69. Find the cube root of 45156047481. 70. Find the distance between the lower corner and the opposite upper corner of a room 18 ft. long, 15 ft. wide, and 12 ft. high. 71. What will I realize from the sale of 120 shares of stock sold at 1114, brokerage %? 72. What per cent. will Georgia 6%'s yield bought at 1193, brokerage %? 73. What time after 4 o'clock will the hour- and minutehands of a watch be opposite each other? 74. A had his house insured for of its value at 11%; soon afterwards it was destroyed by fire, and his loss over the insurance was $1700; what was the value of the house? 75. Find the sum of the infinite series + + a'§, etc. 76. A has a lot which contains of an acre: he made a walk around it which contained 47 of the entire area; re376 quired the width of the walk. 77. What must I ask for goods which cost $120, so that I may deduct $20 from my asking price and still gain 20% ? 78. A lost 35% of his sheep; what per cent. must he gain on the remainder to gain 20% on the cost of all? 79. A has a circular garden, and B square one each contains an acre; a walk 6 ft. wide is made around each garden; vhich walk contains the greater area, and how much? 80. How many cubic yards of earth will be required to over of an acre 10 in. deep? 81. How long will it take two 3-inch pipes to empty a cistern that required three 2-inch pipes 4 hr. to fill? 82. What is the difference between the cube root of the least common multiple of 94106 and 202484 and the square root of their greatest common divisor? 83. A square field containing 10 acres is surrounded by a close board fence 10 ft. high; what did the boards cost, at $13 per M.? 84. The diameter of a circle is 40 ft.; what is the length of 84° 30' 30" of the circumference? 85. I sold a horse so that of the gain equaled 1% of the cost; what was the gain per cent.? 86. A bought a horse at 10% less than first cost, and sold him at 20% above first cost, thereby gaining $60; what was the first cost of the horse? 87. After a rainfall of 14 inches how deep will the water be in a cylindrical cistern 6 ft. in diameter which drains the roof of a house 40 ft. by 30 ft.? 88. A note for $900 was given Apr. 1st at 6% interest, on which a payment of $500 was made Aug. 1st: Nov. 10th the note was purchased at 4% discount on its value at that time; what amount was paid for it? 89. A has a square yard 40 ft. on a side: on each corner is the centre of a circle 20 ft. in radius; find the area within the square and without the circles. 90. B pays a tax of 4% on his income over $2000, and after paying his tax he has remaining $4200; what is his whole income? 91. A horse is tied to the top of a post 6 ft. high by a rope 20 ft. long; over how many square yards can he graze? 92. If stock bought at 10% above par will pay 6% on the investment, what % will it pay if bought at 10% below par? 93. A general formed his army into a solid square, and had 200 men over: he then received a reinforcement of 1000 men, and, increasing each side of the square by 5 men, lacked 25 men to complete the square; how many men were there in the original army? 94. A boy hired to a farmer for 30 days on condition that he should receive $30 and a suit of clothes: at the end of 18 days he concluded to quit work, when it was found that he was entitled to $10 and the suit of clothes; what was the value of the clothes? 95. A sells 5% stock, whose par value is $13400, at 933, and invests the proceeds in 4% stock at 85g, brokerage % on each transaction; is his income increased or diminished, and what is his surplus? 96. A sold his farm, and gained a certain per cent.: if the farm had cost him 10% less and sold for the same price, he would have gained 163% more; what was his gain per cent.? 97. Four ladies bought a ball of yarn 3 in. in diameter; what part of the diameter must each wind off to share it equally? 98. What is the length of a tape that will wind spirally around a cylinder that is 75 ft. long and 12 ft. in circumference, provided it passes around the cylinder once every 5 ft.? 99. Find the 6th root of 6321363049. 100. Express .0003986 as a common fraction in its lowest terms. 