5. If 23 tons 8 cwt. 2 qr. 8 lb. can be carried 196 miles for £19 2s. 8d., how much should be charged for taking 27 tons 2 cwt. 150 miles? 6. If 2 clerks working 7 hours a day can copy 630 pages of 35 lines each in 14 days, how many lines must there be in a page if 10 clerks working 9 hours a day can copy 7560 pages in 24 days? 7. If provisions for 155 persons for 48 days cost £325 10s., how long will £173 5s. maintain 132 persons? 8. The carpet of a room being 27 inches wide and 3s. 8d. a yard, costs £11 11s. Find the cost of a carpet 36 inches wide, at 3s. 4d. a yard. 9. If the 4 lb. loaf cost 7d. when wheat is 42s. the quarter, what should be the weight of a twopenny loaf when wheat is 48s. the quarter ? 10. Supposing that 5 colonial labourers are equivalent to 4 English, when working for the same time, and that the former are paid 10s. per day of 7 working hours, while the latter receive 4s. 6d. per day of 10 hours; what would be paid in the colony for work which would cost £346 10s. in England? 11. If in walking 10 miles in 3 hours, 11 steps are taken in 6 seconds, how many steps as long must be taken per minute in order to walk 14 miles in 5 hours? 12. A man completes a journey of 540 miles in 15 days, travelling 8 hours a day. In how many days would he perform a journey of 945 miles, travelling 10 hours a day, at the same rate? MISCELLANEOUS EXAMPLES ON CHAPTERS III. IV. V. 1. Find the L. C. M. of 18, 22, 110, 3, 72, 88; and the G. C. M. of 5489 and 46407. 2. Find the values of (i.) ++25+37; (ii.) 31 −4} +10−7+51; 3-2 ; (iv.) of 23 of 18 of of £1 4s. 81+4 (iii.) 3. Reduce to their lowest terms 3098 and 1557 4. .5135. 3600 1903 Find the fractions equivalent to the decimals 0375, 2·032, and 5. Reduce to decimals 13, 17, and find the values of 8÷04; 80÷ 18592) 04; 008÷40; 008÷004. 6. Reduce £3 15s. 61d. to the fraction of £5, and find the value of 13 of 17 cwt. 3 qr. 8 lb. 12 oz. 7. If a steam-boat move 30 feet forward for each revolution of the paddle wheels, how many revolutions per minute will be required for it to go 270 miles in 24 hours? 8. What is the cost of 43 yards 2 feet 6 inches of oilcloth at 4s. 6d. per yard ? 9. Find the G. C. M. of 18315 and 26730, and the L. C. M. of 18, 24, 192, 72, 60. 10. Add together 23, 4, 6, 1, and from this sum subtract 333 Reduce 311, 11, to decimals, and 1∙1875, ·6297 to fractions. 249480 13. Multiply 19-23 by 0024 and divide the product by 720. 14. Find what fraction 2s. 3d. is of £10, and find the value of 34 of 1 ton 18 cwt. 1 qr. 15. Express 2d. as the decimal of £100, and find the value of 7825 of 12s. 6d. 16. What quantity of oats at 3s. a bushel would pay for half a mile of draining pipes, each pipe being 16 inches in length, and the price £1 5s. per 100 ? 17. After paying a tax of 7d. in the £ on his income, a gentleman lays by of the remainder and spends £5 16s. 6d. a week. What is his gross annual income? (1 year=52 weeks.) 18. Find the value of 6 acres 2 roods 20 perches at £2 5s. 6d. per acre. 19. If by working 9 hours a day 8 men can earn £450 in 25 weeks, how many men must work 8 hours to earn £120 in 4 weeks? 20. Find the G. C. M. of 26400 and 5104, and the L. C. M. of 24, 15, 8, 45, 36. 21. 2048, and 58764 1900 2250' 80004 Reduce to their lowest terms 475 22. Find by Practice the value of 3 tons 5 cwt. 2 qr. 12 lb. at £16 16s. per ton, and obtain the same result by Rule of Three. 23. Add together 4, 3, 13, 61, 1, and reduce to fractions 4.93, .17.106039. 24. A father being 38 years of age and his son 6, how long will it be before the son is half the age of his father? 25. A grandfather is 78 and his grandson 18 years of age. Find how long ago the grandfather was 5 times as old as his grandson, and also what was the age of the latter when the grandfather was 877 times as old. 26. A winding road up a mountain has a uniform rise of 220 feet in a mile, and the cost of making it is 4s. 6d. per linear yard; what would be the expense of carrying it to a height of 2000 feet? 27. Find the value of 213 of 23 bushels 1 peck 1 gallon, and reduce 8 dwt. 12 gr. to the fraction of 3 lb. troy. 28. Find the area of a room 18 ft. 9 in. long, and 13 ft. 9 in. wide, the number of yards of carpet 2 ft. 1 in. in width necessary to cover it, and the cost of the carpet at 2s. 8d. per yard. 29. Find the value of 08375 of 7 cwt. and reduce 16 lb. 10 oz. to the decimal of a ton. 30. Multiply 14-17378048 by '0088191. 