22. If 67 tons 3 qrs. can be carried 72 miles 3 fur. for £71 16s. 7d., how far can 79 tons 7 cwt. be carried for the same money? Ans. 61 miles 1 fur. 34yds.+ 23. In the last example, how far would 67 tons 3qrs. be carried for £36 17s. 2d. ? Ans. 37m. lfur. 23yds. 24. If 3 bushels 2 pecks of corn last 27 men 16 days, how long will the same quantity serve 37 men? Ans. 113 days. 25. If 67 men eat 671qrs. 2bus. of corn, how much will 345 men eat in the same time? Ans. 3456 qrs. 33 bus. 26. If a coach fare be 17s. 6d. for 31 miles, how far ought I to ride for £3 17s. Ans. 136 miles. 27. Bought 7 tons 3 cwt. 1 qr. of coals for £7, how much can I purchase for £10 7s. 9d.? Ans. 10 tons 121283 cwt. 2240 28. The expenses of a parish are £729 16s. 7d., at 1s. 2d. in the £, what was the rateable value? Ans. £12511 7s. 1 d. 29. A person walks at the rate of 7m. 16ft. in 8 hrs. 20 minutes, at what rate does he walk per hour? Ans. 44373 ft. 30. If £490 6s. 7d. gain £37 16s. 6d. interest, how much will £876 17s. 7d. gain at the same rate, and in the same time? Ans. £67 12s. 10 d. + 31. If 7 cwt. 3 qrs. be bought for 71 guineas, how much can be obtained for 79 guineas 17 shillings? Ans. 8 cwt. 2 qrs. 231043 lbs. 32. If 64 men do a piece of work in 37 days, how long will 74 men be doing it? Ans. 32. 33. If a steeple 167ft. high casts a shadow 79ft. 6in. long, what is the height of a pole which casts a shadow of 22 ft. 9 in. Ans. 475 ft. 34. What weight of sugar, at 5 d. per lb., ought I to receive in exchange for 79 lbs. of tea, at 3s. 6d. per lb.? Ans. 577 lbs. 35. A person spends 13s. 74d. weekly, and saves £9 17s. 6d. per month of 13 to the year, what is his annual income? Ans. £163 16s. 6d. 36. If 7 lbs. of bacon cost 5s. 2d., what will 397 lbs. cost? Ans. £13 4s. 10d. 37. If 65 cows cost £8796 17s. 6d., what will 35 cost? Ans. £4736 15s. 613d. 38. A bankrupt owes £846 17s. 9d., his effects are worth £672 18s. 6d., what can he pay in the £. Ans. 15s. 101d.+ 39. If 64cwt. 2qrs. 17 lbs. cost £817 18s. 6d., what will 31 tons 1 cwt. 3 qrs. 9 lbs. cost? Ans. £7866 18s. 5 d. + 2598 711 2897 40. How much coffee can I buy for £67 13s. 6d., if £33 17s. 9d. buys 3 cwt. 17 lbs.? Ans. 704lbs. +251 41. How much wine, at £7 3s. 74d. for 13 gals., can be bought for £72 16s. 7d.? Ans. 131 gals. +37 42. If 16 qrs. 1 sack 3 bus. of barley can be bought for £39 18s. 7d., what will 72 qrs. 3 bushels cost? Ans. £171 5s. 01d. 344 43. If a fourpenny loaf weighs 2 lbs. when wheat is 4s. 6d. per bushel, what will it weigh when wheat sells at 6s. a bushel? Ans. 1 lbs. 44. A man has a rent roll of £8796 18s. 6d., on which he pays a tax of 34 per cent.; what is his nett income? Ans. £8511 Os. 6d. 45. The rateable value of a parish is £1796 18s. 2d., what does the highway rate amount to, at ls. 3§d. in the £? Ans. £116 1s. 0,19 d. 240 46. A bankrupt paid altogether to his creditors £876 18s. 6d., at 13s. in the £, what were his debts? Ans. £1349 2s. 3 d. 47. In the last example, shew if his debts were £1349 2s. 3 d., and his assets £876 18s. 6d., that he paid a dividend of 13s. in the £. 48. I lend £674 18s. 6d. for 6 months, how long ought I to borrow in return £874 18s. 6d. 4 months. 3499 Ans. 49. If it takes 67 blocks of marble 2 ft. long, 1 ft. wide, and 6 in. deep, to construct a wall, how many will it take 3 ft. long, 2 ft. wide, and 7 in. deep? Ans. 19. 50. A pole casts a shadow 117 ft. long; what is its length, if 6 ft. of length give a shadow of 9ft. 6in. ? Ans. 731. PROPORTION-COMPOUND. In compound proportion there will still be one unknown quantity put in the place of the fourth term, and only one third term; but the ratio between the third and fourth will be made to depend on the ratios of more than one first and second term. Having arranged the third and fourth terms, as in simple proportion, proceed to arrange the first and second terms, attending to one condition of the question only at once. Thus, if 939 men consume 702 quarters of corn in 84 days, how many soldiers will consume 2408 qrs. in 112 days? } 2408 x 84 x 939 702: 2408 :: 939: x x= =11268 112: 84 Here the answer is to be men, so the third and fourth terms are 939 and x. Attending only to the question of qrs. of corn, it is seen that the ratio is in an increasing order, from 702: 2408, since a must be greater than 939, if x men have to eat a larger quantity of corn. Conversely with respect to time, a less number of men will be required to consume the corn in a greater length of time, and the order is decreasing from 112 to 84. As before, the product of the means equals that of the extremes. If £50 in 2 years gain £7 interest, what is the interest of £1142 for 3 years. Ans. £239 16s. 44d+20. 