49. Explain the nature of 'Stock'-(1) If the three per cents. are at 89, what should be the price of the three and a-half per cents.? If the latter are at 104, which is the better investment? What dividend will a man receive who invests £3107 in each? PERCENTAGES. 1. How much p. c. is 7 of 16, 69 of 300, 187.98 of 56.394? 2. In standard gold, 11 parts out of 12 are pure gold; what percentage is there of alloy? 3. The former population of a parish was 1775, now it is 1917; what has been the increase per cent. ? 4. The population of a town in 1857 was 15,786, and in 1877 it was 19,670; what was the increase per cent.? 5. How much per cent. is (a) 2d. in the shilling, and (¿) 2s. 9d. in the ? 6. What is the percentage on 378 at 5, at 17:5, at 20625, and at 3? 7. A cask of rum containing 78 galls. leaked 29 p. c.; what quantity remained in the cask? 8. What number does 7.875 p. c. on a million and threequarters amount to? 9. A clock goes '04 p. c. too fast; how much will it gain in a day? 10. How often will a tumbler containing 1 of a gill be filled out of a cask which originally contained 20 galls., but had leaked 10 p. c.? 11. If 113 galls. of spirits be diluted with 37 galls. of water, what are the percentages of spirit and water? 12. If a tradesman takes off 91 p. c. for ready money payment, what should he be willing to accept down for a bill of £81, 5s.? 13. Find the percentage of each ingredient, and the quantity of each ingredient, in 11 cwts. of adulterated coffee, each pound of which contains 3 ozs. of chicory. 14. A gardener sows a drill 44 yards in length with a quart of peas; the plant fails partly, and on transplanting he finds that he has a row of only 108 feet long: what does he lose per cent. ? 15. If in a school of 360 children, 27 play truant, and 63 are sick, what percentage of non-attendance is due to truancy and to sickness respectively? 16. If the duty on an article be in 5 consecutive years 1993, 20, 17:5, 23'1, and 186 p. c., what is the average yearly duty per cent. ? 17. If 1185 parts of copper be added to 715 parts of tin and 100 parts of zinc, what is the percentage of each metal in the compound? 18. The population of a country amounts to 26,584,000, and increases at the rate of 10 p. c. in every 10 years; what will it amount to in 30 years? 19. If the population of the globe be eleven hundred millions of souls, and 3,300,000 of these be Jews, 172,700,000 Mahometans, 337,700,000 Christians, what is the percentage of each? 20. Between 1821 and 1831 the population of a certain town increased by 24 p. C., and in the last-named year amounted to 62,093 ; what was the population in 1821 ? 21. A grocer uses for a lb. weight one which weighs only 1575 Ozs. ; to what extent per cent. are his customers defrauded? 22. Find the percentage of alloy in sterling gold, if 10} dwt. contain 21 grains of alloy. 23. What percentage of 89 is '056, and what percentage of the square root of '04 is the of 19? 24. An army consists of a number of men equal to the quotient of 72 by ‘0045; what percentage of men may be killed so as still to leave a number equal to the square root of 225 millions ? 25. The annual consumption of meat in the United Kingdom being 33,697,785 cwt., what amount of saving would be effected to the community by a reduction of 24d. per lb., and what percentage would be saved by such reduction if we take the present average price of meat 91d.? 26. A certain officer has a salary of £1250 per ann. ; what is the salary of his chief clerk, which is 44 p. c. of his own? The junior clerk's salary is 78 p. c. of the senior's; what is the junior's salary per week? 27. In 1878 the number of deaths in a certain kingdom was 391,369; the decrease per cent. was 8.18103 from the preceding year: what was the number of deaths in 1877? 28. A cubic boiler half full of boiling water contains 500 cub. in. of steam; if the water be boiled down to a depth of only 298 in., what percentage of the cubical space of the boiler will be occupied by steam? 29. I bought 5 cwt 3 qrs. 14 lbs. for £9, 8s., and sold them for £11, 18s. 11d.; what was the percentage of gain, and what the gain per cwt. ? 30. (a) If 50 quarters of wheat sell for 77s. 8d. per quarter, and 100 quarters for 78s. 3d. per quarter, what is the average price per bushel? (b) If the population of Great Britain in 1851 was 21,121,967, and the increase during the preceding half-century was 93°47 p. c., what was the population in 1801? 31. Out of 360 children in a mixed school, 29.16 p. c. are girls, 333 p. c. boys, and the remainder infants. On a certain day of each are present; how many boys, girls, and infants respectively are registered? 32. 5 per cent. on a given sum yields £377083; give 51 per cent. on half that sum in £ s. D. 33. If the ton be diminished 10714285 per cent., and the ounce avoirdupois be increased 25 per cent., how many lbs. would there be in a ton? 34. John had 3s., and gave away 1d.; William had 4s. 8d., and gave away 31d.: how much more per cent. of his money did the latter give than the former? 35. People sometimes speak of an acre as 70 yards square. What percentage of error is involved in this assumption, and what amount of error would arise in calculating the area of Ireland (32,000 square miles)? 36. If pure gold is worth £4, 5s. per oz., and silver is worth 5s. 6d. an oz., what would be the weight of a 15s. piece, containing 92.5 per cent. of value pure gold, and the rest silver? 37. What would be the weight of the piece in the above question if '925 per cent. of weight' be substituted for '92.5 per cent. of value? 38. A ship worth £8100 being entirely lost, of which belonged to A, to B, and the rest to C; what loss will each partner sustain, supposing the property to be insured up to 60 p. c. of its value? 39. If the population of a country increased from 2,800,000 to 3,500,000 in 31 years, what is the rate of increase p. c. per ann. ? 40. What percentage of 32 is the square root of that number? 41. What was the original population of an island, which was reduced 40 p. c. in 1 years by a plague carrying off 25 inhabitants on an average per week? 42. A sample of bone dressing was found to contain 15.83 per cent. of sulphate of lime. Find the weight of sulphate in 108 tons of dressing. 43. In 1851 the population of a certain kingdom had increased from 1841 at the rate of 73.361818 p. c., and had reached 27,674,352; what was the population in 1841? 44. If a certain article weighing 24 cwt. contain 89 per cent. of copper and the remainder tin, what weight of tin does it contain? 45. A cask containing 2000 gallons of gin leaked to the extent of 27 per cent. ; how much gin remained in the cask? per cent., 2 per cent., and 46. Express in decimal form 5 per cent. 47. If out of a school of 150 children, 7 p. c. are up to Standard VI., and 11 p. c. up to Standard v., how many children are below these two standards? 48. Write in a decimal form 1, 1, 2, 3, and 4 per cent. 49. If iron ore produces 39 p. c. of pure metal, how much ore will be required to yield material for nine 35-ton guns, and 10,467 shells each weighing cwt.? 50. The population of a parish is 2000, of which 3 are males, *175 females, and the rest children. Find the number of each class, and the percentage of each class in the parish. 51. A town contains a population of 5005 persons, of whom ought to be at school; if 819 only are present, what is the percentage of truants? 52. X, Y, and Z each laid out £9019 in railway stock; X gained 50 p. c., Y lost 75 p. c., Z 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 29s. 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 125 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 former. 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 |