i ought to be at school ; if 819 only are present, what is the percentage of truants ? 52. X, Y, and each laid out £9019 in railway stock; X gained 50 p. C., Y lost 75 p. C., 2 gained 96 p. c. : what sum had each then got? 53. In a school of 1000 children, 24 p. c. are presented for examination in grammar, and of these 26.6 p. c. fail; how many children passed ? 54. I bought 15 dozen of wine, '2 of it at 295. a dozen, 6 of it at 375. a dozen, and the remainder at 40s, a dozen; how much more per cent. had I to pay than if I had been charged 335. 4d. a dozen all round? 55. The standard height for enlistment being 5 feet 5 inches, out of 1950 recruits 748 were under 5 feet 6 inches, 500 between 5 feet 6 inches and 5 feet 7 inches, 429 between 5 feet 7 inches and 5 feet 10 inches, 273 were 5 feet 10 inches and upwards. What percentage of the recruits would have been rejected if the standard had been raised to 5 feet 7 inches, and what p. c. if to 5 feet 10 inches ? 56. If a railway 11 miles long ascends 1'25 feet p. c. for 63 of its length, and descends 175 feet p. c. for the remainder, what is the difference of elevation between starting-point and terminus ? 57. A, B, and C having a joint capital of £10,000, buy with 93 of it a ship and her cargo, the latter being worth of the fornier. The ship is lost, the cargo saved; what amount per cent. on his whole capital does each partner lose? 58. A flask contains of brandy and water ; the owner drinks half of its contents, and then fills up the flask with water; he then drinks half again, and again fills up with water. What is the percentage of the brandy, and what is that of the water, after each dilution ? 59. A contractor undertakes a job which will cost him £9000 to execute, but for which he is to be paid £10,986, subject to a forfeiture of 50 guineas for each day's delay beyond the term fixed for its completion; what percentage of his profits will a delay of 13 days cost him? 60. If, when 25 per cent. is lost in grinding wheat, a 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 1 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 maies alone is 4:6 per cent., and the increase in the number of females is 9-8 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 .!! the alphabet put together, how many of that letter will be Te quired 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 ch:dren are present when the attendance is only 94 per cent. f the average ? 68. If gold be worth £3, 175. 6d. per oz., and silver be Forth 45. 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, şof 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 2. (a) What is the yearly interest on £27,225 bought into the 31 p. c. at 973? (6) What is the annual interest on £1470 bought into the 2! p. c. at 75? 3. What sum invested in the 3} p. c. at 934 will produce £61, 5s. per annum? 4. Find the yearly income arising from the investment of £6040 in the 3 p. c. consols selling at 943 p. C 5. Find the yearly income from investing £3960 in railway stock standing at 103, and paying 54 p. c. (brokerage being & per cent.). 6. If a person invested in 4 p. c. stock at 773, at what rate per cent. will he receive interest for his money? 7. Which is the better stock for investment, the 31 p. c. at 925, or the 31 p. c. at par? 8. What must be the market value of 3 P. c. stock, so that, after deducting an income tax of rod. in the £, it may yield 3) per cent interest? 9. Find the selling price of the 3 p. C. consols, when an out. lay of £3020 produces a yearly income of £96. 10. Compare the incomes arising from £9855 invested in ? per cents. standing at go, and £10,201 invested in 34 p. c. standing at 101. 11. At what rate should money be invested in 34 p. c. to obtain (a) 3 and (6) 41 per cent interest for it? 12. If I give so part of my income to charity, what sum will be due from me to the charity six months after my investing £1958, 6s. 8d. in 31 per cents. standing at par? 13. What is my whole income from both my investments at Ahe end of the second year, if, having £22,500 in 35 p. C., at the end of the first year I invest the interest of that sum in 10 p. C. stock at par? 14. When a 31 p. c. stock is at 93, find what price a 4} p. c. stock must be at in order that an investment may be made with equal advantage in either stock. 