175 MISCELLANEOUS EXAMPLES. 1. What decimal of a £ is £465, and what fraction of a shilling is .6258. ? 2. What fraction of a half-crown is 2ins. ? 3. What is the interest of £400 at 3) per cent. for 2 years and 39 days ? 4. What is the interest of £712 6s. for 8 months, at 7 per cent. ? 5. Required the price of 73 lbs. 5 oz. 15 dwt. of silver, at 58. 9d. per oz. 6. How much must be paid for the carriage of 8 cwt. 3 qrs. 7 lbs., if 10d. be charged for 1 stone of 14 lbs. ? 7. How many men will be sufficient to dig a trench 135 yards long in 8 days, when it is known that 16 men can dig 54 yards of it in 6 days? 8. What is the price of 7985 articles at 78. 104d. each? 9. What does the commission on £530 2s. 9d. amount to at 2s. 6d. per cent. ? 10. What is the worth of £4563 108. Bank Stock, at 1273 per cent. ? 11. If 5 cwt. 3 qr. 14 lbs. be bought for £9 88., and sold for £11 188. 11d., what is the gain per cent. ? 12. If the prime cost of an article be at the rate of £4 16s. per cwt., how much per cwt. must it be sold at to pro duce a gain of 15 per cent. ? 13. What sum of money will produce as much interest in 34 years as £210 38. will produce in 5 years and 5 months, at the same rate per cent. ? 14. At the battle of Bunker Hill, in America, the roar of the cannon was so distinct at Hanover, 120 miles distant, that business was for a time suspended there; how long was the sound in travelling ? 15. A cistern holding 400 gallons is supplied by a pipe at the rate of 7 gallons in 5 minutes, but a gallon leaks 3 minutes ; in what time will it be full ? 16. What is the least common multiple of 12, 26, 56, and 182 ? 17. At what time between 9 and 10 o'clock are the hour and minute hands of a watch exactly together? 18. Find the square-root of 29929, and the cube-root of 228099131. 5 19. Required the values of 378314 and 1 20. How long will it take to count a million, at the rate of 100 a minute, for 10 hours a day? 21. If 56 lbs. of bread be sufficient for 7 men 14 days, how much will serve 21 men 3 days? 22. Find the values of 733, 274, and 15719140625. 23. If oz. avoirdupois cost js., what will lb. cost? 24. How much Stock, at 111% per cent., can be purchased for £10000 ? 25. What decimal of 1 lb. avoirdupois is 7 drams? 26. What difference is there between the Banker's discount of £350, at 4 per cent., for 8 years, and the true discount of the same sum, for the same time, and at the same rate per cent. ? 27. For what sum must an insurance be effected, in order to cover a loss of £3500, together with the premium of £3 8s. per cent. ? 28. What is the interest of £51.425, at 4:125 per cent. ? 29. What sum of money will produce £•35 interest in 1 year, at 4 per cent. ? 30. A Bill of £170 was due August 12, and left unpaid till Sept. 18, when £54 was paid : the balance remained till Oct. 17, when £56 was paid; and, finally, the whole was settled Nov. 14: how much interest was due at 5 per cent. ? 31. How much sugar, at 4 d. per lb., ought to be given in exchange (in barter, as it is called) for 17 cwt. of cheese, at £3 10s. per cwt. ? 32. If 7 gallons of brandy be worth 9 gallons of rum, and 9 gallons of rum worth 12 gallons of geneva, what is the price of a gallon of each separately, when the three gallons together cost £2 28. 6d.? 33. What is the true present worth of £357 10s., due 9 months hence, interest being 5 per cent. ? 34. What are the values of ✓27%-745, and 12124 5184 35. Required the values of Vand 774 to six decimals. 36. A person has but £100 to pay the following sums; namely, to A, £48 158. ; to B, £72 10s. ; and to C, £84 138. 4d. : what share ought to be paid to each ? 37. If A can do a piece of work in 10 days that B can do in 13, in what time can they do it together? 38. How many square yards are there in a piece of ground 846 ft. 3 in. long, and 62 ft. 6 in. wide ? 39. What is the premium of insurance on £675 118. 8d. at £5 138. 9d. per cent. ? 40. Two persons, A and B, enter into partnership; the stock of A, £280, is employed for 5 months, and that of B, £266 138. 4d., for six months; the profits are £331 128. 6d.: divide them equitably.* 41. Three persons, A, B, and C, trade in concert; A con tributes £89 58. for 5 months; B, £92 15s. for ñ months; and C, £38 10s. for 11 months; how should the profits, namely, £88 168., be divided ? 42. Multiply ·134786 by •288793 to as many places as can be depended upon; the last decimal in each factor being only approximately true. Also, divide 14 by -7854, the last decimal being only approximately true. 43. How much tin and copper is a bell of 150 lbs. composed of, there being in it three times as much copper as tin ? 44. Proof spirits contain 48 parts of pure spirit, and 52 of water; how much of each is there in 84 gallons of proof spirits ? 45. At what rate per cent. will £956 amount to £1314 108. in 7 years, simple interest ? 