46. A stick 2 ft. 11 in. high, standing perpendicularly on a level ground, throws a shadow 3 ft. 6 in. long. What is the height of a tower, and of a flagstaff on the top of it, throwing a shadow of 126 feet, the flagstaff being the height of the tower? 47. Find the cost of 1019 yards of velvet, if 7 yards can be had for £2, 18s. 5 d. 48. If u horses require as much hay as 19 cows, and 19 tons is sufficient for 38 horses for 34 months, what quantity will suffice for 19 cows for the same time? 49. Seventeen boxes of tea, each containing on an average 1. cwt., are sold for £ 520, 125. 6d. ; how much is that per lb.? 50. If the price of the 4 lb. loaf be 8!d. when wheat sells at 45. 3d. a bushel, what should be its price when the bushel costs 55. 6d. ? 51. Two boys were picking up potatoes; while one picked up 10, the other picked up 11. When the first boy had 11 score, how many had the other? 52. Find the cost of 1663 pints of spirit at 195. 2d. per gallon. 53. If 8 cwt. 3 qrs. 22 lbs. II oz. of coffee cost £50, 25. 8ļd., what must be given for 2 tons of it? 54. My rental increased from £1000 in 1871 to £1256, ros. in 1876 ; in the former year I paid £72, 18s. 4d. poor rate, in the latter my rate amounted to £109, 18s. 101d. What did I pay in the £ in the former, and what in the latter year? 55. I spent £4908, 155. on equal quantities of wheat at 2 guineas a quarter, barley at i guinea a quarter, and oats at 145. a quarter; what quantity of each shall I have? 56. A race-horse goes 5 miles in 32 minutes; how long will he be in going 1650 yards ? 57. The annual poor rate on a net rental of £1096, is. 9d. amounts to £109, 6s. 3d. ; what is the net rental of an estate for which the poor rate amounts to £24, 55. rod. a year? 58. What quantity of sugar can be bought for £324, if 14 cwt. 3 qrs. 14 lbs. of the same cost £367 59. If i cwt. I qr. 21 lbs. of sugar cost £3, 75. Id., what quantity of the same quality can be had for £29, 155. ? 60. A lump of gold, at £3, 175. 10 d. per oz., is worth £150; what will be the worth of a lump of silver of equal weight, at 545. 6d. per lb. ? 61. If I can travel 198 miles by train for £2, 9s. 6d., how far ought I to be carried at the same rate for £8, os. 10d. ? 62. How much may I spend in 73 days if I wish to lay by in the year 50 guineas out of my income of £450? 63. What quantity of wine, at the rate of £31, 16s. 4d. per 46 gallons, may be got for £117, 118. 8d. ? 64. If 55 score of sheep eat bare 80 acres of grass in 6 weeks and 2 days, how long would that quantity of pasture serve for 968 sheep? 65. What is the price of a millionth part of 83 tons 14 cwt. 12 lbs. at the rate of one-millionth part of £3125 per oz.? 66. If the one-thousandth part of £3, 2s. 6d. will pay for I 02., what must be paid for the millionth part of 167 tons 8 cwt. 24 lbs. ? 67. If a man has £1553, 6s. 8d. remaining after paying an income tax of 7d. in the £, what is his gross income? 68. A clerk's net salary, after paying 6d. in the £ income tax, is £195; what would it have amounted to had there been no income tax ? 69. After paying an agent 6d. in the £, my net receipts for rents came to £390; what was the total amount paid by the tenants ? 70. A rent-collector, after deducting his commission of gd. in the £, paid to his employers £ 1203, 2s. 6d. ; what was the total amount of the rents collected ? 71. After paying 7d. in the £, a gentleman had 4,971, 16s. 1d. over; on what amount had the tax been charged ? 72. A bankrupt fails for £9619, 145. 6d., and his property remaining amounts to £1603, 5s. od. ; how much can he pay in the £? 73. If 77 tailors can execute an order for regimental clothing in thirty days, how many more tailors must be engaged to do the work 8 days sooner? 74. Thirty-three masons can build a wall in 47 days, but after working 11 days, 15 of them strike; in how many days after the strike will the wall be finished ? 75. A salmon leaves Berwick at 7 o'clock on Saturday evening, and swims 8 miles an hour; when will he pass under Peebles Bridge, the distance by water being 69 miles ? 76. A clock set on Wednesday at 9 in the evening gains 15 sec. in 4 hours; what is the correct time when the clock points 4 to 3 hrs. 4 min. 7 sec. on Saturday afternoon ? 77. If 64 men can do a job in 57 days, and if, after they have been working for 12 days, notice is sent to finish the job 9 days before the time agreed upon, how many additional men must be put on? 78. Five pheasants are worth 4 grouse, 5 grouse worth 8 partridges, 2 partridges worth 5 snipes; how many snipes should be given for 10 pheasants ? PROPORTION (Compound). 