15. How much stock can be purchased for £3116, 55. in the 3) p. C. standing at 103}, and what income will it yield ? 16. I sold out of the 3 p. c. at 96, and invested the sum accruing in railway 5 p. c. stock, thereby increasing my income 50 p. c.; what was the price of the railway stock? 17. What must be the market value of 3 p. c. stock in order that, after deducting income tax of 7d. in the £, it may yield 3 per cent interest? 18. What is the yearly interest on £76,978 bought into the 3. p. c. at 77? What sum would be gained by selling out at 773? 19. How much must a 3} P. C. stock fall below par in order that a broker, charging $ p. c. fees, may get 4. p. c. interest for my money? 20. If a man receives 43 p. c. interest on his capital by investing in the 3} p. c., what is the price of stock, and how much stock can be bought for £1200 ? 21. If I transfer £2000 stock from the 3. p. c. at 99 to the 3 p. c. at 365, what is the difference in my income? 22. What sum mușt a person have invested in the 3 p. c. at 90, if a transfer of of his capital to the 4 p. c. at 115 would increase his income £7? 23. What percentage and what amount of interest will an investor receive, who puts his capital (£19,500) into the 3 p. c. standing at 89%, commission being per cent. ? 24 How much money will be required to purchase £8621, 1os. 5d. stock in the 3 p. c. standing 875, and what income will the purchaser receive? 25. A man invests £9600 in the 4 p. c. at 80, and at the end of each year invests the dividend which becomes due in the same stock. Find his dividend at the end of the third year, the funds remaining all the time at 80. 26. Find the simple interest for 7 years on £10,416, 135. 4d. of stock sold out when standing at 96, and the resulting sum invested in 51 p. c. debentures at par. 27. The value of money increases from 4 p. c. to 5 p. c.; supposing this to have a corresponding influence on the funds, how much ought the 3 p. c. consols to fall? 28. A capitalist invests £5187, 1os. in the 3 p. c. at 83; he transfers of this sum to the 4 p. c. at 96. Find the alteration in his income. 29. Two persons buy respectively with the same sums of money into the 3 and into the 33 per cents., and get the same amount of interest, the 3 per cents. standing at 75 ; what do the 3 per cents. stand at? market, he sells it at 120 per cent profit, receiving for it the same gross sum as is received by another dealer who purchased a sound cargo and sells it for 32 per cent. profit; find the value of the second cargo. 81. A man buys a house for £450, keeps it empty for 12 months, and then sells it so as to gain 15 per cent. ; would he have done better or worse if he had let it for the last 8 months out of the twelve at 8 guineas a month, and sold it for cost price at the year's end ? 82. A woman buys a certain number of eggs at 22 for a shilling, and the same number at 18 for a shilling, mixes them and sells at 20 a shilling ; how much does she gain or lose by the sale of eggs which cost her £1, 135. 4d. ? 83. Bought a quantity of quills at 4s. 7d. a hundred, and sold them so as to gain three-eighths of the selling price; what was the selling price, and what was the profit per cent. on the cost price? 84. A man sold a quantity of snuff for £50, and by so doing lost 33 per cent. ; what sum should he have sold it for to get 210 times what he had given for it? 85. A bookseller bought 85 dozens of books at is. 8d. per book, 61 dozens at as: 7d. per book, and 94 books at 325. 6d. per dozen; at what price per book, on an average, must he sell in order to gain 10 p. c on the whole transaction ? 86. A speculator buys shares when they are at 191, £15 having been paid up, and sells them again at £32, 95. when £,25 has been paid up; how much per cent. does he gain or lose ? 87. A dealer buys 80 tons of coals, and, after selling them again at is. 6d. per sack, finds he has gained £4. Had he sold them at is. 4d. per sack he would have lost £6. Find the cost price per ton, and the weight of a sack of coals. 88. A dealer lost a sum equivalent to 9} per cent on the sale of goods which cost him £3, 198. 2d., but gained a sum equal to 9% per cent. on a lot which cost him £7, 1os.; how much per cent. had he gained or lost at the end of both transactions ? 89. A merchant sells 72 qrs. of grain at a profit of 8 per cent., and 37 qrs. at a profit of 12 per cent. ; but if he had a |