101. How many cannon-balls 2 inches in diameter can be made from a cubic foot of iron? 102. The sum of the interest, amount, present worth, and true discount of a certain sum of money is $800; what is the amount? 103. Find the side of a square whose area is equal to the area of a triangle 16 feet on a side. 104. What principal at 5% compound interest will amount to $259.085 in 5 years? 105. What is the shortest distance from the lower corner of a room 40 ft. long, 30 ft. wide, and 12 ft. high to the opposite upper corner, keeping on the surface of the room? 106. At how many minutes after 3 o'clock will the hour- and minute-hands of a watch be opposite each other? 107. A pays $2 a month dues to a building association; how much has he paid in at the end of 9 years and 2 months? 108. John can do a piece of work in 4 days of 10 hours each, and James in 3 days of 9 hours each; how many hours will they require to finish the job, working together? 109. Find the contents of a cone whose slant height is 10 feet and the radius of the base 6 feet. 110. Find the amount of $946.75 for 6 yr. 4 mo. 17 da. at 71%. 111. How much leather will be required to cover a base-ball 3 inches in diameter? 112. I sold through a broker 50 shares of bank stock ($100) at % premium, and invested the proceeds in railroad stock ($50) at % discount; how many shares did I buy, and what was the surplus, brokerage being 1% for buying and selling? 113. A has a circular lot 10 rods in diameter, and B has a square one whose diagonal is 12 rods; which is the larger, and how much? 114. A piece of work can be done in a day of 11 hours by 2 men, 5 women, or 12 boys; in what time can it be done by 1 man, 1 woman, and 1 boy? 115. A merchant bought a steer weighing 960 pounds for $50, which lost 40% of its weight in dressing; how much per cent. did he gain if he sold the beef at an average price of 10 cents per pound? 116. I buy muslin at 64 cents a yard, and mark it at a gain of 20%: finding it damaged, I sell it at 75% of the marked price; what is my gain or loss per cent.? 117. A gave his note for 4 months, which when discounted at a bank at 1% a month gave $500 proceeds; what was the face? 118. A cistern 3 ft. 4 in. long, 2 ft. 9 in. wide, and 7 ft. 6 in. deep has a supply-pipe which pours in 7 gallons of water in 5 minutes, and a waste-pipe which draws out 2 gallons in 6 minutes; how long will it take to fill the cistern if both pipes aro open at the same time? 119. On the 1st of Oct., 1893, I borrowed from Mr. Bonn $500, to be paid in 3 months without interest: on July 1, 1894, I paid him $75; on Jan. 1, 1895, I paid him $100; how much was due April 1, 1895? 120. What is the amount of the following bill of lumber at $16 per thousand: 2 pieces 8 X 4 in. 40 ft. long, 3 pieces 8 X 5 in. 20 ft. long, 4 pieces 6 × 4 in. 18 ft. long, 38 pieces 3 × 4 in. 16 ft. long, 80 pieces 2 × 4 in. 18 ft. long, 48 pieces 2 × 8 in. 10 ft. long, 24 pieces 2 × 7 in. 20 ft. long, and 40 pieces 11⁄2 X 6 in. 16 ft. long? 121. A miller bought a ton of wheat at 60 cts. a bushel, which he manufactured into flour; what was his gain per cent. if each bushel yielded 371⁄2 pounds and he received $4.20 a barrel for the flour? 122. My agent sold 5500 lb. of poultry at 8 cts. a pound, and 8040 lb. of butter at 22 cts. a pound, on 31% commission: he remitted me the proceeds in a 60-day draft, which was discounted at a bank 15 days after date at 10%; what did I realize from the sales? 123. If oranges are bought at the rate of 6 for 5 cts. and sold at the rate of 5 for 6 cts., what is the gain per cent.? 124. A coal-dealer buys a car-load of coal, 33600 lb., at $4.25 a long ton, which he retails at $5.50 a ton; what per cent. does he gain, allowing 3% loss in handling? 125. A vessel is 71⁄2 inches in diameter at the base and 101 inches at the top; how many gallons of water will it hold if it is 11 inches high? 126. Find the square root of 2561068449. 127. Find the cube root of 66814683180552. 128. Find the value of √2 − √2 + √3. 129. What must. be paid for 41% stocks to realize 6% on the investment? |