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RULE 1. Multiply the whole gain or loss by the fractions denoting each partner's part of the whole stock, and the products will be the respective shares of the gain or loss of each partner. Or,
As the whole stock is to each partner's stock, so is the whole gain or loss to each partner's gain or loss.
EXAMPLES FOR PRACTICE.
2. Three merchants, A, B, and C, engaged in trade. A put in $ 6000, B put in $ 9000, and C put in $5000. They gain $840. What is each man's share of the gain?
Ans. A's gain $252, B's gain $ 378, C's gain $ 210.
3. A bankrupt owes Peter Parker $ 8750, James Dole $ 3610, and James Gage $7000. His effects, sold at auction, amount to $6875; of this sum $375 are to be deducted for expenses, &c. What will each receive of the dividend?
Ans. Parker, $2937.7519; Dole, $1212.03; Gage, $2350.208.
4. A merchant, failing in trade, owes A $ 500, B $386, C $ 988, and D $126. His effects are sold for $100. What will each man receive?
Ans. A receives $ 25.00, B $ 19.30, C 49.40, D $ 6.30.
5. A, B, and C, engaged in trade. A put in $700, B put in $300, and C put in 100 barrels of flour. They gained $90; of which sum C took $30 for his part; what will A and B receive, and what was C's flour valued per barrel?
Ans. A receives $ 42, B $ 18, C's flour $5
per barrel. 255. To find each partner's share of the profit or loss, when the stock is employed UNEQUAL TIMES.
Ex. 1. Josiah Brown and George Dole trade in company. Brown put in $600 for 8 months, and Dole put in $400 for 6 months. They gain $60. What is each man's share of the gain?
$ 600 X 8
4888, Brown's share in the partnership.
$40, Brown's gain; of $60 $ 20, Dole's gain.
254. The rule for finding the shares of profit or loss when the stock is employed the same time?
$600 for 8 months is the same as $ 600 × 8=$4800 for 1 month, because $4800 would gain as much in 1 month as $ 600 in 8 months; and $400 for 6 months is the same as $ 400 X 6 = $ 2400 for 1 month. The question hen is the same as if Brown had put in $ 4800 and Dole $2400 for 1 month each. The whole stock would then be $4800+ $2400 $7200, and Brown's share of the gain would be 4800 = } of $ 60 = $40; and Dole's share, 4108 — § of $ 60 = $ 20.
OPERATION BY PROPORTION.
$7200: $4800::$60: $ 40, B's share. $7200 $2400::$60: $ 20, D's share.
RULE 1. ·Multiply each partner's stock by the time it was in trade, and consider each product a numerator, to be written over the sum of the products, as a common denominator. Then multiply the whole gain or loss by each of these fractions, and the product will be the respective shares of the gain or loss of each partner. Or,
RULE 2. Multiply each partner's stock by the time it was in trade; then, as the sum of these products is to each product, so is the whole gain or loss to each partner's gain or loss.
EXAMPLES FOR PRACTICE.
2. A, B, and C trade in company. A put in $700 for 5 months; B put in $800 for 6 months; and C put in $ 500 for 10 months. They gain $399. What is each man's share of the gain? Ans. A's gain $ 105, B's gain $144, C's gain $ 150.
3. Johnson, Hyde, and Tyler enter into business, under the firm of Johnson, Hyde, & Co. Johnson put in at first $1000, and at the end of 6 months $500. Hyde put in at first $800, and at the end of 4 months $ 400; but, at the end of 10 months, he withdrew $ 500. Tyler put in at first $1200, and at the end of 7 months $ 300, and at the end of 10 months $ 200. At the end of the year they found their net gain to be $1000. each man's share?
What is Ans. Johnson's gain $ 348.0231, Hyde's $ 273.78, Tyler's $378.19
4. George Morse hired of William Hale, of Haverhill, a horse and chaise for a ride to Newburyport, for $3.00, with the privilege of one person's having a seat with him. Having rode 4
255. What are the rules for finding the shares of profit or loss when the stock is employed for unequal times? Why do you multiply each man's stock by the time it was in trade?
miles, he took in John Jones, and carried him to Newburyport, and brought him back to the place from which he took him. What share of the expense should each pay, the distance from Haverhill to Newburyport being 15 miles?
