27. In 1878 the number of deaths in a certain kingdom was 391,369; the decrease per cent, was 8.18103 from the preceding year: what was the number of deaths in 1877?

28. A cubic boiler half full of boiling water contains 500 cub. in. of steam; if the water be boiled down to a depth of only 298 in., what percentage of the cubical space of the boiler will be occupied by steam?

29. I bought 5 cwt. 3 qrs. 14 lbs. for £9, 8s., and sold them for £11, 18s. 11d.; what was the percentage of gain, and what the gain per cwt. ?

30. (a) If 50 quarters of wheat sell for 77s. 8d. per quarter, and 100 quarters for 78s. 3d. per quarter, what is the average price per bushel?

(b) If the population of Great Britain in 1851 was 21,121,967, and the increase during the preceding half-century was 93'47 p. c., what was the population in 1801?

31. Out of 360 children in a mixed school, 29'16 p. c. are girls, 33°3 p. c. boys, and the remainder infants. On a certain day of each are present; how many boys, girls, and infants respectively are registered?

32. 5 per cent. on a given sum yields £377083; give 51 per cent. on half that sum in £ s. D.

33. If the ton be diminished 10714285 per cent., and the ounce avoirdupois be increased 25 per cent., how many lbs. would there be in a ton?

34. John had 3s., and gave away d.; William had 4s. 8d., and gave away 31d.: how much more per cent. of his money did the latter give than the former?

35. People sometimes speak of an acre as 70 yards square. What percentage of error is involved in this assumption, and what amount of error would arise in calculating the area of Ireland (32,000 square miles)?

36. If pure gold is worth £4, 5s. per oz., and silver is worth 5s. 6d. an oz., what would be the weight of a 15s. piece, containing 92.5 per cent. of value pure gold, and the rest silver?

37. What would be the weight of the piece in the above question if '92.5 per cent. of weight' be substituted for '92.5 per cent. of value?'

38. A ship worth £8100 being entirely lost, of which belonged to A, to B, and the rest to C; what loss will each partner sustain, supposing the property to be insured up to 60 p. c. of its value?

39. If the population of a country increased from 2,800,000 to 3,500,000 in 3 years, what is the rate of increase p. c. per ann. ?

40. What percentage of 32 is the square root of that number?

41. What was the original population of an island, which was reduced 40 p. c. in 1 years by a plague carrying off 25 inhabitants on an average per week?

42. A sample of bone dressing was found to contain 15.83 per cent. of sulphate of lime. Find the weight of sulphate in 108 tons of dressing.

43. In 1851 the population of a certain kingdom had increased from 1841 at the rate of 73.361818 p. c., and had reached 27,674,352; what was the population in 1841?

44. If a certain article weighing 24 cwt. contain 89 per cent. of copper and the remainder tin, what weight of tin does it contain?

45. A cask containing 2000 gallons of gin leaked to the extent of 27 per cent.; how much gin remained in the cask?

46. Express in decimal form per cent., 23 per cent., and 5 per cent.

47. If out of a school of 150 children, 7 p. c. are up to Standard VI., and 11 p. c. up to Standard v., how many children are below these two standards?

48. Write in a decimal form 1, 12, 21, 3, and 43 per cent.

49. If iron ore produces 39 p. c. of pure metal, how much ore will be required to yield material for nine 35-ton guns, and 10,467 shells each weighing cwt.?

50. The population of a parish is 2000, of which 3 are males, *175 females, and the rest children. Find the number of each class, and the percentage of each class in the parish.

51. A town contains a population of 5005 persons, of whom

2 ought to be at school; if 819 only are present, what is the percentage of truants?

52. X, Y, and Z each laid out £9019 in railway stock; X gained 50 p. c., Y lost 75 p. c., Z gained 96 p. c.: what sum had each then got?

53. In a school of 1000 children, 24 p. c. are presented for examination in grammar, and of these 26'6 p. c. fail; how many children passed?

54. I bought 15 dozen of wine, 2 of it at 29s. a dozen, ·6 of it at 375. a dozen, and the remainder at 40s. a dozen; how much more per cent. had I to pay than if I had been charged 335. 4d. a dozen all round?

55. The standard height for enlistment being 5 feet 5 inches, out of 1950 recruits 748 were under 5 feet 6 inches, 500 between 5 feet 6 inches and 5 feet 7 inches, 429 between 5 feet 7 inches and 5 feet 10 inches, 273 were 5 feet 10 inches and upwards. What percentage of the recruits would have been rejected if the standard had been raised to 5 feet 7 inches, and what p. c. if to 5 feet 10 inches?

