what time can A., B., C., and D. do it together, and in what time can each do it by himself? Ans. 19, together; A. 108 days., B. 5618da., C. 43ļda. D.1080da, 8. If I would exchange £1055 15s. for dollars, at 9s. a-piece, ducats at 11s. 4d. a-piece, and crowns at 12s. 2d. a-piece; and would have 6 dollars for 4 ducats, and 3 dollars for 4 crowns; how many of each sort must I have? Dollars, 644,5 Ans. Ducats, 42911. Crowns, 858 9. A. and B. dissolve partnership, and equally divide their gain: A.'s share, which was $332 50cts., lay for 21 months; B.'s for 9 months only: the adventure of B. is required. Ans. $775 83 cts. 10. If 4 years should be added to a lease of 12 years yet to come, the advance rent being $720 25cts. per annum, what should be paid down for the additional 4 years, discount being allowed at 5 per cent. per annum, compound interest? Ans. $1422 14cts. 8m. 11. A gate-keeper is to receive 6cts. for every wagon, 4cts. for every gig, 2cts. for every horseman, and 1ct. for every footman, that passes the gate: at the year's end, he found that 3150 gigs had passed; and that 7 gigs passed when 5 wagons did; and 4 horsemen passed when 6 footmen did; and 5 footmen passed when 3 gigs did: what number of wagons, horsemen, and footmen, passed; and how much did the gate-keeper receive? Gigs, Ans. Footmen, 3150. 2250. 5250. 3500. Amount of toll, $383 50cts. 12. If a water-hogshead holds 110gal., and the pipe which fills the hogshead discharges 15gal. in 3 minutes, and the tap will discharge 20gal. in 5 minutes, and these were both left running one hour, how many gallons would the hogshead then contain; and if the tap was then stopped, in what time would the hogshead be filled? Ans. 60gal., and filled in 10min. 13. A. has 28cwt. of cotton, which cost him $264: how must he rate it per pound to D., so that by taking his note, payable at 9 months, he may clear $30, allowing interest at 6 per cent. per annum? Ans. 9cts. 7m. 14. A., B., and C., in company, had put in $5762: A.'s money was in 5 months, B.'s 7, and C.'s 9 months: they gained $780, which was so divided, that of A.'s was of B.'s, and of B.'s was of C.'s: but B., having received $2087, absconded: what did each gain, and put in; and what did A. and C. gain or lose by B.'s misconduct? A.'s share of profit, $260 B.'s do. Ans. do. $325 C.'s do. do. $195 A. and C. would gain $697 39cts. 15. A. had 20 hogsheads of sugar, which he sold to B. at 5 per cent. loss; who sold them to C. for $20 75cts. clear; C. parted with them to D. for $1000, and thereby cleared 52 per cent.: what did the sugar cost A. per hogshead? Ans. $48 93cts. 5m. 16. Suppose A. lets B. have a hogshead of sugar, of 10 cwt., worth $7, for $11 per cwt., one-third of which, he is to pay in cash; B. has paper, which cost $4 50cts. per ream, which he gave A., for the rest of his sugar, at $5 25cts.: which gained most by the bargain? Ans. A. gained most, by $27 77cts. 8m. 17. A father left his estate of $1300 to his only son; but he being only 14 years of age, his guardian was to pay $100 per annum for board, education, &c., and the surplus was to be put out to interest, for his benefit, at 6 per cent. compound interest: now, allowing no loss, what sum had his guardian to pay him when he was of age? Ans. $1115 33cts. 5m. 18. There are two columns, in the ruins of Persepolis, left standing upright; one is 64 feet above the plain, the other 50. Between these, in a right line, stands an ancient statue, the head whereof is 97 feet from the summit of the higher, and 86 feet from the top of the lower column, and the distance between the lower column and the centre of the statue's base, is 76 feet; the distance between the top of the columns is required. Ans. 157+feet. Note.-Sound, if not interrupted, will move at the rate of about 1150 feet in a second of time. 19. If I see the flash of a cannon, fired from a fort on the other side of a river, and hear the report 47 sec onds afterwards, what distance was the fort from where I stood? Ans. 54050 feet. 20. If a vessel, in time of distress, shall discharge a gun, in what time will the report be heard by another vessel, at a distance of 15 miles 7 furlongs from them? Ans. Imin. 121sec. 21. Hiero, king of Sicily, ordered his jeweller to make a crown, containing 63 ounces of gold. The workman thought, that substituting a part silver was only a proper perquisite; which taking air, Archimedes was appointed to examine it, who, on putting it into a vessel of water, found it raised the fluid 8.2245 cubic inches; and having discovered that the inch of gold weighed 10.36 ounces, and that of silver but 5.85 ounces, he found what part of the king's gold had been changed. Repeat the process, and inform us what part of it was gold, and what silver. 