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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 i per cent of the bargain. What was the Swiss watchmaker's price?

62. Certain goods were sold at £12.6, 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 4:6 per cent., and the increase in the number of females is 98 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, 175. 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 goo children. Of the first, 12

9 13

per cent. are generally absent; of the second, 17'5; and of the third, 17°5. 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 ?

72. In a borough returning 2 members, and having a population of 30,000, of whom i 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, 8.1 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 ad class 30 per cent. below the ist, and if return tickets are issued at a fare and three-quarters, what ought to be the exact price of a return ticket, ist 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 uri (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 ?

78. A contributes £93501974 to a fund of £30,000, B £740977, C £3284, 35, 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. 3.d. a year?

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



and of these 30°369230 per cent. were in Standards iv. to vi. ; 17 children failed in the first three Standards, and the percentage of failures for the whole school was 10: how many children passed in Standards iv. to vi. ?

80. Out of an invading army of 62,000 men, 18:25 per cent. perished by fatigue and disease, 27.8 per cent. fell in action, and the remainder returned home safe; what percentage of the whole army escaped, and how many fell in action ?

81. What is the average height of 107 recruits, if 49 of them are 5 feet 6 inches high ; 37, 5 feet 7 inches ; 13, 5 feet 8} inches ; 6, 5 feet 10 inches; and 2, 6 feet high? And what percentage of them would have been rejected if the standard had been 5 feet 8 inches ?

82. A boy lost all his marbles but one on Monday; on Tuesday he won back within one of the number he lost the day before, and lost 5 per cent. on the two days' play : how many marbles had he to start with ?

83. Of five casks, containing each 150 gallons of rum, one leaked 45 per cent., another 34, the third 31, and the fourth 35 per cent., the fifth remained staunch; how inuch was left in the casks?

84. Sugar being composed of 49.856 per cent. of oxygen, 43*265 of carbon, and the rest of hydrogen, express in decimals the number of lbs. of each of those ingredients in a ton of sugar.

85. The goods on board a shipwrecked vessel were damaged 39 per cent., and the repairs of the vessel cost £7000. The ship herself was worth 11 times her freight, and the ship and freight together were worth £90,000. My share of her being or part, what money do I lose by the wreck?

86. Three candidates stand for a borough of 12,000 inhabitants, of whom is possess the elective franchise. A polls 3 p. C. of the whole population, B polls 15 p. c. of the electors, and C polls 20 p. c. of those who actually voted. Give the number polled by each candidate.

87. A farmer insured his crops at the rate of 6d. an acre, and calculated that the produce of his 55 acres would be worth £550. The value of the crops fell short of his estimate by 25 P. C.; what percentage on their actual value did he pay in insurance?

88. In the shipwrecks of 1861, 16 p. c. of the crews and passengers were lost; 13) P. c. were saved by life-boats; by rocket apparatus, 8 p. c.; by ships' boats, 62 p. c. ; by individuals, } p. C. If 864 lives were lost, how many were saved by each of the above means ?

89. A father bequeaths half of his property to his eldest son, } of it to his second, and of it to his youngest, but the sons went to law as to which of the three should have the remainder; what percentage of difference on the portion of each would be made by the decision of the court?

90. Two women in the habit of buying between them 120 oranges a day at 3d. a dozen, and selling them at 5 for 2d., club together, and one taking the best half sells them at 2 a penny, the other selling the remainder at 3 a penny. How much better off are they at the end of six days' traffic, and what percentage of increased profit do they make by the latter plan?

91. A boy playing at marbles lost in the first hour all he had, and got into debt for half a dozen more; in the second hour he gained double of all that he had lost in the first, and 40 p.c. besides of the number he started with, which, after he had paid his debt, increased his total store of marbles at the end of his play by 48 : what number had he to start with ?

92. The section of a telegraph cable is half an inch in diameter, the central wire is į of an inch in diameter, and there are four protecting wires of inch section embedded in

jo the hempen cable ; what percentage of the cable consists of metal, and what of hemp?

93. The proportion of unpaid letters to the whole number posted in a certain district was 8 p. C, and of the paid letters 29 P. c. carried more than one stamp, 20 p. c. a {d. stamp, and the remainder a id. stamp. How many were there posted with a penny stamp if the whole number of letters was 450,000 ?

PROPORTIONAL PARTS. 1. Divide 12,012 in the proportion of 2, 53, 54.

2. Divide 2856 into two parts in the proportion of 'ż and


3. Divide (a) £1 among 3 persons in the proportion of 3451, 2156, and 1113; or (o) a shilling among 5 persons in the proportion of 39, 91, 117, 156, 221.

4. Divide 5 guineas among George, John, and Henry, who respectively claim s, t, and }, so that they may have proportionate shares.

5. A field of grass is rented by 2 persons for £27; one keeps in it 15 oxen for 10 weeks, the other 21 oxen for 7 weeks : what rent must each pay?

6. Divide £153 among 5 persons in the proportion of the fractions }, , }, }, .

7. If the proportion of nitrogen in the air is 79 p. c., and of oxygen 20 p. c., what quantity of nitrogen and oxygen respectively will there be in an apartment containing 908,500 gallons of air?

8. Divide seven guineas among A and B so that B's share may be ii of A's. Give the answer in £ s. D.

9. A legacy of £2979, 16s. 3d. was left to four heirs, in the proportion of d, 3, 4, and respectively. Find the share of each.

10. Divide £177, 75. od. among four persons in the proportion of }, }, }, d.

11. Divide £11,000 among four persons, A, B, C, D, in the proportion of 4, }, , }

12. Divide 8o guineas among three persons, A, B, and C, so that their shares may be as 73, 103, 14} respectively.

13. Divide 8008 guineas among A and B so that '5 of A's money shall equal 6 of B's.

14. If gunpowder contains 76 p. c. of nitre, 9'5 p. c. of sulphur, and 14'5 p. c. of charcoal, what weights of nitre, sulphur, and charcoal severally will there be in 2 tons of gunpowder ?

15. A bankrupt surrenders his property, worth £336, to three creditors, to whom he owes respectively £450, £560, and £670. Divide the property fairly among them.

16. Find the value of •2615384 of £6, 1os., and divide it among three persons so that the ist shall have twice as much as the 2nd, and the 2nd twice as much as the 3rd.

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