369. To find each partner's share of the gain or loss, when the stock of each is employed for the same time. Make each man's stock the numerator, and the whole stock the denominator of a common fraction; multiply the gain or loss by the fraction which expresses each man's share of the stock, and the product will be his share of the gain or loss. Or, multiply each man's stock by the whole gain or loss; divide the product by the whole stock, and the quotient will be his share of the gain or loss. PROOF.-Add the several shares of the gain or loss toge ther, and if the sum is equal to the whole gain or loss, the work is right. (Art. 284. Ax. 11.) OBS. 1. This rule is applicable to questions in Bankruptcy, General Average, and all other operations in which there is to be a division of property in specified proportions. 2. The preceding case is often called Single Fellowship. But since a partnership is always composed of two or more individuals, it is somewhat difficult to see the propriety of calling it single. 2. A, B, and C entered into partnership; A put in of the capital, B, and C ; they gain $4800: what was each man's share of the gain? 3. A, B, and C form a partnership; A furnishes $600, B $800, and C $1000; they gain $480: what is each man's share of the gain? 4. A Bankrupt owes A $1200, B $2300, C $3400, and D $4500; his whole effects are worth $5600: how much will each creditor receive? 5. A, B, C, and D make up a purse to buy lottery tickets; A puts in $30, B $40, C $60, and D $70; they draw a prize of $2000: what is each man's share? 6. A, B, and C freight a vessel with a cargo worth $30000; of which A owned $8000, B $10000, and C $12000; in a gale the master throws of the cargo overboard: what was each man's loss? QUEST.-369. How is each man's share of the gain or loss found, when the stock of each is employed for the same time? How is the operation proved? Obs. To what is this rule applicable? What is it sometimes called? CASE II. 7. A and B formed a partnership; A put in $300, and B $200. At the end of 2 months A took out his stock, while B's was employed 6 months; they gained $150: what was each man's just share of the gain? Note. It is obvious that the gain of each depends both upon the capital he furnished, and the time it was employed. (Art. 364.) Solution. Since A's capital $300, was employed 2 mo., his share of the gain is the same as if he had put in $600 for 1 mo.; (Art. 365;) for $300×2=$600. Also, B's capital $200, being employed 6 mo., his share of the gain is the same as if he had put in $1200 for 1 mo.; for $200×6=$1200. The sum of $600 and $1200 is $1800. A's share of the gain must therefore be 0. B's 66 Now $150x=$50, A's share. 66 And $150x-$100, B's share. Hence, 370. To find each partner's share of the gain or loss, when the stock of each is employed for different periods. Multiply each partner's stock by the time it is employed; make each man's product the numerator, and the sum of the products the denominator of a common fraction; then multiply the whole gain or loss by each man's fractional share of the stock, and the product will be his share of the gain or loss. OBS. This case is often called Compound or Double Fellowship. 8. A, B, and C enter into business together; A puts in $500 for 4 months, B $400 for 6 months, and C $800 for 3 months; they gain $340: what is each man's share of the gain? 9. A and B hire a pasture together for $60; A put in 120 sheep for 6 months, and B put in 180 sheep for 4 months: what should each pay ? QUEST.-370. When the stock of each partner is employed for different periods, how is each man's share found? Obs. What is this case sometimes called? 10. The firm A, B, and C lost $246; A had put in $85 for 8 mo., B $250 for 6 mo., and C $500 for 4 mo.: what is each man's share of the loss? EXCHANGE OF CURRENCIES. 371. The term currency signifies money, or the circulating medium of trade. 372. The intrinsic value of the coins of different nations, depends upon their weight and the purity of the metal of which they are made. (Art. 203. Obs. 1.) Note.-1. The present standard gold coins of Great Britain are 22 parts of pure gold and 2 parts of copper, i. e. 22 carats fine. The standard silver coins are 37 parts of pure silver and 3 parts of copper. A Pound Sterling or Sovereign weighs 123.274 grs., and a shilling, (silver,) 3 pwts. 15 grs.* 2. For the present standard weight and purity of gold and silver coins of the United States, see Art. 203. Obs. 2. 