CASE I. 335. When the capital of each partner is employed for equal time. 1. A, B, and C enter into partnership; A furnishes $5000, B $2500, and C $7500; they gain $600; what is each partner's share? Since A's stock is equal to 3, B's to, and C's to, of the entire stock, A must have 1, B, and C, of the gain; hence, A's share is equal to of the $600, or $200, B's to of the $600, or $100, and C's to of the $600, or $300. RULE. Apportion to each partner such a part of the gain or loss as his stock is of the entire stock. Examples. 2. A, B, and C form a joint capital for conducting a business, of which A contributes $1500, B $1950, and C $2100. At the end of a year the profits are $1665; what share should each receive? Ans. A $450, B $585, and C $630. 3. A, B, and C traded together. A put into the business $240, B $360, and C $120. They gained $350; what was each partner's share of the gain? 4. A, B, and C had 108 tons of freight on board a ship, of which A had 48 tons, B 36, and C 24; but in a storm 45 tons were washed away; what was each man's share of the loss? What is the Rule? 5. A and B, with equal stocks, clear in trade $2000; A is to have 3 parts of the profits, and B 2 parts, because A managed the business; what is each one's share of the profits, and how much did A receive for his services? Ans. A's share $1200; B's share $800; and A for services $400. 336. The rule applies to distributing the assets of bankrupts, and other like apportionments. 6. A bankrupt, whose property is only worth $6000, owes A $8000 and B $12000; what should each of these creditors receive? Ans. A $2400, and B $3600. 7. Three persons rent a pasture for the summer; the first puts in 21 horses, the second 17, and the third 47. The rent is $307; what part of it must each pay? Ans. The first $75.84+, the second $61.40, and the third $169.75+ 8. A gentleman left by will to his wife $5000, to his elder son $3000, and to his younger son $2500. But it was found that the property, after paying debts, was only $7475; how should this be apportioned under the will? Ans. To the wife $3559.52+; to the elder son $2135.71+; and to the younger son $1779.76. CASE II. 337. When the capital of the partners is employed for unequal times. 1. A and B trade in company; A puts in $500 for 8 months, and B $600 for 10 months. They gain $240; what is each partner's share of it? OPERATION. A's $500 for 8 mo. = 10 mo. = $4000 for 1 mo. ; Entire stock the same as $10000 for 1 mo. How does the Rule apply? $500 for 8 months is the same as $4000 for 1 month, and $600 for 10 months is the same as $6000 for 1 month; hence the entire stock is the same as $4000+ $6000, or $10000, for 1 month. If $10000 gain in a certain time $240, $4000, or of that sum, must gain of $240, or $96, and $6000, or of the sum, & of $240, or $144. RULE. Multiply each partner's stock by the time it was invested, and apportion the gain or loss in proportion to the products. Examples. 2. A, B, and C commenced trade together the first of June, on $6000 put in by A; the first of August B put in $9000, and the first of September C put in $12000. At the end of the year their gains amounted to $4500; what was each partner's share? Ans. A's $1400, B's $1500, and C's $1600. 3. A, B, and C enter into partnership; A put in $500 for 18 months; B $380 for 13 months; C $270 for 9 months. They lost $818.50; what was each man's share? Ans. A's $450, B's $247, and C's $121.50. 4. Jones and Smith rent a pasture for $275; Jones puts in 80 sheep and Smith 100, but at the end of 6 months they each dispose of half their stock, and allow Hall to put in 50 sheep, what should each pay toward the rent at the end of the year? Ans. Jones $103.12, Smith $128.90g, and Hall $42.963. 5. A and B entered into partnership for 1 year. A at first put in $500, and at the end of 5 months he put in $150 more; B at first put in $600, and at the end of 9 months took out $200. Their year's profits were $682.50; what was each Ans. A's $352.50, and B's $330. man's share? Explain the operation. Repeat the Rule. 6. A builds a mill at a cost of $35000; 2 months after its completion B buys stock in it of A to the amount of $11000; and in 3 months more C purchases also of A $4000 worth of stock. They run the mill for 7 months, and gain during that time $9700; what portion of this belongs to each? Ans. A's share $7205.71+, B's share $2177.55+, and C's share $316.73+. 7. S, T, and Y entered into partnership. S kept his stock in 1 year; T put in as much as S, and for 10 months; Y put in as much as S, and for 4 months. They gained $3400; what was each one's share of the profit? Ans. S's share $2400, T's share $400, and Y's share $600. EQUATION OF PAYMENTS. 338. Equation of Payments is the process of finding the average or equitable time for paying several sums due at different times. 339. The Equated Time is the date at which the items due at different times may be justly paid together. 340. The Average Term of Credit is the time that must elapse before the equated time. CASE I. 341. To find the equated time when the terms of credit begin at the same date. 1. I owe, July 1, to John Wentworth, $600, of which $200 is due in 2 months, $300 due in 4 months, and $100 in 8 months; required the equated time of paying the several items at once. REVIEW QUESTIONS. What is a Compound Proportion? (332) The Rule? (333) Partnership? (334) The Rule when the capital of each partner is employed equal times? (335) When for unequal times? (337) What is Equation of Payments? The Equated Time? The Average Term of Credit? A credit on $200 for 2 mo. is equal to a credit on $1 for 200 times 2 mo., or 400 mo.; a credit on $300 for 4 mo., to a credit on $1 for 300 times 4 mo., or 1200 mo.; and a credit on $100 for 8 mo., to a July 1+4 mo. = November 1, Ans. credit on $1 for 100 times 8 mo., or 800 mo. Hence, the entire credit is equal to a credit on $1 for 2400 mo. ; and a credit on $1 for 2400 mo. is equal to a credit on $600 for of 2400 mo., or 4 mo.; hence, 4 mo. from July 1, or November 1, is the equated time RULE. Multiply each term of credit by the number denoting its debt, and divide the sum of the products by the number denoting the sum of the debts; the quotient will be the average term of credit. The average term of credit, added to the date of the debts, will give the equated time. When any of the items have cents, if 50 or more, reckon them as one dollar, but if less than 50 cents, neglect them. Also, when any result has a fraction of a day, if it is or more, reckon it one day, otherwise neglect it. Examples. 2. Required the average credit for the payment of $500 payable in 2 months, $1000 in 5 months, and 1500 in 8 months. Ans. 6 months. 3. I owe $1600 payable now, and $800 in 90 days; what is the average term of credit? Ans. 30 days. 4. Required the equated time from March 1st, at which to pay $200, of which $40 is due in 3 months, $60 in 5 months, and the remainder in 10 months. Ans. October 4th. 5. May 16, 1866, Albert Day owes $199.50 payable in 30 days, $150.15 in 60 days, and $300 in 90 days; what is the equated time? Ans. July 20, 1866. Explain the operation. Repeat the Rule. How do you proceed when any of the items have cents? When any result has a fraction of a day? |
