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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 i} p. c. per ann. of the deaths are due to disease, is to old age, i 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, ros. for a year, and G £3180 for 7 months. They clear £350 ; what is each partner's share of the gain ?

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 21 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 13:11:14 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 £1ooo 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 7}d. was divided among A, B, and C in such proportions that A received 1 d. 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. 8fd. among A, B, C, D, so that A's share may be of D's, C's share io 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 2.

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 p. C. per ann. respectively, shall all be equal.

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 ļ (A), } (B), 1 (C), đ (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 most be paid yearly on an insurance for £9626, 115. 3d., at £2, 125. p. c.?

2. An agent gets £45, 125. 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?

4. A shipowner, insuring a certain steamer for £17,000, paid as insurance 24 guineas p. c., policy £t p. C., brokerage £? Y. C., commission £1} p. c. She received damage to the extent of £3750. What sum should the shipowner recover, after deducting expenses of insurance, and allowing 2 p. c. discount on the damage?

SQUARE ROOT.
Find the square root of:

1. 50,0 13,184.
2. 1'094116 and of 585.
3. 8 and 17: to four places of decimals.
4. N 53111.8116+201.
5. What fraction of v z] is v.04?

CUBE ROOT.
Extract the cube root of :-

1. 2000.
2. 357,911 ; or of 91125; or of 3727.

MISCELLANEOUS EXAMPLES. 1. If £1=10 florins = 100 cents = 1000 mils, express £37, 155. 7.d. in this coinage. What is the difference between a farthing and a mil?

2. A mechanic, paid at the rate of 5d. per hour, does 7 hours' work on Monday, 11 on Tuesday, 9. on Wednesday, and 11) on Thursday; what are his average earnings per day?

3. What would che mechanic in the last question have gained or lost per cent. if he had worked regularly 101 hours a day?

4. A ship has five masts, the height of one 72 ft., of two others 63 ft., of the fourth 42 ft. ; what is the height of the fifth mast, if the average height of the five is 58 ft. ?

5. An oblong apartment, 18 ft. longer than broad, measures 104 ft. in circuit; find its length and breadth.

6. A mixture of 49 gallons of wine (at 15s.) and brandy (at 18s.) contains only i gallon of brandy; how much water should be added to it that it may contain in each 49 gallons '2 of a gall. of brandy, and what should be the price per gallon of the whole mixture?

7. What fraction of £213,921 is the simple interest of £7506, for 74 years at 4i per cent. ?

8. If Australian wool is worth 25. 3d. per lb., and English wool only is. 8d. per lb., how many feeces of English wool ought to be set off against 1000 Australian, a fleece of the latter weighing only 15 of a fleece of the former?

9. On 15 different occasions I was entrusted with £1000, and directed to pay out of it £49, 135. 9d., retaining as my remuneration the difference between 8 and 8 per cent. on the remainder; how much did I receive for my services?

10. A clock goes at the rate of os per cent. too fast for 9 months, is re-set and loses at the same rate for 3 months ; how much would it have gained or lost at the end of a year of 365 days?

11. A man invests half his fortune in land, a fifth in trade, a sixth in funds, and loses the remainder (viz. £2000) in speculation ; what sum had he to start with?

12. An Australian miner has soo lbs. of gold dust; 8 p. c. of this is alloy beyond the standard, and coining it into sovereigns costs him 5 p. c. : what is its value, the sovereign weighing 122'274 grs.?

13. A certain pudding consists of 3 parts of raisins at 6d. a pound, 4 parts of suet at 8d. a pound, and 2 parts of flour at 3d. a pound, and it costs altogether 75. ; what was the cost of each of the ingredients ?

14. In a gale a flagstaff 20 yards high standing on level ground snaps 28.8 feet from the bottom, and the upper portion not being wholly broken off, the top touches the ground. How far is its point of contact with the ground from the bottom of the staff?

15. A certain number is divided into two parts, such that 10 times the first added to 18 times the second gives 15 times the entire number; what fraction of the whole is each of these parts?

16. What is meant by the ‘reciprocal' of a number? What fraction divided by its reciprocal gives the quotient=145?

17. What is the total, and what the average value, of 11,328 articles, for } of which I pay at the rate of 3 of 7s. 6d. each, for

at the rate of •3 of 75. 6d., and for 4 at the rate of 'oz of

75. 6d. ?

18. What is the smallest alteration of the number 831,600 which, either by addition or subtraction, will make it a perfect cube?

19. A starts on Monday, and walks 10 miles a day due south ; B starts from the same place on Tuesday, and walks 20 miles a day due west. How far apart will A and B be on Wednesday night?

20. Four talents are calculated as equivalent to 375 lbs. avoirdupois, and each talent contains 3000 shekels. Find the weight of a shekel, and the value of a talent at the rate of £3:89375 per oz

21. No. 1585 of a weekly publication came out on the 13th of March 1879; when did No. 1 appear?

22. Incomes below £150 being subject to income tax of 5d. in the £, and incomes above £150 to a tax of 7d., find what income above £150 a man must have to be just 7d. a year poorer than the man with £149, 1os. a year.

23. Find the cost of papering a room 12 feet 4 inches high, 16 feet long, and 14 feet 3 inches wide, the paper being 2 feet 6 inches wide, at 3s. 6d. a yard, and the labour charged at d. per square foot.

24. If a four-oared boat cost £50, what would a six-oared boat cost, on the supposition that the expense of setting up a boat is proportionate to the square of the number of oars, and which would cost least per head?

25. English money bearing a premium of 5 p. c. in the United States, how much sterling should be given for 750 dollars, each worth 45. 6d. at par?

26. A woman sold 7 dozen apples for 6s. 2d. ; some at the rate of 3 for 2}d., and the rest at 8 for 6}d. How many at each rate?

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