2. If 16 men mow 80 acres in 7 days, how many will 48 men mow in 14 days? Ans. 480 acres. 3. If 4000 horses consume 3000 qrs. of oats in 24 days, how much will 4 horses consume in 8 days? Ans. 8 bushels. 4. If a ditch 750 yards long, 12 yards wide, and 3 deep, be dug in 60 days of 6 hours each by 140 men, how many will be required to dig a ditch 5280 yards long, 4 yards wide, and 2 yards deep, in 250 days of 5 hours each? Ans. 63+ 5. If the carriage of 17 cwt. for 60 miles be £3 16s. 6d., what will be the carriage of 2 cwt. for 40 miles? Ans. 6s. 6. If £160 gains £5 6s. 8d. in 8 months, what will £240 gain in 8 months? Ans. £8. 7. If 24 men build 533 feet of wall in 72 days, working 9 hours per day, how much will 9 men build, working 8 hours per day, in 36 days? Ans. 88 ft. 8. If 6 men mow 16 ac. in 2 days, how long will 10 men be mowing 40 ac. at the same rate? Ans. 3 days. 9. If a man travel 540 miles in 24 days of 6 hours a day, how far will he travel in 3 days of 8 hours per day? Ans. 90 miles. 10. If 32 persons spend £853 6s. 8d. in 8 days, how much will 24 persons spend at the same rate in 2 months? Ans. £4480. 11. If 64 men in 72 days of 8 hours mow 87a. 2rds., how much will 37 men mow in 28 days of 12 hours each? Ans. 29,781 acres. 1536 12. If 46 men make a cutting 760 yds. long, 2 ft. deep, and 17 yds. wide, in 76 days of 9 hours each, how long will 36 men be cutting out 37 yds. long, 12 yds.wide, and 7 ft. deep, in days of 11 hours each? Ans. 910 days. 13. If for £67 18s. 74d. I can have 7 tons 13cwt. 2qrs. carried 27 miles, how far can I have 131⁄2 tons carried for £71 18s. 11d.? Ans. 1633601 miles. 130428 14. If it costs £87 16s. 8d. to cut a trench 79 ft. long, 3 ft. broad, and 7 ft. deep, how much will it cost to dig a trench 158 ft. long, 1 ft. broad, and 14 ft. deep? Ans. £175 13s. 5d. 15. If it cost £87 16s. 7 d. to build a wall 37 ft. long, 17 ft. high, and 17 in. thick, how much will it cost to build a wall 74 ft. long, 8 ft. high, and 8 in. thick? Ans. £43 18s. 3 d. 16. If 18 men in 7 days mow 225 acres of grass, how many men can mow 315 acres in 11 days? Ans. 162. 17. If £225 15s. in 11 months gain £7 13s. 4d. interest, how much will £75 5s. gain in 9 months? Ans. £2 1s. 9 d. + 18. If it costs £2 4s. for the carriage of 17 cwt. 3 qrs. for 25 miles, how much will 1 ton 3 cwt. cost for 18 miles ? Ans. £2 1s. Od.+ PROPORTION-COMPOUND. In compound proportion there will still be one unknown quantity put in the place of the fourth term, and only one third term; but the ratio between the third and fourth will be made to depend on the ratios of more than one first and second term. Having arranged the third and fourth terms, as in simple proportion, proceed to arrange the first and second terms, attending to one condition of the question only at once. Thus, if 939 men consume 702 quarters of corn in 84 days, how many soldiers will consume 2408 112 days? 702: 2408 112: 8408} qrs. in 2408 x 84 x 939 =11268 702 × 112 :: 939: x x= Here the answer is to be men, so the third and fourth terms are 939 and x. Attending only to the question of qrs. of corn, it is seen that the ratio is in an increasing order, from 702: 2408, since a must be greater than 939, if x men have to eat a larger quantity of corn. Conversely with respect to time, a less number of men will be required to consume the corn in a greater length of time, and the order is decreasing from 112 to 84. As before, the product of the means equals that of the extremes. If £50 in 2 years gain £7 interest, what is the interest of £1142 for 3 years. Ans. £239 16s. 44d+20. 2. If 16 men mow 80 acres in 7 days, how many will 48 men mow in 14 days? Ans. 480 acres. 3. If 4000 horses consume 3000 qrs. of oats in 24 days, how much will 4 horses consume in 8 days ? Ans. 8 bushels. 4. If a ditch 750 yards long, 12 yards wide, and 3 deep, be dug in 60 days of 6 hours each by 140 men, how many will be required to dig a ditch 5280 yards long, 4 yards wide, and 2 yards deep, in 250 days of 5 hours each? Ans. 63+ 5. If the carriage of 17 cwt. for 60 miles be £3 16s. 6d., what will be the carriage of 2 cwt. for 40 miles? Ans. 6s. |