51. If of an acre produces $13.25 worth of fruit, how many acres would produce $177.77 worth, at the same rate? 52. If a ship sails 72 miles in 8 hours 32 minutes, in what time would she sail 165 mi. 9 rd.? 53. If a gallon of wine costs $3.165, what is the cost of 11 gal. 2 qt. 14 pt., at the same rate? 54. If 11 yd. of cloth cost $4.121, what will 8 yd. cost? 55. A, B, and C own a vessel, A owning of it, and B and C having equal shares in the remainder; A sells of what he owns for $3680; what is C's share worth, at the same rate? 56. If the railroad fare of 5 men for a certain distance is $9.60, what is the fare of 9 men and 7 children for the same distance, children half fare? 57. A can mow a field in 3 days, B in 4 days, and C in 5 days; in what time can they mow it, working together? 58. There are 2111 gallons of water in a certain cistern, and by one pipe 233 gallons run out in one hour, while by another 524 gallons run in; in what time will the cistern be filled, its entire capacity being 8 hogsheads? 59. A and B can do a piece of work in 123 days, and A alone can do it in 28 days. In what time can B alone do it? 60. A, B, and C together own a farm; A and B together own of it, and B and C together own of it. If the whole value is $18200, what is the value of B's share? 61. If 10 men and 7 boys can do a piece of work in 33 days, how many men can do it in 8 days, allowing the work of 9 boys to equal the work of 5 men? 62. M is 136 yards ahead of N, and N walks 5 yards while M walks 35 yards. How many yards must N walk to overtake M? 63. For 2 lb. of tea I can get 14 lb. of sugar or 43 lb. of coffee; what then is the value of 51⁄2 lb. of tea, 13 lb. of sugar, and 5 lb. of coffee, if 8 lb. of tea are worth $5.60? 64. A can mow an acre in 7 hours, and A and B can mow 2 acres in 63 hours; in what time can B alone mow 2 acres? 65. A can do a piece of work in 84 days, and B in 7 days; they do the work together, and receive in payment $11.22, which they divide between them, each being paid in proportion to his work. What does each receive? 66. of A's money to A's? of B's; what is the ratio of B's 67. Find the unknown term in each of the following: 5×4: 7×8:9 × 10: what? 3 × 45 × 6 :: what : 8? What: 168::14:54 : what :: 5 : 148? 68. If 17 yd. of carpet, yd. wide, cost $21.50, what will 111 yd., yd. wide, cost, at the same rate? 69. If $30 is the interest of $2000 for 3 mo., at 6%, what is the interest of $168 for 16 mo., at 71% ? 70. If $800 gain $96 in 18 mo., at 8%, what sum will gain $28.50 in 6 mo., at 6% ? 71. If $550 gain $41.25 in 1 yr. 3 mo., at 6%, in what time will $320 gain $72, at 9% ? 72. If 264 bricks, each 8 in. long and 44 in. wide, will pave a given area, how many bricks, 84 in. long and 4 in. wide, will pave 3 times that area? 73. What is the cost of 8 pieces of paper, each 13 yards, at $1.75 per piece of 11 yards? 74. 64 men engaged to do certain work in 30 days; at the end of 18 days, finding that of the work was done, the employer discharged a number of the men, the remainder being able to finish the work in the given time. How many men were discharged? 75. If 10 horses can eat 201 bundles of hay in 11⁄2 mo., how many horses will eat 127 bundles in 73 mo.? 76. If 15 apples cost 10 cents, when apples are $1.50 a bushel, what should 25 apples cost, at 62 cents a bushel ? 77. If $5 gain 15 mills in 20 days, what will $326.26 gain in 265 days, at the same rate? 78. One man and one boy agreed to mow 21 acres of grass in 6 days, working 12 hours a day; at the end of 44 days, only 12 acres having been mowed, another man, who works at the same rate as the first, is hired; the three, working 103 hours a day, finish the work in the given time; in how many days of 9 hours each could one man alone have done the work, and what is the ratio of the boy's work to the man's? 79. If 500 stones, each 71⁄2 in. long and 6 in. wide, are required for a pavement of a certain area, how many stones, 61 in. square, will lay a pavement of that area? 80. In the composition of water, the quantity of oxygen by weight is 8 times that of hydrogen; what is the weight of hydrogen in a wine gallon, which is to the imperial gallon as 5 to 6, the imperial gallon weighing 10 lb. Avoirdupois? 