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30. A merchant bought 49 tuns of wine for $910 ; freight cost $90 ; duties, $40; cellar, $31,67 ; other charges $50, and he would gain $185 by the bargain ; what must I give him for 23 tuns ?
Ans. $0 13,33. 31. The earth being 360 degrees in circumference, turns round on its axis in 24 hours ; how far does it turn in one minute, in the 43d parallel of latitude ; the degree of longitude, in this latitude, being about 51 statute miles ?
Ans. 12 minutes. 32. There is a cistern having 4 cocks; the first will empty it in ten minutes ; the second in 20 minutes ; the third in 10 minutes; the fourth in 80 minutes ; in what time will all four running together empty it? 10
6 As 40
As 114 : 60 :: 1 : 51 Ans: 60
Cist. : 60 :: 1
111 33. A. and B. depart from the same place, and travel the same road ; but A. goes 5 days before B. at the rate of 20 miles per day ; B. follows at the rate of 25 miles per day; in what time and distance will he overtake A ?
Ans. 20 d. and 500 mls. 34. A merchant bought a number of bales of velvet, each containing 12947 yards, at the rate of $7 for 5 yards, and sold them out at the rate of $11 for 7 yards ; and gained $200 dollars by the bargain ; how many bales were there ?
Ans. 9 bales. 35. Suppose 450 men are in a garrison, and their provisions are calculated to last but 5 months ; how many must leave the garrison, that the same provisions may last those who remain, 9 months ? Ans. 200 men.
36. If a piece of land, 40 rods in length, and 4 in breadth, make an acre, how wide must be, when it is but 19 rods long, to make an acre ? Ans. 8 r. 6 ft. 111; in.
37. If 9 men can build a house in 5 months, by working 14 hours per day, in what time will the same number of men do it, when they work only 10 hours per day?
Ads. 7 months. 38. What number of men must be employed to finish in 9 days, what 15 men would be 30 days about? Ans. 54
39. If a field will feed 6 cows 91 days, how long will it feed 21 cows ?
Ans. 26 days. 40. A regiment of soldiers, consisting of 745 men, is to be clothed, each suit is to contain 31 yards of cloth, which is 13 yard wide, and lined with shalloon of a yard wide ; how many yards of shalloon will line them?
Ans. 40974 yards. 41. What quantity of water must I add to a pipe of wine, valued at $110, to reduce the first cost to $0,75 ?
Aas. 20 gallons. 42. If a person, having of a coal mine, sells of his share for $570, what is the whole mine worth?
Ans. $1266,666. 43. A. borrowed of his friend $833,333 for 7 months, promising to do him the like kindness ; sometime after, B. had occasion for $1000, how long may he keep it to receive full amends for the favour ?
Ans. 5 months and 25 days. 44. If the keeping of one horse be 16 cents per day, what will be that of 11 horses for a year ? Ans. $642,40.
45. Bought 3 casks of raisins, each weighing 2 cwt. 2 qrs. 25 lb. what will they come to at $6,943 per cwt?
Ans. $56,721. 46. If an ingot of gold, weighing 9 lb. 9 oz. 12 pwt. be worth $1372, what is that per grain ? Ans. $0,024.
47. If I borrowed 185 quarters of corn when the price was $3,166, how much must I pay to indemnify the lender, when the price is $2,89 ? Ans. 2021118
48. If my horse and saddle are worth 18 guineas, and my horse be worth six times as much as my saddle, what is the value of my horse ?
Ans. $72. If 120 bushels of corn will serve 14 horses 56 days; how many days will 94 bushels serve 6 horses?
Ans 10215 days. 50. If the transportation of 13cwt. Iqr. 72 miles be $8,416, what will be the transportation of 7cwt. 3qr. 112 miles ?
Ans. $7,395. If a regiment of soldiers, consisting of 939 men, consume 351 quarters of wheat in 7 months; how many
soldiers will consume 1464 quarters in 5 months, at that Fate ?
Ans. 54830's. 52. If 248 men in 5 days, of 11 hours each, dig a trench 230 yards long, 3 wide, and 2 deep, in how many days of 9 hours long, will 24 men dig a trench of 420 yards long, 5 wide and 3 deep?
Ans. 2888 53. If the freight of 12 cwt. 2qr. 6lb. 275 miles cost $27,78; how far may 60cwt. 3qr. be shipped for $234,78 ?
Ans. 480 miles. 54. If the freight of 9hhd. of sugar, each weighing 12cwt. 20 leagues, cost $53,33; what must be paid for 50 tierces ditto, each weighing 2 cwt. 100 leagues ?
Ans. $308,62. 55. There was a certain edifice completed in a year by 20 workmen; but the same being demolished, it is necessary that just such an one should be built in 5 months. I demand the number of men to be employed about it?
Ans. 48 men.
FELLOWSHIP AND LOSS AND GAIN.
Tut. What is fellowship ?
Tut. Fellowship is a rule by which traders, and others doing business in company, determine each partner's particular share of the gain or loss, according to the proportion of his share to the joint stock or capital.*
Fellowship is of two kinds, single and double.
Single fellowship is when the stocks of the partners are employed equal times.
A. B. and C. put $1000 each, into trade ; at the end of one year, they find they have gained $1200; what is each partner's share of the gain ?
* In commercial language, the sum of all the money or property which the partners put into trade is called the stock or capital; the gain to be divided is called the dividend.
Now the sum of the stocks is $3000, and the whole gain is $1200; and each partner's gain ought to be such that it will have the same proportion to the whole gain, that his share of the whole stock, has to the whole stock ; thus the proportion will be,
3000 : 1000 :: 1200. Hence the reason of the following rule for,
As the whole stock is to each partner's share of the stock, so is the whole gain or loss to his share of the gain or loss.
A. B. and C. companied ; A. put in $400, B. $800, and C. 1200, and they gained $600; what was each partser's share of the gain ?
1200 2400 : 600 :: 400 : 100 A's share. 800 2400 : 600 :: 800 : 200 B's share. 400 2400 : 600 :: 1200 : 300 C's share.
Whole stock 2400
Pup. This is very plain, for I see nothing is it different from the single rule of three.
Tut. There is nothing different, except in preparing the question for statement, which you will readily understand from the example given above.
Double fellowship is when the stocks are employed unequal times.
A. and B. enter into partnership; A. puts in $400 for 4 months; B. puts in $800 for 8 months ; at the end of the trade they have gained $200; what is each partner's share ?
Now had the stocks been equal, B. would have had double the share of A. because he continued his stock in trade double the time of A.; and had the times been equal, B. would have had double the share of A. because he had double the stock of A. But as B: had double the stock of A. and continued it in trade double the time of A. he must have 4 times as much of the gain as A. The
stock of A. multiplied by the time it was continued in trade gives a product of 1600 ; B's stock multiplied by the time it was continued in trade, gives a product of 6400. 6400 is 4 times 1600, and as B's share of the gain ought to be 4 times as much as A's share, the proportion will be, as the sum of these products is to each partner's product, so is the whole gain to each partner's share of the gain, thus,
6400 8000 : 1600 :: 200 : 40 A's share.
Hence the following rule for
Multiply each partner's share of the stock by the time it was continued in trade. Add together these several products; then say, as the sum of these products is to each partner's product, so is the whole gain to each partner's share of the gain.
A. and B. hold a piece of ground in common, for which they are to pay $36. A. put in 23 oxen for 27 days, and B. 21 oxen for 35 days; what part of the rent ought each man to pay