per cent. interest, should amount to the same sum when they should arrive at the age of 21. What did each receive?

Ans.

{

The eldest, $546.153+. The youngest, $453.846+. 92. A hare starts 12 rods before a greyhound, but is not perceived by him till she has been up 45 seconds. She scuds away at the rate of 10 miles an hour, and the dog, on view, makes after, at the rate of 16 miles an hour. How long will the course hold, and what space will be run over from the spot where the dog started? 97 seconds. 2288 feet.

Ans.

93. There is a circular field, surrounded by a rail-fence 10 rails high, each one rod in length, and the number in the fence equals the number of acres in the field? What is the area of

the field?

Ans. 201062.4 acres. 94. How much greater is the circle described by the head of a man 6 feet high, than by his feet, in the revolution of the earth on its axis?

95. In an orchard, the trees bear apples, pears, plums,

and 50 of them produce nothing. How many trees are there in all ?

Ans. 600.

96. Sound moves at the rate of 1142 feet in a second. If the time between the lightning and the thunder be 30 seconds, what is the distance of the explosion? Ans. 6.488+ miles.

97. In a thunder-storm I observed by my watch that it was 6 seconds between the lightning and the thunder. At what distance was the explosion? Ans. 6852 feet.

98. Tubes may be made of gold, weighing not more than at the rate of 1625 of a grain per foot. What would be the weight of such a tube, which would extend across the Atlantic, from Boston to London, the distance being 3000 miles?

Ans. 1 lb. 8 oz. 6 pwt. 33 grs.

99. Suppose one of those meteors called fireballs, to move parallel to the earth's surface, and 50 miles above it, at the rate of 20 miles per second, in what time would it move round the earth?

The earth's diameter being 7964 miles, the diameter of the orbit will be 7964+50 × 2=8064, and 8064 x 3.1416 =25333.8624, its circumference. Then 25333.8624-20= 1266.693120=21′ 6′′′ 41′′ 35'''' 13''''' 55'''''', the Ans.

100. In giving directions for making a chaise, the length of the shafts between the axletree and back-band being settled at 9 feet, a dispute arose whereabout on the shafts the centre of the body should be fixed. The chaise-maker advised to place it 30 inches before the axletree; others supposed that 20 inches would be a sufficient incumbrance for the horse. Now, supposing 2 passengers to weigh 3 cwt., and the body of the chaise cwt. more, what will the horse, in both these cases, bear in addition to his harness?

Ans. 116. {1163.

101. A piece of square timber is 10 feet long, each side of the greater base 9 inches, and each side of the less 6 inches. How much must be cut off from the less end to contain a solid foot? Ans. 3.392 feet. 102. A carpenter put a curb of oak round a well the inner diameter of the curb was 3 feet, and its breadth 71 inches. What was the expense of it, at 8d. per square foot?

Ans. 5s. 21d.