28.8035+oz. silver. Ans. 34.1964+oz. gold. 22. If a mess of 6 men receive for 3 rations 716. of beef and 5lb. of bread a day, the beef cost 53cts. per pound, and the bread 6cts. per pound: now if the beef for a certain number of men cost $34 50cts., what will it cost for bread for them? Ans. $25 71cts. 4m.+ 23. What number is that, to which, if of of 283 be added, the total will be 1? Ans. 21929 29169 24. What is the difference between the interest of $1000 at 6 per cent. for 8 years, and the discount of the same sum at the same rate, and for the same time? Ans. The interest exceeds the discount by $155 67cts. 5m. 25. What is the difference between the sum of the square root of 32 and 24, and the cube root of 67? Ans. 6,496. 26. What will purchase $2450 stock, at 1053 per cent.? Ans. $2587 20cts. 27. A. has B.'s note for $500 75cts., with 9 months' interest, at 6 per cent., due on it, for which B. gave him 5064 feet of boards, at 21cts. per foot, with 140 pounds of tallow, at 13cts. per pound, and is to pay the rest in flax-seed, at 923cts. per bushel: how many bushels of flax-seed must A. receive, to balance the note? Ans. 40915 bushels. 28. A father, desirous to encourage his son at school, promises to give him 6cts. the first quarter, 9cts. the second, increasing arithmetically: the boy has now been at school 9 years, and wishes to know what is due him.... Ans. $21 06cts. 29. A sum of $2363 383cts. is left to be paid in 5 years' time; but the person holding the money is willing to pay it at the expiration of 2 years and 3 months, upon being allowed discount at compound interest at 6 per cent.; which being agreed to, what must he pay? Ans. $2012 82cts. 9m. 30. A bond was given on the 14th of January, 1802, at 5 per cent. per annum, for the sum of $1854 69cts.; on the 5th of July, 1807, $285 were paid off, and a fresh bond entered into for the remainder, at 43 per cent. per annum; at the time the interest of this last was $52 65cts., there was paid off $102 43cts., the old bond being then taken up, a new one was then given for the residue, which being paid off on the 26th of October, 1813, the bond-owner gave a receipt in full for $2497 03cts. 2m.; at what rate then did he take interest per cent. per annum, upon the last renewal of the bond? Ans. 4 per cent. 31. A person having driven a stock of cattle to market, received for them all $456: he received $50 for each horse, $20 for each cow, and $4 for each sheep; the number of cows was double the number of horses, and there were three times as many sheep as cows: what did he receive for the horses, what for the cows, and what for the sheep; and how many of each sort were there? Ans. { 24 sheep, $96. cows, $160. 4 horses, $200. 32. How much gold, of 17 and 24 carats fine, must be melted with 10 oz. of 16 carats fine and 20 oz. of 19 carats fine, to make a mixture of 50 oz. 19 carats fine? Ans. 10 of 17 carats, 10 of 24 carats. 33. A case of goods, amounting to £230 5s. Sterling, is sold at Philadelphia at 20 per cent. advance: what is the amount in Federal money? Ans. $1227 87cts. 7m. 34. If a tower be built in the following manner, of its height of stone, 27 feet of brick, and of its height of 1 wood, what was the height of the tower? 87 Ans. 113 feet 4 inches. 35. When I, by disposing of a yard of cloth, at $7, gain 56 cts., what would I gain by selling 3 pieces, which cost me $400? Ans. $32 14cts. 36. If a man buy 25 yards of lace, at 30cts. for the first yard, and for the last yard 96cts. the price of each yard increasing in arithmetical progression, what did the whole amount to? Ans. $15 75cts. 37. If of two numbers 47 is the less, to which the other is in proportion as 9 to 4, what is their sum, and the product of their sum and difference? Sum, Ans. Difference, 152.75. 58.75. Product of sum and dif. 8974.0625. THE END. |