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and of these 30769230 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 much 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 1 times her freight, and the ship and freight together were worth £90,000. My share of her being To part, what money do I lose by the wreck?

86. Three candidates stand for a borough of 12,000 inhabitants, of whom 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 of an inch in diameter, and there are four protecting wires of inch section embedded in 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. ad. stamp, and the remainder a 1d. 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, 5.

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

3. Divide (a) £1 among 3 persons in the proportion of 3451, 2156, and 1113; or (b) 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, 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,,,,t

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 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,,, and respectively. Find the share of each.

10. Divide £177, 7s. od. among four persons in the proportion of,, }, J.

11. Divide £11,000 among four persons, A, B, C, D, in the proportion of 1, 1, 1, 1.

12. Divide So guineas among three persons, A, B, and C, so that their shares may be as 73, 103, 143 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 145 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, 10s., and divide it among three persons so that the 1st shall have twice as much as the 2nd, and the 2nd twice as much as the 3rd.

17. A guinea is divided between A, B, and C. A's share is of B's, but it is also of B's and C's together; how was the guinea divided?

18. In a population of 85,000, the death-rate is 1 p. c. per ann. of the deaths are due to disease, to old age, to accidents, and the rest to unknown causes; how many deaths are attributable every year to each cause?

19. D and G enter into partnership, D putting in £587, 10s. for a year, and G £3180 for 7 months. £350; what is each partner's share of the gain?

They clear

20. Divide £11,875 among A, B, and C, so that as often as A gets £4, B shall get £3, and as often as B gets £6, C shall get £5.

21. A carries on a business for 3 months, when B joins him, and they both have, at the end of 6 months more, made a profit of £115. B's original capital having been † of A's, and A's capital having been 2 of the profits gained, how ought these profits to be divided between A and B?

22. A field of 7 acres is sown with turnips, beet, and cabbages, the area covered by the crops being respectively as 1: 1:14. If the value of an acre of each be also in the same ratio, and an acre of turnips is worth £7, what is the crop worth?

23. A and B enter into partnership, A contributing £500, and B £300; at the end of 9 months they take C as a partner, who brings £1000 into the business. The profits, £2000, being divided at the end of another 9 months, what share did each partner receive?

24. A legacy amounting to £1500 is left to 3 persons in the proportion of 1, 2, and 3. Find the sum received by each, after deducting 10 p. c. legacy duty.

25. The sum of 73d. was divided among A, B, and C in such proportions that A received 1d. more than C, and B 24d. less than C. Had a sovereign been divided among them in the same proportion, what would each have received?

26. Divide a legacy of £2375, 45. 2d. among a son, a wife, and a daughter, so that the son's share shall be three times the wife's, and the wife's three times the daughter's.

27. Divide 16s. 81d. among A, B, C, D, so that A's share

of D's, C's share

may be of A's, and B's share the sum of A's and C's. What should each receive?

28. Find the interest on £34,675 for 17 days at 5 p. c. per ann., and distribute that interest among 3 persons, A, B, and C, in the ratio of 1, 1, and 21.

29. A man makes his will that the first four legatees are to be paid in full before anything is given to the others. He bequeaths to A £3750, to B £3525, to C £3280, to D £2000, to E £1895, to F £1750, to G £1668, to H £1745, to K £1475, and to L 1067. The whole estate turns out to be worth £19,575; how should the money be distributed? 30. Divide £36, 8s. into four parts, so that their simple interests for 4, 6, 7, and 10 months, and at 3, 4, 5, and 6 per ann. respectively, shall all be equal.

P. c.

31. A bankrupt owes £2085, of which £235 is due to A, £325 to B, £525 to C, and the rest to D. How much must he pay in the that D's receipts may be what C's ought to have been, and how much will his other creditors have each to receive?

32. A sum of £4000 was bequeathed to four persons (A, B, C, D), but by an inadvertency in the will it was stated that they were to receive in the proportions (A), ₫ (B), † (C), † (D) of the whole sum respectively. How much should each receive, according to the spirit of the will?

33. A legacy of £2100 is to be divided among A, B, and C, in the proportion of 2, 3, and 7 respectively; how much will each receive, and what percentage will A's and B's shares together be of C's?

INSURANCE, COMMISSION, Etc.

1. What must be paid yearly on an insurance for £9626, 11s. 3d., at £2, 125. p. c.?

2. An agent gets £45, 12s. 6d. for selling goods at the rate of 2 p. c.; what value of goods did he sell?

3. An agent, collecting rents at a commission of 2 p. c., paid, after deducting his commission, £770, os. 1d.; what amount of rents did he collect?

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