56. If a railway 11 miles long ascends 125 feet p. c. for 63 of its length, and descends 175 feet p. c. for the remainder, what is the difference of elevation between starting-point and terminus?

57. A, B, and C having a joint capital of £10,000, buy with 93 of it a ship and her cargo, the latter being worth of the former. The ship is lost, the cargo saved; what amount per cent. on his whole capital does each partner lose?

58. A flask contains of brandy and water; the owner drinks half of its contents, and then fills up the flask with water; he then drinks half again, and again fills up with water. What is the percentage of the brandy, and what is that of the water, after each dilution?

59. A contractor undertakes a job which will cost him £9000 to execute, but for which he is to be paid £10,986, subject to a forfeiture of 50 guineas for each day's delay beyond the term fixed for its completion; what percentage of his profits will a delay of 13 days cost him?

60. If, when 25 per cent. is lost in grinding wheat, a

country has to import ten million quarters, but can maintain itself on its own produce if only 5 per cent. be lost, find the quantity of wheat grown in the country.

61. A man bought a Swiss watch bearing a duty of 25 per cent., and sold it at a loss of 5 per cent. Had he sold it for £3 more, he would then have cleared 1 per cent. of the bargain. What was the Swiss watchmaker's price?

62. Certain goods were sold at £126, realizing a profit of 22 92682 per cent.; what was their prime cost?

63. If the increase in the number of male and female convicts be 18 per cent., while the decrease in the number of males alone is 46 per cent., and the increase in the number of females is 9.8 per cent., compare the number of male and female convicts respectively?

64. There are in a school 52 boys, 38 girls, and 58 infants; what is the percentage of each? If the infants were separated off, what would be the percentage of girls in the school?

65. A school consists of 97 boys, 108 girls, and 145 infants; how many children are assembled on a day when there are only 18 p. c. absent?

66. If, in composition, the letter e occurs 8.5 per cent. of all the alphabet put together, how many of that letter will be required to print a book containing 500 pages, each page with 30 lines, averaging 11 words of 4 letters in each line?

67. A school has 500 children on the books, but the average attendance is 23 per cent. below that number; how many children are present when the attendance is only 94 per cent. of the average?

68. If gold be worth £3, 17s. 6d. per oz., and silver be worth 4s. 2d. per oz., what percentage in value of gold, and what of silver, will go to make up a statuette consisting of 10 parts silver and one part gold?

69. There sailed in an emigrant ship 280 men, of that number of women, and half as many children as men and women reckoned together; what percentage of men, of women. and of children were on board?

70. There are 3 schools-one of 500 children, another of 600 children, and a third of 900 children. Of the first, 12

per cent. are generally absent; of the second, 17'5; and of the third, 175. What is the average attendance in each ?

71. A man, having a fortune of £5000, spends 46 of the money in the purchase of two houses. The larger house, which cost half as much again as the smaller one, was burnt down; what percentage of his whole fortune did he lose by

the fire?

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72. In a borough returning 2 members, and having a population of 30,000, of whom have votes, A polls 100 plumpers and 840 split votes, B 200 plumpers and 890 split votes, and C 110 plumpers and 730 split votes; what percentage of those who had votes gave them?

73. 100 gallons of liquid contain 70 per cent. wine and the rest water; how much wine should be added to raise the strength of the wine to 80 per cent. of the whole ?

74. A newspaper contains 48 columns, averaging 100 lines in each, 8 words in each line, 44 letters in each word; what number of consonant letters will be required to print the paper if the vowels are 35 per cent.?

75. If the penny-a-mile railway fare be 40 per cent. below 2d class fare, and the 2d class 30 per cent. below the 1st, and if return tickets are issued at a fare and three-quarters, what ought to be the exact price of a return ticket, 1st class, for 250 miles ?

76. In a common school for 3 hamlets A, B, C, 60 per cent. of the scholars belong to A, 28.8 per cent. to B, and 11'i (only 7 boys and 3 girls) to C; what is the number of children in the school, and what number belong to A, B, C respectively?

77. Two bottles of sherry and six pints of ale cost 125. If the price of the sherry rose 10 per cent., and that of the ale 50 per cent., the cost would be 145. What was the original price of a bottle of sherry and of a pint of ale?

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78. A contributes £9350 to a fund of £30,000, B £740911, C £32841, and D the remainder; what is the average sum contributed by the last three, and what annual percentage of profit does the largest contributor receive if he gets £497, 16s. 31d. a year?

79. 260 children were presented for examination in a school,