4. A shipowner, insuring a certain steamer for £17,000, paid as insurance 2 guineas p. c., policy £ p. c., brokerage £ v. 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. 50,013,184.

2. 1094116 and of 587.

3. 8 and 17 to four places of decimals.

MISCELLANEOUS EXAMPLES.

1. If £110 florins = 100 cents = 1000 mils, express £37, 15s. 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 the mechanic in the last question have gained or lost per cent. if he had worked regularly 10 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 1 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 7 years at 4 per cent. ?

8. If Australian wool is worth 25. 3d. per lb., and English wool only is. 8d. per lb., how many fleeces of English wool ought to be set off against 1000 Australian, a fleece of the latter weighing only 1 of a fleece of the former?

9. On 15 different occasions I was entrusted with £1000, and directed to pay out of it £49, 13s. 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 o8 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 100 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 7s.; 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=1?

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 7s. 6d., and for at the rate of oz of 7s. 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 £389375 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 7ąd. a year poorer than the man with £149, 10s. 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 4s. 6d. at par?

26. A woman sold 7 dozen apples for 6s. 2d.; some at the rate of 3 for 24d., and the rest at 8 for 6d. How many at each rate?

27. The difference of two numbers is 477, and one of them is to the other as of 23 of 153 is to 51 of 44. Find the numbers.

28. There are four pieces of cloth of equal length. From each of the first two if 27 yards be taken, and if 21 yards be cut off from each of the two others, the remnants taken together will be 104 yards; what was the length of the pieces at first?

29. If £110 florins = 100 cents = 1000 mils, find the value in our present coinage of £1, 8 florins 7 cents 5 mils. Point out any advantage which you think would arise from the adoption of a decimal coinage.

30. A young clerk is offered a salary of £50 a year, or of £35 a year with an increase of £2 per quarter. Compare the sums total of his earnings at the end of 5 years, according as he adopts one or the other alternative.

31. A and B can do a piece of work together in 4 hours, A and C together in 33 hours, B and C together in 5 hours. In what time will each do the work alone?

32. How many feet in 150 feet must a tramway 10,798 feet long, rise to be carried from a plain to a hill 463 feet in perpendicular height?

33. If the large wheel of a bicycle is 5 feet high, and the small one 15 inches, assuming the circumference of a circle to be 31416 times its diameter, what is the mean number of revolutions made by the wheels in travelling

mile?

34. Divide 100 guineas into an equal number of guineas, half-guineas, crowns, half-crowns, shillings, and sixpences, and reduce the remainder to the fraction of £1.

35. In return for 146 qrs. of wheat at 70s. per quarter, I received Wiltshire cheese at 88s. per cwt., and Cheddar at 6os. per cwt., obtaining 6 cwt. of Wilts for every 5 of Cheddar. How many cwts. of each cheese were received?

36. One (English) yard is equivalent to 915 (French) centimetres. State in decimals of a yard the average length of four sticks, one measuring 113'501, another 78.073, the third 29034, and the fourth 9.789 centimetres.

37. Find the average cost in £ s. D. of 5 houses, the first

F

costing £205785, the second £3909'73, the third £111195, the fourth £1000, and the fifth £287095.

38. Find the average age (in years) of the boys in a school of 25 boys, one of whom is 17 years old, two 16, four 151, one 14, five 13, ten 12, and two 10 years.

39. I paid £1, 11s. 8d. for 4 railway tickets-2 first-class, I second, and the fourth a half first-class for a child. The cost of a second-class ticket was two-thirds of that of the first. Find the price of each ticket.

40. (a) What is the average annual income of 5 persons, of whom A gets the interest of £15,520 in 3 p. c. at par, B 2s. 6d. a day, C a guinea a week, D 18 of £5 a calendar month, and E £1000 a year?

(b) If the income tax be 7d. in the the first half of the year, and 3d. only in the second, what is the net income of an individual whose gross income is £1542, 1os. 6d. ?

41. An estate in the Highlands contains 5 square miles, of which 1800 acres are under cultivation, yielding a rent of £1361, 5s. per annum; 1000 acres are moorland, let at 5s. 10 d. per acre; and the remainder is unproductive. What is the average income per acre derived from the estate?

42. Two couriers start at the same time from two places 280 miles apart; when will they meet on the road, if they travel towards each other, one at the rate of 9 miles an hour, and the other at the rate of II?

43. Find the value in English money of goods sold for 6347 francs 30 centimes, the exchange being 25 francs 35 centimes for £1.

44. A farmer had 50 couple of poultry-turkeys, ducks, and chickens. The turkeys were worth 15s. each, ducks 5s., chickens 2s. 6d. ; but he had the same value in money of each kind. How many birds of each description did he keep, and what was the value of his whole stock?

45. An army is in 3 divisions; of each consists of artillery,of each of cavalry, and the remainder of foot soldiers. The first division is twice as numerous as the second, and the second twice as numerous as the third, and in the second there are 1600 more cavalry than artillery. What is the number of the army?