31. A rod of brickwork being 2721 square yards 14 inches thick, how many bricks 9 inches long, 4 inches broad, and 2 inches thick would it contain, supposing that the mortar occupied space of the work? of the whole 32. The gas burned in a house between Sep. 29 and Dec. 31 costs 19s. 4 d. at 48. 2d. per 1000 feet. What is the average daily consumption? 33. A father leaves his money to his eldest son, as much to his second son, and £500 each to his two daughters. What does he leave altogether? 34. What will be the cost of 3-025 at 31d. per lb. ? 1+2.0625 40 of 1.03 of 3 qr. 4 lb. of sugar 35. What is the value of a silver cup weighing 13 oz. 3 dwt. 18 gr. at 5s. 4d. per oz. ? 36. The carpet for a room 21 ft. 6 in. long and 17 ft. 11 in. wide costs 5 times as much as the paper, and its width is 1, and its cost per yard 121⁄2 times that of the paper. Find the height of the room. 37. Find the value of 285714 of £3 + ·629 of 9s. +7.342 of 2s. 6d., and reduce the result to the decimal of 2 of £5 2s. 3d. 38. Multiply £14 3s. 2d. by 2.065, and divide 2 miles 1 furlong 140 yards by 1.2125. 39. There are two competing lines of omnibuses along the same road. The first consists of 20 omnibuses, each making the double journey 5 times in a day, and taking on the average 9s. each way. The second consists of 15, going and returning 6 times in a day, and taking an average of 7s. 6d. The profits of the second line, which are of the total receipts, are of the profits of the first line. What fraction of the receipts of the first line are profits? 40. The ratio of the circumference to the diameter of a circle is the value of this ratio correct to 6 places of decimals. 41. If 17 acres 3 roods 800 yards cost £72 5s. 2d., what will be the price of 2 roods 15 perches? 42. A clock is 5 minutes slow at 10 P.M. Sep. 27, and 4·148 minutes fast at 20 minutes to 7 P.M. Oct. 4. At what time was the clock exactly right, and what would be the true time when the clock indicated 5 br. 36 m. 5 sec. A.M. on Oct. 6? 43. If 2875 of a pint of oil is worth 1.509375d., what should be given for 9 gallons? 44. Reduce 0325 × 1.6 ·25-0173 ⚫3693 = to a decimal. 45. Find the value of ⚫5303 × 3·428571 × ·625 × 2·43902 × ·846153 × 4.1 of 1 mile 5 fur. 46. Find, without calculating the decimals themselves, the numbers of non-circulating and circulating figures in the decimals equivalent to the 3 lb. troy. 17 days 1 min. 21 sec. following fractions: 11 lb. av. ; 41 years 14 wk. 3 days' ; 211 × 19 × 424 863 992 47. If 2 tons 3 cwt. 1 qr. 3 lb. of iron cost £6.925, how much may be bought for £•96? 48. If first, second, and third-class railway fares are in the propor tion of 9: 7:4; and 31, 43, and 67 passengers by each class respectively can go 25 miles for £22 1s. 8d., how far can 11 first-class, 27 second-class, and 53 third-class go for £31 15s. 5d.? 49. Find the value of the infinite series 2+1+ ' 2 x 3 x 4 x 5 + &c. correct to 6 places of decimals. 1 1 + 2 x 3 2 x 3 x 4 + 50. A certain weight less than 27 cwt. when expressed as a decimal of that quantity has 4 decimal places, and when expressed as the decimal of 68 cwt. has 2, there being in neither case any circulating period. Find what the weight must be. 117 CHAPTER VI. INTEREST, STOCKS, AND EXCHANGE. Interest is the price paid for the use of money for any given time. When interest is proportional both to the amount used, which is called the Principal, and the time for which it is used, it is called Simple Interest. To find how much interest is due in any particular case, we must therefore know what would be due on some fixed amount for some fixed time, and the question then becomes one of Compound Proportion. This fixed sum of money is by common consent £100, and the fixed time is 1 year, and interest at the rate of £4, £5, or £6 for this amount and this period is shortly termed interest at 4 per cent., 5 per cent., 6 per cent. respectively. Hence the question, 'What is the simple interest on £635 at 4 per cent. for 3 years?' is merely another and a shorter form of the question, 'If £4 be paid for the use of £100 for 1 year, how much should be paid for the use of £635 for 3 years?' By using compound proportion we obtain at once: In cases of this kind, where arithmetical principles are applied to determine practical questions of frequent occurrence, it is often convenient to have a general solution applicable to any special instance. Thus if R be considered to represent any rate per cent., T any time expressed in years or fractions of a year, and I the interest on any R P T PXRxT X = principal P, then I=x 1 100 1 100 whence is |