50. Multiply 42.35 by 3.14159, using the contracted method and finding the result correct to two decimal places. Prove the work by division, using the contracted method.

51. A man borrows $4500, and agrees to pay principal and interest in four equal annual installments. If the rate of interest is 6%, what will be the amount of each annual payment?

52. When it is Monday, 7 A.M., at San Francisco, longitude 122° 24′ 15" W., what day and time of day is it at Berlin, longitude 13° 23′ 55′′ E.?

53. When exchange is at 5.18, find the gain on 100m of silk bought in Paris at 2 francs a meter and sold in New York at 89 ct. a yard, the duty being 6% ad valorem.

54. Find the face of a sight draft that can be bought for $585.80 when exchange is at a premium of 5%.

55. Divide 0.8487432 by 0.075637 and multiply the quotient by 0.835642. Find the result correct to three decimal places, using the contracted methods of division and multiplication of decimals.

56. Express in words each of the following: 600.035,

0.635, 600-800, 5000, 1000

57. A body on the surface of the earth weighs 27 lb. Assuming that the radius of the earth is 4000 mi., find the weight of the same body 2000 mi. above the surface. (The weight of a body above the surface of the earth varies inversely as the square of the distance from the center of the earth.)

58. Washington is 77° 3′ W. longitude and Pekin 116° 29' E. longitude. When it is 9.30 P. M., Tuesday, Dec. 31, 1901, at Washington, what is the time of the day, the day of the week, and the date at Pekin?

59. Find the exact interest on $590 from Sept. 18, 1893, to March 1, 1894, at 41%.

60. Is the merchants' rule or the United States rule for computing partial payments more favorable to the debtor? Give reasons.

42

61. A locomotive runs of a mile in of a minute. At what rate an hour does it run? (Give analysis in full.)

62. The edges of a rectangular parallelopiped are in the proportion of 3, 4 and 6; its volume is 720 cu. in. Find its entire surface.

63. A note for $250, due in 1 yr., with interest at 6%, is dated Jan. 1, 1892. What is the true value of this note

Oct. 1, 1892 ?

64. At 10 A.M. Jan. 5 a watch is 5 min. too slow; at 2 P.M. of Jan. 9 it is 3 min. 20 sec. too fast. When did it mark correct time?

65. A gallon contains 231 cu. in.; a cubic foot of water weighs 62.5 lb.; mercury is 13.5 times as heavy as water. How many gallons of mercury will weigh a ton?

66. Find the face of a note that will yield $861.44 proceeds when discounted for 90 da. at 6%.

67. A merchant buys goods listed at $2500, getting successive trade discounts of 20, 10 and 5; he sells his goods at 20% above the cost price, taking in payment a note at 60 da. without interest; he then gets the note discounted at 6% and pays his bill. Find his entire gain.

68. A person deposits $100 a year in a savings bank that pays 4% interest, compounded annually. How much money stands to his credit immediately after the fifth deposit?

69. Change 200332 in the quinary scale to an equivalent number in the decimal scale, and prove the work.

70. A New York merchant remitted to London through his broker £12000 188. 9d. Find the cost of the draft if exchange is at 4.891 and brokerage is 1%.

71. In extracting the cube root state and explain the process of (a) separating into periods, (b) forming the trial divisor, (c) completing the divisor.

72. A merchant buys goods at a list price of $800, getting discounts of 10, 20 and 5 with 60 da. credit, or a further discount of 5% for cash. How much will he

gain by borrowing at 6% to pay the bill?

73. At a certain election 510 votes were cast for two candidates; of those cast for one equaled of those cast for the other. How many votes were cast for each candidate?

74. If the cost of an article had been 8% less, the gain would have been 10% more. What was the per cent gain?

75. Prove that the excess of 9's in the product of two numbers is equal to the excess in the product of the excesses in the two factors.

76. Derive a rule for marking goods so that a given reduction may be made from the marked price and a given profit still made on the cost.

77. The greatest common divisor and the least common multiple of two numbers between 100 and 200 are respectively 6 and 3150. Find the numbers.

78. How much will the product of two numbers be increased by increasing each of the numbers by 1? Give proof.

79. The longer sides of an oblong rectangle are 15 ft and the diagonal is 20 ft. Find its area.

80. Find the fourth term of the following proportion and demonstrate the principle on which the operation is based: 8:12 = 10 : x.

81. Demonstrate the following: If the greater of two numbers is divided by the less, and the less is divided by the remainder, and this process is continued till there is no remainder, the last divisor will be the greatest common divisor.

82. Find in inches to two places of decimals the diagonal of a cube whose volume is 9 cu. ft.

83. Compare the standard units of money of the United States, England, France, and Germany as to relative value. Find the value of $100 in each of the other units.

84. A dealer sent a margin of $1500 to his broker, April 16, 1905, and ordered him to buy 100 shares of American Sugar stock. The broker filled the order at 1317 and sold the stock May 1 at 1261, charging% brokerage each way and 6% interest. How much money should be returned to the dealer?

85. A four months' note for $584, without interest, is discounted at a bank at 5% on the day of its issue. Find the proceeds of the note.

86. What is the difference between a discount of 10% and two successive discounts of 5% each on a bill of $832?

87. If I buy cloth at $1.20 a yard, how must I sell it so as to gain 25% ?

88. Find the cost of paving a walk 140cm wide and of a kilometer long at $1.25 a square meter.

89. Indicate the factors which, multiplied together, equal the square root of 441.

90. A newsboy buys 144 daily papers at 20 ct. a dozen, and sells them at 3 ct. each. At the end of 6 da. he has How much has he made during the

18 papers on hand.

week?

91. The diameters of two concentric circles are 20 ft. and 30 ft. Find the area of the ring.

92. What yearly income will $2267.50 produce when invested in U. S. 4's at 1131, brokerage %?

93. Find the amount of $486.50 for 1 17 da. at 51% simple interest.

5 mo. yr.

and

94. I buy stocks at 4% discount and sell at 4% premium; what per cent profit do I make on the investment?

95. A merchant buys goods to the amount of $1575 on 9 months' credit; he sells them for $1800 cash. Money being worth 6%, how much does he gain?

96. Find the cost, at 60 ct. a yard, of carpeting a room 16 ft. 4 in. wide and 21 ft. 6 in. long with carpet 27 in. wide, if the strips of carpet run lengthwise.

97. Find the cost at 45 ct. a roll of papering the walls of a room 161 ft. long, 15 ft. wide, and 12 ft. high, making no allowance for openings.

98. Find the cost of plastering the four walls and the ceiling of a room 15 ft. long, 12 ft. wide and 9 ft. high at 15 ct. a sq. yd., allowing 6 sq. yd. for openings.