Ans. Morse pays $1.90, Jones pays $ 1.10.
5. J. Jones and L. Cotton enter into partnership for 1 year. January 1, Jones put in $1000, but Cotton did not put in any until the first of April. What did he then put in, to have an equal share with Jones at the end of the year ?
6. S, C, and D engage in partnership, with a capital of $ 4700. S's stock was in trade 8 months, and his share of the profits was $96; C's stock was in the firm 6 months, and his share of the gain was $90; D's stock was in the firm 4 months, and his gain was $80. Required the amount of stock which each had in
S's stock $1200.
7. A, B, and C engage in trade. A put in $300 for 7 months, B put in $500 for 8 months, and C put in $200 for 12 months; they gain $85; what share of the gain does each receive?
Ans. A $21, B $ 40, and C $24.
8. A and B engage in trade, with $500. A put in his stock for 5 months, and B put in his for 4 months. A gained $10, and B gained $12; what sum did each put in?
Ans. A $ 200, B $ 300.
9. A and B trade in company. A put in $ 3000, and at the end of 6 months put in $2000 more; B put in $ 6000, and at the end of 8 months took out $3000; they trade one year, and gain $1080; what is each man's share of the gain?
Ans. A's share is $ 480, B's $ 600.
10. Four men hired a pasture for $50. A put in 5 horses for 4 weeks; B put in 6 horses for 8 weeks; C put in 12 oxen for 5 weeks, calling 3 oxen equal to 2 horses; and D put in 3 horses for 14 weeks. How much ought each man to pay ?
Ans. A $6.66, B $ 16.00, C $ 13.334, and D $ 14.00.
11. A, B, and C contract to build a piece of railroad for $7500. A employs 30 men 50 days; B employs 50 men 36 days; and C employs 48 men and 10 horses 45 days, each horse to be reckoned equal to one man, and he is also to have $112.50 for overseeing the work. How much is each man to receive? Ans. A receives $ 1875; B, $ 2250; C, $ 3375.
256. The Currency of a state or country is its money or circulating medium of trade.
In the United States, the gold, silver, and copper coins of the country, foreign coins whose value has been fixed by law, and bank-notes, redeemable in specie, pass as money.
The Legal Tender, in this country, in payment of debts, is gold
The Intrinsic Value of foreign coins is their mint value, or that depending upon the weight and purity of the metal of which they are made; their Commercial Value is the price they will bring in the market, and their Legal Value is that fixed by law. The value of some foreign coins, as fixed by present laws of the United States, is shown in the following
The legal currency of this country, previous to 1786, was sterling money, or that of pounds, shillings, and pence. On the adoption of the currency of dollars and cents, there were in circulation colonial notes, or bills of credit, which had depreciated in value. This depreciation being greater in some sec
256. What is currency? What pass for money in the United States ? What is the intrinsic value of foreign coins? The commercial value? The legal value? Mention some of the foreign coins whose value has been fixed by law. What was the currency of this country previous to 1786?
tions than in others, gave rise to the variation, in the States, as to the number of shillings equivalent to a dollar, as shown in the following
$ 1 in
$ 1 in
6s.£, called New Eng. currency; of which i£ $3; 1s.
18£ 15s. 6d. 18.775£. 18.775 $62.58}.
4s. 8d.=£, called Georgia currency; of which 1£ =$44; 1s. = 21 cts.
5s.£, called Canada currency; of which 1£= $4; 1s.
415s. 25£, called English or Sterling money; of which 1£$4.84; 1s. 24 cts.
The old currencies of the States are no longer used in keeping accounts, yet the price of articles is still named by some traders in the old currency of their State.
257. Reduction of Currencies is the process of finding the value of the denominations of one currency in the denominations of another.
258. To reduce old State currencies to United States money.
Ex. 1. Reduce 18£ 15s. 6d. New England currency to United States money. Ans. $62.584.
We first reduce the shillings and pence to the decimal of a pound (Art. 188), and annex it to the pounds; we then divide the
256. What gave rise to the variation in the old currency of this country? Repeat the table. How are the old currencies of the States now used? 757. What is reduction of currencies ?