46. If 3 lbs. of tea be worth 7 lbs. of coffee, and 13 lbs. of coffee worth 48 lbs. of sugar, and 15 lbs. of sugar worth 28 lbs. of soap; how many lbs. of soap are 6 lbs. of tea worth? 47. A guinea is given to be divided among four persons, A, B, C, and D, with the direction that A is to have į; B, } ; C, 1 ; and D, }; but as this division is found to be impossible, find how the division must be made, so that each may receive his proper share. * This is the same as if A contributed 5 times £280 for one month, and B, 6 times £266 138. 6d. for one month; and in all questions of this kind, the sum contributed by each partner being multiplied by the number of months it was employed, the shares of the profit must be proportional to the resulting products. In like manner, the interest of a sum to be paid in 5 months is the interest of 5 times that sum to be paid in 1 month, and so on; so that if different sums are to be paid at different times, then if we multiply each sum by the number of months, or weeks, &c., which are to elapse before payment is to be made, and then divide the sum of the products by the sum of the bills, the quotient will be what is called the equated time in which all should be paid if they are paid at once. Examples 50 and 51 illustrate this principle. and a 48. What is the net weight of 152 cwt. 1 qr. 3 lbs., 10 lbs. per cwt. being allowed for tare, and zo of what remains for tret? See page 96. 49. If the rents of a parish amount to £2340 178. 6d., rate of £137 108. 8d. be levied, what portion of it must be paid by an estate of which the rental is £143 9s. 10d. ? 50. A person engages to pay a debt of £2330 as follows: £630 in 5 months, £300 in 6 months, £500 in 7 months, and the remaining £900 in 8 months; but he afterwards proposes to pay the whole in one sum; in what time should it be paid ? 51. Goods are purchased on the following conditions, namely, that £50 are to be paid on the 1st of May, £64 on the 4th of June, £86 on the 1st of August, and £90 on the 5th of September; when should these sums be paid, if all are paid at once ? 52. A ship's company take a prize of £4000, which is to be divided amongst them in proportion to their pay, and the time they have been on board. There are 6 officers, who have £6 a month each, and have been on board 6 months ; 12 midshipmen, who have £2 a month each, and have been on board 4 months; 110 sailors, who have £1 10s. a month each, and have been on board 3 months ; what share of the prize must each receive ? + * Agreeably to what is said in the foot-note, p. 177, we should mul. tiply £630 by 5, £300 by 6, £500 by 7, and £900 by 8; but it is better to find how long after 5 months (the shortest of the periods) the whole payment should be made; as then the multipliers, instead of 5, 6, 7, and 8, will be only 1, 2, and 3, applied respectively to the sums after the first. + This question may be worked by the same principle as that employed in the solution of the two preceding questions, combined with the principle of art. (112). The claim of the 6 officers at £6 a month, is the same as would be the claim of 6 x 6 officers at £l a month ; and the claim of these for 6 months' service is the same as would be the claim of 6x6 x 6 officers for 1 month's service. And the learner will observe, that the mode of solution recommended in this and in the two preceding questions is only a modification of the double rule of three, combined with the rule for proportional parts. A TABLE Of those Factors of the Composite Numbers from 75 to 10000, which fall within the Limits of the Multiplication Table. 75 98 105 112 125 126 128 135 147 154 162 165 168 175 176 189 192 196 198 216 224 225 231 242 243 245 252 256 264 275 288 294 297 308 315 324 336 343 352 363 375 378 384 385 392 396 5 5 3 7 7 2 7 5 3 8 7 2 5 5 5 9 7 2 8 8 2 9 5 3 7 7 3 11 7 2 992 11 5 3 8 7 3 7 5 5 ll 8 2 9 7 3 12 8 2 7 7 4 11 9 2 12 9 2 8 7 4 9 5 5 11 7 3 11 11 2 9 9 3 7 7 5 12 7 3 8 8 4 11 6 4 11 5 5 12 12 2 7 7 6 11 9 3 11 7 4 9 7 5 9 9 4 12 7 4 7 7 7 11 8 4 11 11 3 5 5 5 3 9 7 6 8 8 6 11 7 5 8 7 7 11 9 4 405 432 441 448 462 484 486 495 504 512 525 528 539 567 576 588 594 605 616 625 648 672 675 686 693 704 726 729 735 756 768 784 792 825 847 864 875 882 891 896 924 945 968 972 1008 1024 995 12 9 4 9 7 7 8 8 7 11 7 6 11 11 9 96 11 9 9 8 7 8 8 8 7 5 5 3 12 11 4 11 7 7 9 9 7 12 12 4 12 7 7 11 9 6 11 11 5 11 8 7 5 5 5 5 9 9 8 12 8 7 9 5 5 3 7 7 7 2 11 97 11 8 8 11 11 6 9 99 7 7 5 3 12 97 12 8 8 8 7 7 2 12 11 6 11 5 5 3 11 11 7 12 9 8 7 5 5 5 9 7 7 2 11 9 9 8 8 7 2 12 11 7 9 7 5 3 11 11 8 12 99 12 12 7 8 8 1029 1056 1078 1089 1125 1134 1152 1155 1176 1188 1215 1225 1232 1296 1323 1331 1344 1372 1375 1386 1408 1452 1458 1485 1512 1536 1568 1575 1584 1617 1694 1701 1715 1728 1764 1782 1792 1815 1848 1875 1925 1936 1944 2016 2025 2048 7 7 7 3 9 7 2 8 7 7 3 9 7 7 3 7 7 4 9 9 2 9 7 7 4 8 7 4 11 11 5 3 11 8 7 3 5 5 5 5 3 11 7 5 5 11 11 4 4 9 9 8 3 9 8 7 4 9 9 5 5 8 8 8 4 |