4 feet long; what was the circumference of the track described by the outer wheel? Ans. 56.548+feet. 61. A person went to a store, borrowed as much money as he had, and spent 16 cents; he then went to a second store, borrowed as much as he then had, and spent 16 cents; he repeated this at a third and fourth store, and then had no money remaining; how much had he at first? Ans. 159. 62. Three persons took a house in partnership for a year at a rent of $750; at the expiration of three months they took in three more tenants, and at the end of every three months till the expiration of the time they took in four more; how much should one of each class pay? 63. $750. Ans. $125; $6311; $324; $131. For value received, I promise to pay H. S. Snyder, or order, on demand, Seven Hundred and Fifty Dollars, without defalcation. I. REIMEL Indorsements: March 1, $50; June 11, $200; July 10, $25; Sept. 9, $250; Dec. 1, $150. What is due Jan. 1, 1876 ? Ans. $102.40. 64. A and B set out from the same place and traveled in the same direction, A at the rate of 20 miles a day. After they had been gone 4 days, A goes as far back as B has traveled in that time; he then turns, and pursuing his journey, overtakes B 25 days from the time they set out; at what rate does B travel? Ans. 15 miles a day. 65. A general drew up his brigade in the form of a square and had one man left over; but receiving a reinforcement of 423 men, he was able to increase the side of the square by 4 men; how many men had he at first? Ans. 2602. 66. A speculator invests $2120 in grain, including 4% for freight and 2% for commission, then sells the grain at 20% advance on the cost price for a note at 60 days, which he gets discounted at bank at 6%, and repeats this operation every 10 days; how much will his gains amount to in a month, if he invests the whole proceeds each time? Ans. $859.95. 67. I have a garden 214 rods long and 101⁄2 rods wide; it is surrounded by a fence 71 feet high; a walk is laid out within the fence which is 74 feet wide at the sides of the garden, and 6 feet wide at the ends; how much is left for cultivation? Ans. 5341812 sq. ft. 68. A bath-tub will hold 160 gallons of water; it is filled by a faucet discharging 60 gallons in 5 minutes, and emptied by a waste-pipe discharging 46 gallons in 4 minutes; if both are opened at 6 o'clock in the morning, and then the waste pipe closed at 8 o'clock, at what time will the tub be full? Ans. 8 h. 8 min. 20 sec. A. M. 69. A tree stands exactly opposite the front door of my house, which looks towards the northeast, but the distance cannot be directly measured on account of a small pond lying between them. I therefore measure 60 yards due north from the front door, and then 120 due east, when I find I am exactly 40 yards to the north of the tree; what is the distance from the front door to the tree? Ans. 121.65 yards. 70. Wishing to speculate in land, I obtained at a bank on my note payable in 3 months money enough to buy 50 acres at $75 per acre, and also borrowed of a friend sufficient to buy another lot of the same size and value, giving my note payable on demand, interest 6%; I sold both lots in time to take up my note at bank when it became due, and found that the price received for 36 acres would pay for it. What did I gain by my speculation, supposing that I paid my demand note at the same time as that in bank? Ans. $2963.50. 71. A land-owner who held his lots for sale at $4 per foot ground rent, agreed with a tricky builder to give him a bonus of $9000 cash with 180 feet of his lots, taking groundrent at $7 per foot in return. The builder erected 10 houses upon them, costing $2000 each, and then sold them at $1800 cash each, subject to the ground-rent; how much did the builder make by the operation? Ans. $7000. 72. Bought $5000 gold @113 on Feb. 1, paying a commission of %; on Feb. 25, I sold it at 114ğ; what is my gain, interest at 6% ? Ans. $33.60. 73. I bought a 6% mortgage for $2500 at 5% discount, with two years to run; what interest do I get on the money invested if the mortgage is satisfied at maturity? Ans. 818%. 74. A is enrolled as a life-member of the Fairmount Park Art Association upon contributing $50; at the same time B becomes a member, and for 20 years makes the yearly contribution of $5; at the end of this period, which has contributed the larger sum, interest included? Ans. B, $47. 75. The "Consolidated Virginia" silver mine rose from 94 to 590; what gain per cent. was this, and what would I have made if I had held 750 shares? Ans. 52744%; $372,000. 76. Bought 50 shares bank stock ($100) at 108; at the end of 5 yr. 6 mo., having regularly received a semi-annual dividend of 5%, I sold the stock at 110; what did I gain, money worth 6% compound interest? Ans. $1222.44. 