209. Partnership. Two or more persons, uniting for the purpose of carrying on business together, form what is called a PARTNERSHIP, FIRM, or COMPANY. The capital invested by them is called their STOCK IN TRADE. It is evident that the profit or loss made by the company should be shared among its members in proportion to what the use, or interest, of each man's stock for the time it was invested is worth. When the stocks of the several partners are invested for the same length of time, their use, or interest, will be proportioned to the stocks themselves, and hence each partner's gain or loss will be the same part of his stock that the entire gain or loss is of the entire stock; or it will be the same part of the entire gain or loss that his stock is of the entire stock. 1. A, B, and C trade in company. A puts in $250, B puts in $750, and C puts in $500. At the end of 6 months they find that they have gained $472.50. What is each man's share of the gain? First Solution. - Since A's stock = $250, B's $750, and C's = $500, the entire stock $250 + $750 + $500 = $1500; and as the gain $472.50, it must equal, or 20% of the stock. There = 6 3 63 fore, each man's gain will be of his stock, which gives for A's gain $78.75, for B's gain $236.25, and for C's gain $157.50. = 250 Second Solution. · Since A's stock = $250, B's $750, and C's = $500, the entire stock must equal $1500, of which A's stock - 1500 , B's = 7500 3. Therefore, A should have 500 , C's= 1500= , B should have 2, and C should have of the gain. of $472.50 $78.75 A's share; of $472.50 = $236.25 = B's share; of 2. X, Y, and Z traded in company for 1 year. X put in $1000, Y put in $1500, and Z put in $2000. At the end of the year they found that they had gained $1800. What was each man's share of the gain? 3. A man, failing in business, finds that he owes A $424, B $638, C $197, D $338, and E $574, and that his whole available property amounts only to $1173. How much ought he to pay to each creditor? Suggestion. Since he owes $2171, and has but $1173, he can pay but 17 of his debts. Therefore, he ought to pay A 17 of $424, B of $638, &c. 4. The stock of a bankrupt is valued at $1200, and he owes $4200. How many dollars ought he to pay the person to whom he owes $546? to whom he owes $338.73 ? 5. A, B, C, and D agree to cut 500 cords of wood for $300. When the job is finished, they find that A has cut 125 cords, B 100 cords, C 150 cords, and D the rest. How many dollars ought each to receive? 6. A and B traded in company. A put in $200, and B put in $300. A's share of the gain was $84.56. What was B's share? 7. A and B traded in company, and gained $348, of which B's share was $261. If A's stock was $175, what was B's stock, and A's share of the gain? 8. Samuel Greene and Joseph Irons traded in company. Greene paid in 3 times as much of the stock as Irons, and they gained $1176. What was each one's share of the gain? Suggestion. Since Greene paid in 3 times as much as Irons, both together must have paid in 4 times as much as Irons. Therefore, Irons paid in, and Greene of the stock. 9. William Balch and Joseph Adams bought a ship together, Balch paying in twice as much money as Adams. At the end of one year they sold her, and found that they had realized a profit of $15,000 from her. What was each partner's share? 10. Anderson and Parker, after trading in company for 2 years, found that their profits had been $2400. Allowing that Anderson's stock was of Parker's, how many dollars of the profit ought each to have? 11. A, B, and C traded in company. A put in of the stock, B put in of it, and C put in the rest. On dividing the gain, they found that C's share of it was $321. What was the gain of each of the other partners? 12. William Hall, Edward Johnson, and Henry Whiting traded in company, and gained $6534, of which Johnson's share was $1089. If Johnson's and Whiting's stock was together equal to twice Hall's, what was Hall's share of the gain? What was Johnson's share? 13. A small estate belonged to a large number of heirs: 2 members of the family of A each owned of the estate; 4 of the family of B each owned of it; 4 of the family of C each owned of it; 2 of the family of D each owned 3' of it; 4 of the family of E each owned of it; 3 of the family of F each owned of it; 4 of the family of G each owned of it; 6 of the family of H each owned 3 of the family of I each owned of it. agent for the above-named individuals, sold the estate for $350. How many dollars ought he to give to each? Answer. $ 3.123 to each member of A's family. of it; Mr. Byram, as their interest in NOTE. The above example is a statement of transactions which actually occurred. It was brought to the author for solution, by the agent of the parties. 210. Partnership on Time. In dividing the gain or loss among the partners, when their shares of the stock are invested for unequal times, it becomes necessary to consider both the stock and the time, or to consider the interest of each man's stock for the time it was in trade. The following examples and solutions will illustrate 1 A, B, and C traded in company. A put in $750 for 10 months, B put in $375 for 12 months, and C put in $1125 for 16 months. They gained $860. What was each man's are of the gain? Therefore, A should have, or, of the gain, = : $215. The use of $ 750 for 10 mo. is worth the use of $ 7500 for 1 mo. The use of $ 375 for 12 mo. is worth the use of $ 4500 for 1 mo. The use of $1125 for 16 mo. is worth the use of $18000 for 1 mo. Use of whole stock is worth the use of $30000 for 1 mo. Therefore, A should have 3000, or, of the gain, = $215. 7500 When the stocks of the several partners are convenient multiples or fractional parts of each other, a very neat solution can be given. Thus, in the above example, by noticing that B's stock equals and that C's stock equals of A's, we may have the following: — of A's, Third Solution. - The use of A's stock 10 mo. use of 10 times A's stock for 1 mo. The use of B's, or of A's stock, 12 mo. = use of 12, or 6 times A's stock for 1 mo. The use of C's, or of A's stock, 16 mo. use of, or 24 times A's stock for 1 mo. Use of whole use of 10 + 6 + 24, or 40 times A's stock for 1 mo. Therefore A should have 18, or ; B, or 2; and C2, or 3, of the gain, which will give the same answer as before. 2. Charles French, Francis Baker, and Otis Atherton traded in company, under the name of Charles French & Co. French put in $1000 for 20 mo., Baker put in $800 for 16 mo., and Atherton put in $500 for 20 mo. They gained $1500. How many dollars of the gain ought each to receive? 3. George Jackson, William Leach, and Albert Buflington traded in company. Jackson put in $144 for 6 mo., Leach put in $72 for 7 mo., and Buffington put in $216 for 6 mo. 20 da. They gained $114. What was each man's share of the gain? 4. A, B, C, and D hired a pasture together, in which A pastured 4 cows 13 weeks, B pastured 5 cows 16 weeks, C pastured 8 cows 10 weeks, and D pastured 4 cows 16 weeks. The rent of the pasture was $102. How many dollars ouglit each man to pay? 5. Samuel Austin, Jacob Brown, and Moses Sumner formed a partnership for 2 years, under the name of Samuel Austin & Co. Austin at first paid in to the stock $1000, but after 8 mo. had elapsed he paid in $500 more. Brown at first paid in $1250, and 16 mo. afterwards he paid in $250 more. Sumner at first paid in $1500, but at the end of 16 mo. he took out $500. They gained $3600. What was each man's share of the gain? By this, it appears that the interests of their respective stocks, for the time they were in trade, were alike. equally, and each partner should have Hence, the gain should be divided of $3600, which is $1200. character to those given to the NOTE. Other solutions similar in first example might have been added; but as the pupil can readily discover them, they have been omitted. 6. Joseph Southwick, Francis Lowe, and Henry Taft formed a partnership for 3 years, under the name of Southwick, Lowe, & Taft. When they commenced business, each partner put in $3000; but at the end of the first year Southwick put in $3000 more, and Lowe withdrew $1500. At the end of the second year, Southwick withdrew $2000, and |