81. What will it cost to cover a floor 18 ft. square with carpetyd. wide, at $1.80 per yard? 82. If 26 yards of muslin cost as much as 3 yards of silk, and 13 yards of silk will pay for 4 pair of shoes, what is the price of the shoes per pair, 5 yd. of muslin being worth 69 cents? 83. A merchant buys herring at 2 s. 8 d. for 120, and sells them at 4 s. a hundred; how many hundred must he sell to gain £10? 84. If $1999.82 are paid for 18 A. 17 sq. rd. of land, what will be the cost of 231 A. 120 sq. rd., if the latter is worth 20% less per acre than the former? 85. If it costs $10.24 to carry 1500 lb. 356 miles, what will it cost to carry 2700 lb. 890 miles? 86. If 3 men or 5 boys can do a piece of work in 113 days of 12 hours each, in how many days of 10 hours each can 5 men and 3 boys do the work? 87. If of a ton of coal cost $3.16, how much will 11⁄2 tons cost, the latter being cheaper per ton than the former? 88. If 3 cords 10 cord feet of wood cost $27, what is the cost of 5 cords 5 cord feet 5 cu. ft., at 50% less per cord than the former? 89. If £17 11 s. 11 d. gain £1 9 s. 3 d. in 5 mo. 10 da., how much should £35 9 s. 3 d. gain in half the time, at 2 times the rate? 90. If I can read a book of 200 pages in 3 days, reading 4 hours a day, in how many days, at the same rate per hour, can I read a book of 800 pages, reading 2 hr. 20 min. a day, each page of the second book containing twice as much reading-matter as a page of the first? 91. If 14 men, in 3 days of 7 hours each, can do a piece of work, in how many days of 8 hours each can 11 men do the work? 92. If 1214 yd. of silk, 2 yd. wide, cost $2.50 a yard, what is the cost of 1714 yd., 14 yd. wide, and 20% cheaper per yard than the first? 93. How many miles will a locomotive run in 1012 hours, its wheels, 5 ft. in diameter, making 16 revolutions in 5 seconds, the diameter being to the circumference as 113 to 355? 94. If 8 men or 15 boys can plough a field in 15 days of 9 hours each, how many boys, at the same rate, must assist 16 men, if the work is to be done in 5 days of 10 hours each? 95. If 9 horses, or 18 sheep, or 12 cows, can eat 4 tons of hay in 32 days, how many horses, cows, and sheep, of each an equal number, will, feeding together, eat 1 tons in 94 days? 96. A's money is 20% less than B's; B's is 12% more than C's; and C's is 33% less than D's; if A has $900, how much has D? 97. John has done 150 yards of certain work before James begins to do his share of the work; John can finish 20 yd. an hour, while James can finish 25 yd. and have 10 minutes' idle time in an hour; if John continues to work, and James does not idle at all, in how many hours will he have done as much work as John? 98. If 331% of a man's fortune, invested at 7%, makes $750 in 8 mo. 10 da., in what time will 87% of his fortune, invested at 5%, make $1080? PARTNERSHIP, EQUATION OF PAYMENTS, AND AVERAGING OF ACCOUNTS. 1. THREE men, A, B, and C, employ $25000 in partnership. A's share of the gain is $1000; B's share is $500; C's share $800; what is the amount of each man's capital? 2. Two men lose $1600 in business; A's capital is $9000, and B's $4000; what is the loss of each? 3. A gain of $2250.30 is to be divided in the proportion of 1, 5, and 7; what is the value of each share? 4. A man bequeaths $6000, $7000, and $8000 to his three sons respectively, but the estate proves to be worth only $8000; what is the share of each? 5. Two men, with a capital of $7500, gain $1200; what is the capital of each, if one of them gains $250? 6. A, B, and C gain $4200; A's stock is $2100, B's stock is $3200, and C's gain is $750; what is the gain of each, and what stock has C? 7. A and B commence business with a capital of $13000; at the end of a year A is worth $8200 and B is worth $5200; what was the original stock of each? 8. Two merchants gain $3300 on a joint capital of $6000; what is the share of each, if one of them puts in $2800? 9. Four men, associated in business, gain $250, $175, $240, and $125 respectively; what is each man's share of $3000 capital? 10. A, B, and C lost 10% on a capital of $17000; A's share of the loss was $500; B's capital was $6000; what was the capital of each of the others? 11. Two men, trading together, with a capital of $4400, gain 15%; the gain of one is 50% less than that of the other; what is the capital of each? |