77. Buy ground "in fee" for $400, and build a house costing $1000, and pay for them by subscribing for 10 shares Building Association, new series, and buying a loan at $60 premium, Net plan. If I rent the house for $15 a month, and pay taxes and water rent equal to $3 a month, what will my house cost me without interest, and what with interest, if the series runs out in 10 years? Ans. $600; $781.50. 78. Bought a check on a suspended bank at 75%, and exchanged it for railroad bonds of the same nominal value at 85%, bearing 7% interest; what rate of interest do I receive on my investment? Ans. 91%. 79. Four men agree to perform a certain piece of work for $428. A, B, and C can do it in 24 days; B, C, and D in 30 days; A, C, and D in 35 days; and A, B, and D in 42 days; what share of the money should each receive? Ans. A, $92; B, $140; C, $188; D, $8. 80. There are two clocks, one of which gains 30 seconds a day and the other loses 25 seconds. If the pendulums beat together when both clocks indicate exactly 6 o'clock, what time does each show when they next beat together? Ans. 1st., 26 min. 115 sec. past 6; 2d, 26 min. 10,5 sec. past 6. 81. A merchant bought 15 pieces of cloth, each containing 20 yards, @ $54, on a credit of 8 mo., and sold them @ $63, on a credit of 3 mo.; what was his cash gain at 6% ? Ans. $295.92. 82. Two girls, each 10 years old, receive legacies from a relative; the sum left to the first is invested at 8% simple interest, and the sum left to the second at 6% compound interest, and each investment will amount to $5000 when the owner is 18 years old; what were the legacies? Ans. 1st, $3048.78; 2d, $3137.06. 83. How many cannon balls, 6 inches in diameter, are contained in a cubical vessel whose side measures 2 feet, and how many gallons of water will it hold after it is filled with the balls? Ans. 64 balls; 28.5 gal. 84. How many cannon balls, 8 inches in diameter, are contained in a cubical vessel whose side measures 6 feet, and how many gallons of ale can be poured in after the vessel is filled with balls, each ball containing a hollow 5 inches in diameter, and the opening containing 14 cubic inches? Ans. 729 balls; 803.6237 gal. 85. Four men buy a grindstone 32 inches in diameter, with a square hole whose diagonal is 4 inches; if each grinds off his share in turn, how much of the semi-diameter will each one take? Ans. 2.108 in.; 2.4905 in.; 3.2165 in.; 6.185 in. 86. A father left $61,248 to be divided among his four sons, aged respectively 16, 14, 12, and 10 years, so that their respective shares being invested at 10% simple interest, shall amount to the same sum when they become 21 years old; what was the share of each? Ans. $18,088; $15,960; $14,280; $12,920. 87. Two men in Philadelphia hired a carriage for $25 to go to Trenton, a distance of 30 miles, and back, with the privilege of taking in three more persons. At Bristol, 19 miles from Philadelphia, they take in Mr. Jones; at Trenton they take in Mr. Newell; and 15 miles from Philadelphia they take in Mr. Stokes; what is each one's share of the cost? Ans. $8.2931; $4.34; $2.814; $1.25. 88. Sold for % of consignor on September 3, $5230.43 on 4 months; Sept. 10, $437 for cash; October 15, $3730.37 on 60 days; Sept. 2, paid freight on this stock, $97.46, and our commission for selling is 5%; what is due to consignor, and when shall the proceeds be remitted? Ans. $8830.45; Dec. 22. 89. Mr. Green took 20 shares in a building association which runs out in 10 years; Mr. Gray bought a 6% mortgage at 3.2% discount, interest payable annually, for a sum which will give the same interest as the periodic payment on 20 shares for 10 years; if the mortgage is paid off in 10 years, which of the two realizes the larger sum on his equal investment? Ans. Green, $1797.50. 90. A, B, and C are to travel a distance of 40 miles; A walks at the rate of 1 mile an hour, B 2 miles an hour, and C, with a horse and buggy, goes 8 miles an hour. C, at the start, takes in A and carries him so far that if he returns and meets B, and takes him in, they will get to the end of the journey at the same time that A does ; required the distance A and B walk, C rides, and the time of each and all. Ans. A, 535 mi.; B, 1347 mi.; C, 8040 mi.; 105 hours. 91. Paul B. Myers, of Philadelphia, received per steamer Cynthia, one case of cigars, Londres brand, marked PBM#1, containing 1000 1st quality @$55 †M., 1300 2d quality @ $45, 700 3d quality @ $35; charge for case, carting, export duties, etc., $12; com. 21%; the gross weight was 60 lb., tare, 15 lb. Make out the invoice and find the amount of duty @ $2.50 a lb., and 25% ad valorem. Ans. $151. What was the duty in currency, gold being 112 ? Ans. $82.99. |