373. The relative value of foreign coins is determined by the laws of the country. By act of Congress, 1842, OBS. 1. The legal value of a Pound Sterling has been changed several times. By the law of 1842, its value was fixed at $4.84, and it now passes for this sum in all payments to or from the Treasury, and in reckoning duties on imported goods whose invoice is in Sterling money. 2. In 1798, the value of a Pound Sterling was fixed at $4.443, which is now called its nominal value. QUEST.-371. What is currency? 372. On what does the intrinsic value of the coins of different countries depend? 373. How is the relative value of foreign coins determined? What is the value of a Pound Sterling? Of a guinea? A franc? Five-franc piece? A doubloon? *Hind's Arithmetic. 374. The process of changing money expressed in the denominations of one country to its equivalent value in the denominations of another country, is called Exchange of Currencies. Ex. 1. Change £20 sterling to Federal money. Suggestion. Since £1 is worth $4.84, £20 are worth 20 times as much; and $4.84×20=$96.80. Ans. 2. Change £5, 13s. 6d. to Federal money. Operation. £5, 13s. 6d. £5.675. (Art. 200.) to the decimal of a Value of £1=$ 4:84 Ans. $27.467. (Art. 215.) Reduce 13s. 6d. pound, and multiply the sum by $4.84. 375. Hence to reduce Sterling to Federal money. Set down the pounds as whole numbers, and reduce the given shillings, pence, and farthings to the decimal of a pound; then multiply the whole sum by $4.84, (the value of £1,) point off the product as in multiplication of decimals, and it will be the answer required. OBS. 1. Guineas, Francs, Dubloons, and all foreign coins, may be reduced to Federal currency, by multiplying the given number by the value of one expressed in Federal money. 2. The rule usually given for reducing Sterling to Federal money, Is to reduce the shillings, pence, and farthings to the decimal of a pound, and placing it on the right of the given pounds, divide the whole sum by. This rule is based on the law of 1798, which fixed the value of a pound at $4.414, and that of a dollar at 4s. 6d. But $4.44 is 9 per cent. of itself, or 40 cents, less than $4.84, which is the present legal value of a pound; consequently, the result or answer obtained by it, must be 9 per cent. too small. A dollar is now equal to 49.6d. very nearly, instead of 54d. as formerly. 3. What is the value of £100 in Federal money ? 4. What is the value of £275, 15s. in Federal money? 5. Change £450, 7s. 6d. to Federal money. 6. Change $27.467 to Sterling money. Solution. Since there is £1 in $4.84, in $27.467 there QUEST.-374. What is meant by exchange of currencies? 375. How is Sterling money reduced to Federal? Obs. How may any foreign coins be reduced to Federal money? are as many pounds, as $4.84 is contained times in it; and $27.467+4.84-5.675; that is, £5.675. Reducing the decimal .675 to shillings and pence, (Art. 201,) we have £5, 13s. 6d. for the answer. Hence, 376. To reduce Federal to Sterling money. Divide the given sum by $4.84, (the value of £1,) and point off the quotient as in division of decimals. The figures on the left hand of the decimal point will be pounds; those on the right, decimals of a pound, which must be reduced to shillings, pence, and farthings. (Art. 201.) 7. Change $486.42 to Sterling money. 8. Change $1452 to Sterling money. 376. a. In buying and selling Bills of Exchange on England, the premium or discount is frequently reckoned at a certain per cent. on the nominal value of a Pound Sterling, which is $4.444 (Art. 373. Obs.) 9. What is the worth of a bill of exchange of £100 on London, at 9 per cent. premium? Solution.-£100-$4.444 $444.444, the nominal value. Then, $444.444.09 $40.00, the premium. And $444.44+$40-$484.44. Ans. 10. What is the value of £1325, 10s., at 8 per cent. premium. 377. Previous to the adoption of Federal money in 1786, accounts in the United States were kept in pounds, shillings, pence, and farthings. OBS. At the time Federal money was adopted, the colonial currency, or bills of credit issued by the colonies, had more or less depreciated in value: that is, a colonial pound was worth less than a pound Sterling; a colonial shilling, than a shilling Sterling, &c. This depreciation being greater in some of the colonies than in others, gave rise to the different State currencies. Thus, In New England currency, Va., Ky., and Tenn, 6s. or £ 2=$1. QUEST.--376. How is Federal money reduced to Sterling? 377. Previous to the adoption of Federal money, in what were accounts kept! |