27. The difference of two numbers is 477 it, and one of them is to the other as of 23 of 1'53 is to 51} of 4+. 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 £1=10 florins = 100 cents = 1000 mils, find the value in our present coinage of £1, 8 florins 7 cents 5 miis. 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 3 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 froin 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 3'1416 times its diameter, what is the mean number of revolutions made by tie 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 91'5 (French) centimetres. State in decimals of a yard the average length of four sticks, one measuring 113'501, another 78.073, the third 29'034, 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 £287'095. 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 124, 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 3p. 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, 10s. 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 11? 43. Find the value in English money of goods sold for 6347 francs 30 centimes, the exchange being 25 francs 35 centimes for £I. 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? a 46. Two dozen of port and 16 bottles of sherry were bought for two equal sums of money. If the quantities of the wines had been reversed, the sherry would have cost £3 more than the port. What was the price of each wine per bottle? 47. An upholsterer bought 4 bales of carpeting, the first containing 1 piece of 12 yards, at 6s. 2d. a yard ; the second, 8 pieces of 19 yards, at 2s. 6d. a yard; the third, 3 pieces of 29 yards, at 35. 4d. a yard; the fourth, 8 pieces of 30 yards, at 5s. id. a yard. What was the average length of the pieces of carpet, and what the average cost price per yard all round? 48. Find the difference between the amount of £250 in two years at 3 p. c. per ann., at simple and compound interest, and divide it among two persons in the ratio of 9 to 5. 49. The circumference of a wheel being 3-14159 times its diameter, what would be the amount of error in calculating the distance in which a wheel, iş yards across, could turn 1000 times if the circumference were taken roughly at three times the diameter ? 50. A, B, and C, on an expedition, fall short of provisions. A has 5 threepenny loaves left, B has 3, and C none; they agree to share alike. What should C pay to A and to B respectively at their journey's end ? 51. A quantity of cloth at 35. 6d. a yard, and an equal quantity at 3s. 5 d. per English ell, cost me together £ 17, 105.; how many yards of each did I buy? 52. If a pig and seventeen rabbits cost £2, 11s. 3d., and the pig cost 8s. gd. more than the rabbits, what would each of the rabbits cost ? 53. (a) A, B, and C bought a patent, A taking }, B , and C paying £52, IS. 8d. for the remaining share. B received £2, 1os. per annum on his investment; what rate of interest was that per cent. ? (6) A begins business with a capital of £1600, and at the end of three months takes B into partnership, with a capital of £2000, and at the end of six months more they divide the profits, amounting to £660; what sum should each partner receive? 54. A tradesman starts with a capital of £6500, and makes an annual profit of 124 per cent. ; at what rate do his annual expenses increase if his capital only increases £100 a year, and what are his personal expenses the first year? 55. What is the difference between paying £1200 by four quarterly instalments of £300, each instalment before payment bearing interest at 6 p. c. per ann., and by two half-yearly payments of £600, each instalment bearing interest at 6 p. c.? 56. A steamer is 14 days on a voyage. For the first three days she makes 13 miles an hour; in the next six and a half days she improves upon that speed 17 p. C.; and for the remaining time she runs 390 miles in the 24 hours: what distance has she gone, and what was her average speed per hour? 57. A commission agent offers to take either 21 p. c. on the money passing through his hands, or of the net profit of his sales. The sales amount to £300,000, of which 35 p. C. produce no profit, but the remainder realize a profit of 10 p. c.; what difference will it make to the agent which of his offers his customers accept? 58. A and B together do a piece of work in 11 days; A and C together do the same piece of work in 9 days; and B and C together do it in 8 days: how long would it take each working alone? 59. Compare the relative advantages to the purchaser of the following mvestments :-A gas company guarantees £5 p. c. on shares of £100 each; a railway company offers 48 p. c. on shares of £7, 10s. each : the price of the former is £124, 10s., and of the latter £8, ios. 60. Standard gold being coined at the rate of £3, 175. 10!d. per ounce, what is the least number of ounces that can be coined into an exact number of sovereigns? 61. A man in machine mowing grass advances at the rate of 4 miles an hour; it takes him 72 minutes to do a plot of 4 10,560 sq. yds. : how broad does he now? 62. A steward receives for his landlord £1987 for rent, and spends } of it; he then pays over to the landlord £105, 12S., and invests the remainder in an estate at 30 years' purchase : find the rent yielded by the estate. : 63. If a decimal system of coinage was adopted in which the florin= £io, the cent = 1florin, the mil= of the cent, what decimal and what percentage would each of the new coins be of the existing coins of the nearest value, leaving the twoshilling piece out of calculation? 64. I require to have a sum of £10, 1os. ready at the end of 2 years; what sum must I lodge in a savings bank which will not receive fractions of a shilling, and gives 24 p. c. per ann. simple interest, in order to secure it, and what decimal of a penny will be due to me beyond the sum required ? 65. Two travellers, A and B, arrive at the corner of a rectangular lake. A goes to the opposite corner in a boat, a distance of i} miles; B walks along the shore of the lake, intending to rejoin him, and has to go a mile before he turns the end of the lake : how much farther has B to walk before he rejoins A? 66. A labourer in the fourteenth century received 4d. a day, and the price of meat was fd. per lb. ; at present he receives 25. 4d. a day, and meat is at 10d. per lb. : what fraction of his daily wage must each pay for 1 lb. of meat, and how many times more must one pay for it in proportion to his wages than the other? 67. If the national income and expenditure for the year are £75,000,000, exactly balancing each other, and a little war has cost the country £5,000,000 of the total sum expended in the year; what does that little war' cost me, if my income is £500 a year, and my taxes amount to 7 per cent. of it? 68. A general contracted to pay £5454 for 13,635 pairs of boots and shoes for his army. The price of each pair of shoes was to that of each pair of boots as 5 to 8, but the number of the pairs of shoes was to the number of the pairs of boots as 2 to 1; give the numbers and prices respectively of the pairs of the boots and shoes. 69. A and B each lend £10,000. A receives 5 p. c. per ann. interest, paid quarterly; B receives 5*125 p. c. per ann., paid yearly : how much richer is the one than the other at the end of the year? Give the answer to four places of decimals in the pence. 70. A man allows to his agent 5 P. c. on his gross rental for |