1. If 40 men require £20 worth of bread in 10 days when wheat is at 63s. per quarter, how long would £90 worth serve 54 men when wheat is at 56s. per quarter? 2. If 40 bushels of corn serve 12 horses for 37 days, how many days would 197 bushels of corn serve 9 horses? 3. A stone slab, 2 inches thick, 3 feet wide, 51 feet long, weighs 171 cwt. ; what would be the weight of a slab of the same width, but 3 inches thick and 9 feet long? 4. A family of 8 persons require £5, 5s. to keep them 3 weeks when four is at 6s. 3d. a bushel ; how much should a family of 10 persons require to keep them for 8 days when flour is at is. 3fd. a peck ? 5. If £730 gain £8, 25. 6d. in 120 days, what will £100 gain in a year? 6. If a penny loaf weighs 7 oz. when wheat is 6s. 8d. a bushel, what should be the price of the 4 lb. loaf when wheat is at 55. rod. a bushel? 7. If 7 fires consume 4 tons 7 cwt. of coal in 30 days of 10 hours each, how much will be consumed by 6 fires in 20 days of 14 hours each? 8. 48 men can do a piece of work in 30 days, working 10 hours a day; how many additional men will be wanted to complete it in 20 days, working 8 hours a day? 9. If 5 donkeys require as much hay as 3 horses, and each horse's hay cost 45. a week, what must be spent in supplying 85 donkeys with hay for 6 months ? 10. 75,000 flagstones, each 24 inches long and 5 inches broad, are required to lay down a court; how many stones, each 40 inches long and 6 inches broad, would be necessary for the same purpose ? 11. If 9 men can earn £2, ios. 5ļd. a day, how much will 15 men earn in 13 days? 12. If it costs £17, 155. to fill a coal cellar when coal is at £1, 6s. 7}d. a ton, what will be the cost of filling a cellar half the size of the other when coal is 335. per ton? 13. If 8 fires consume 6 tons 8 cwt. of coal in 6 weeks, in what time will 9 fires consume 10 tons 16 cwt. ? 14. If 23 horses can plough 46 acres in 8 days, how many acres will 7 horses plough in 9 days? 15. If 24 oxen require 6 acres of turnips to supply them for 10 weeks, how many acres would supply 6 score of sheep for 15 weeks, 3 oxen eating as much as ten sheep? 16. If 10 men or 14 women can perform a work in 43! days, how long would 8 men and 12 women working together require for double the work? 17. If 6 horses eat 18 guineas worth of hay in 6 weeks when hay is 9d. a stone, what is its price per stone when 15 horses eat £110, 5s. worth in 21 weeks? 18. If 5 men receive £5, 18s. wages for 12 days, what will be the wages of 16 men for 20 days? 19. If 12 men build a wall 60 feet long, 4 feet thick, and 20 feet high, in 24 days, working 12 hours a day, how many men will it take to build a wall 100 feet long, 3 feet thick, and 12 feet high, in 18 days, working 8 hours a day? 20. A man travels 120 miles in 5 days, at the rate of 3 miles an hour; how many hours a day must he travel at the same rate to go 200 miles in 8 days? a 74. Thirty-three masons can build a wall in 47 days, but after working 11 days, 15 of them strike; in how many days after the strike will the wall be finished? 75. A salmon leaves Berwick at 7 o'clock on Saturday evening, and swims 8 miles an hour; when will he pass under Peebles Bridge, the distance by water being 69 miles? 76. A clock set on Wednesday at 9 in the evening gains 15 sec. in 4 hours; what is the correct time when the clock points to 3 hrs. 4 min. 7 sec. on Saturday afternoon? 77. If 64 men can do a job in 57 days, and if, after they have been working for 12 days, notice is sent to finish the job 9 days before the time agreed upon, how many additional men must be put on? 78. Five pheasants are worth 4 grouse, 5 grouse worth 8 partridges, 2 partridges worth 5 snipes; how many snipes should be given for 10 pheasants? PROPORTION (Compound). 1. If 40 men require £20 worth of bread in 10 days when wheat is at 63s. per quarter, how long would £90 worth serve 54 men when wheat is at 56s. per quarter? 2. If 40 bushels of corn serve 12 horses for 37 days, how many days would 197 bushels of corn serve 9 horses? 3. A stone slab, 2 inches thick, 3 feet wide, 5 feet long, weighs 174 cwt.; what would be the weight of a slab of the same width, but 3 inches thick and 9 feet long? 4. A family of 8 persons require £5, 5s. to keep them 31 weeks when flour is at 6s. 3d. a bushel; how much should a family of 10 persons require to keep them for 8 days when flour is at 1s. 3d. a peck? 5. If £730 gain £8, 2s. 6d. in 120 days, what will £100 gain in a year? 6. If a penny loaf weighs 7 oz. when wheat is 6s. 8d. a bushel, what should be the price of the 4 lb. loaf when wheat is at 5s. 10d. a bushel? 7. If 7 fires consume 4 tons 7 cwt. of coal in 30 days of 10 hours each, how much will be consumed by 6 fires in 20 days of 14 hours each? |