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50. Fifty is how many per cent of 400 ?
51. A note for $5000 dated April 1st, 1872, with interest at 6%, is endorsed as follows: May 1st, 1873, received $1025, June 1st, 1874, $1020, July 1st, 1875, $1015. What was due August 1st, 1876? Ans. $2956.30.
52. What is the bank discount of a note for $600 payable in sixty days, interest at 6%, 3 days grace? and what are the proceeds ?
Ans. Discount $6.30, and Proceeds $593.70. 53. What is the bank discount of $600 for 3 months at 6%?
Ans. $9.30. 54. What is the amount of $600 for 3 years and 4 months at 6 per cent simple interest ? At compound interest?
Ans. $720, and $728.90. 55. A person owning of a mine, sells of his share for $5130; what was the whole mine worth at that rate ?
Ans. $10944. 56. What is the cost of 15 T. 12 cwt. 2 qr. 10 lb. coal, at $6 per ton ?
Ans. $93.78. 57. How is a common fraction changed into a decimal ?
58. How many terms form a ratio ?
59. How many ratios may be formed of any two num. bers either integral or fractional ?
60. What is the present value of the following note to be discounted in bank, interest at 6%?
Ninety days after date, I promise to pay to the order of John Smith, three hundred dollars, value received.
Ans. $295.35. 61. Extract the square root'of .00012544.
62. How many steps of three feet each would a man take in walking a mile ?
63. By what process would 25643.21 be changed to 256.4321 ? 64. Reduce .625 lb. to ounces.
Ans. 10 oz. 65. Reduce 12 lb. 8 oz. 4 drams to the decimal of cwt.
Ans. .125+. 66. Solve the following by proportion, and explain the solution : If 27 acres of land cost $1350, what will 36 acres cost at the same rate ?
Ans. $1800. 67. How many cords of wood can be put in a shed 256 ft. long 20 ft. wide and 8 ft. high? Ans. 320 cords.
68. How many shingles netting 6 in. by 4, will cover a house 50 ft. long and 40 ft. wide, with gable roof and the length of rafter 25 ft. Ans. 15000 shingles.
69. How many square ft. of lumber in one floor of the above house ? Ans. 2000 sq. ft. And how many square yards of plastering in a hall 15 feet high extending over the whole building ? Ans. 522f sq. yds. How many yards of carpeting one yard wide will cover the floor ?
Ans. 2223 yds. 70. The product of two equal factors is 34225; what is each factor? Solve by factoring. By what other method may it be solved ?
71. What is the greatest common divisor of 72 and 1728?
Ans. 72. 72. Find the least common multiple of 6, 9, 12, 18, and 36.
Ans. 36. 73. Reduce } lb. to the decimal of a ton.
Ans. .0000625 ton. 74. What is the amount of $200 for 3 years at 6% compound interest, payable semi-annually ? Ans. $238.81.
75. If 12 men build a wall 36 yds. long in 30 days, working 8 hours a day, how many men can build a wall 84 yds. long in 60 days, working 7 hours in a day?
Ans. 16 men. 76. What is the length of a side of a cubical box containing 48228544 cubic inches ?
Ans. 364 in. 77. Extract the square root of g.
Ans. .745 +. 78. In a series of equal ratios, the first term is 3, the ratio 2, and the last term 192 ; what is the sum of the series ?
Ans. 381. 79. A gentleman giving his daughter in marriage on New Year's day, gave her husband $100 toward her portion, promising to double it on the first day of every succeeding month during the year; what was her portion ?
Ans. $409500. 80. If a man travel 540 miles in 30 days of 9 hours each, how far will he travel in 48 days of 12 hours each ?
Ans. 1152 miles. 81. How many numbers form a proportion ? 82. What are the names of the terms ?
83. How many terms form a ratio ? and what are they called ?
84. The two means of a proportion are 3 and 6, and one of the extremes is 2; what is the other extreme?
Ans. 9. 85. The two extremes of a proportion are 5 and 9, and one of the means is 3; what is the other mean?
86. In a series of ratios forming proportions, what name is given to the odd terms, and what to the even ones ?
87. In the usual method of numeration, how many figures in each period ?
88. Name the first three periods of integers, and the first four places of decimals.
89. How does multiplying the numerator of a fraction affect the value of the fraction? How multiplying the denominator ?
90. How does a zero annexed to a decimal affect the value? If a zero is prefixed what is its effect ?
91. A father left to his four sons $38750, to be divided in such a manner that each one's share being placed at 5% simple interest shall amount to the same when he shall become 21 years
at his death being 13, 15, 17 and 19 years respectively; what principal must be placed at interest for each ? Ans. $8580 youngest; $9240, $10010, $10920 oldest.
The ratios will be
4620 146, 186, 198, 118
5460 14, 18, 19, 11
19375 4, 18, , H =
1 = 4786, 4876, 606, 408
Х = $8580, etc. Reduce to a common denominator, and the numerators express the ratios.
4 2 90 19525
92. The difference of time between Washington and Cincinnati is 29 min. 36 sec.; what is the difference of longitude ?
Ans. 7° 24'. 93. The difference of time between two places is 2 hours 20 min. 40 sec. ; what is the difference of longitude ?
Ans. 35° 10'. 94. The difference of time between Baltimore and New Orleans is 53 min. 30 sec.; what is their difference of longitude ?
Ans. 13° 22' 30". 95. A strip of land is 10 rods wide; how long a piece must be cut off from it to make just of an acre ?
Ans. 12 rds. 96. The diameter of a circle is 10 ft.; what must be the diameter of another circle to contain just ten times the area of the first?
Ans. 31.62 feet. 97. The diameter of a ball weighing 10 lb. is 2 inches; what must be the diameter of a ball of the same material to weigh ten times as much ? Ans. 4.3 inches.
98. A merchant bought a lot of cloth which he marked above cost. Owing to a sudden fall in prices he was obliged to sell it at one dollar a yard, which was one-third off the marked price; what did he lose per yard ?
Ans. 25 cts. 99. Marked goods at an advance of 20% on the cost price; if I take off 20% from the marked price, do I gain or lose, and what per cent ?
Ans. I lose 4% 100. Two men bought a barrel of flour for $9; one paid $44 and the other the rest; what part of the flour ought each to get for his share ?
Ans. The 1st 4, and the other 46 101. Galveston is 14° 43' west of Pittsburg. When it is noon at Galveston, what is the time at Pittsburg?
Ans. 58 min. 52 sec. P. M. 102. The longitude of Rome is 20° 30' east and the ongitude of Baltimore is 76° 37' west. When it is 9 A. M. #t Rome, what time is it at Baltimore?
Ans. 2 h. 31 m. 32 sec. A. M. 103. Seld tea at 90 cts. a pound and gained 20%; what % could be gained by selling at $1 a lb. ?