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Rule. Multiply each partner's stock by the time it was in trade, and divide the entire gain or loss by the sum of the several products; by the quotient multiply the product of each partner's stock and time, and the result will be his share of the gain or loss. Or,

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.

2. Goodwin commenced business January 1, with a capital of $ 3200; May 1, he took Blunt into partnership, with a capital of $ 4200; and at the end of the year they had gained $ 240. What was each partner's share of the gain?

Ans. Goodwin's gain, $ 128; Blunt's gain, $ 112.

3. Three men hire a pasture in common, for which they are to pay $ 26.40. A put in 24 oxen for 8 weeks, 1$ put in 18 oxen for 12 weeks, and C put in 12 oxen for 10 weeks. What ought each to pay?

4. Barclay, Hickman, and Oliver are partners. Barclay furnishes of the capital $ 300 for 5 months, Hickman $ 400 for 8 months, and Oliver $ 500 for 3 months; they gain $ 200. After paying $ 50 for advertising and $ 50 for agency, what will be each partner's share of the net profits?

Ans. Barclay's share, $24.19^-J-; Hickman's, $51.6139T; Oliver's, $24.1fJif

5. A, B, and C engaged in partnership, with a joint capital of $ 1000, A putting in stock for 7 months, B for 8 months, and C for 12 months. Of the profits A's part was $ 21; B's, $ 40; and C's, $ 24. Required the capital each put in.

Ans. A, $ 300; B, $ 500; C, $ 200.

6. White and Daniels traded in company, with a joint stock of $6300. White's money having been employed 12 months, and Daniel's 8 months, on dividing profits, each had gained exactly the same sum. How much of the capital did each furnish?

7. Three men engage in partnership for 20 months. A at first put into the firm $ 4000, at the end of four months he put in $500 more, and at the end of 16 months he took out $1000; B at first put in $3000, at the end of 10 months he took out $1500, and at the end of 14 months he put in $3000; C at first put in $2000, at the end of 6 months he put in $ 2000 more, at the end of 14 months he put in §2000 more, and at the end of 16 months he took out $ 1500; they had gained by trade $ 1420. What is each man's share of the gain?

Ans. A's gain, S 1680; B's gain, $ 1260; C*s gain, $ 1480.

8. Grover and Thorndike are associated in trade, Grover contributing of the capital $12000, and Thorndike $ 18000. At the end of 6 months they reduce the joint stock $ 5000, by each withdrawing an equal sum. 3 months afterwards Thorndike withdraws § 6000, and Grover $ 1000. The business proving a losing one, they dissolve copartnership at the end of the year. Required what part of the stock then remaining, which was only $ 15000, belonged to each of the partners?

Ans. To Grover, $7276.69-£&; Thorndike, $7723.30^%.

9. John Jones, Samuel Eaton, and Joseph Brown formed a partnership, under the firm of Jones, Eaton, & Co., with a capital of $ 10,000; of which Jones put in $4000, Eaton put in $ 3500, and Brown put in $ 2500; but at the end of 6 months Jones withdrew $ 2000 of his stock, and at the end of 8 months Eaton withdrew $ 1500 from the firm; but at the end of 10 months Brown added $ 2000 to his stock. At the end of 2 years they found their gains to be $1041.80. What was the share of each man?

Ans. Jones's gain, $ 300.51+J; Eaton's gain, $300.51+f; Brown's gain, § 440.76T3j.

10. James Bradshaw commenced trade, January 1, 1856. with a capital of $ 10000, and after some time formed a partnership with John Parkman, who contributed to the joint stock $ 2800. In course of time they admitted into the firm Joseph Delano, with a stock of $ 3600. On making a settlement, January 1, 1857, it was found that Bradshaw had gained $ 2250; Parkman, $ 420; and Delano, $ 405. How long had Parkman's and Delano's money been employed in trade, and what rate of interest per annum had each of the partners gained on their stock?

Ans. Parkman's, 8 months; Delano's, 6 months. Gained 22J per cent. interest.

BANKRUPTCY.

419i Bankruptcy refers to business failures and inability to meet pecuniary liabilities.

A bankrupt, or insolvent, is one who fails or becomes unable to pay his debts.

An assignee is a person selected to take charge of the property and effects of a bankrupt, to convert the same into cash, and, after deducting the necessary expenses of settling, to divide the net proceeds, as the law requires, among the creditors.

The distribution is generally made pro rata, each creditor receiving according to his respective demand, or just claim.

420. To find each creditor's dividend or share of the net proceeds of an insolvent estate.

Ex. 1. A bankrupt owes to A $500, to B $1200, and to C $ 4300; and the net cash proceeds of his estate amount to only $ 1500. How much does he pay on $ 1, and what dividend does each creditor receive?

Ans. 25 cents on a dollar. A receives $125; B, $300; and C, $ 1075.

OPERATION.

A's claim, $ 500 $ 500 X -25 = $ 125, A's share. B's " $ 1200 $ 1200 X -25 = $ 300, B's share. C's " $ 4300 $ 4300 X -25 = $ 1075, C's share. Entire claims, $ 6000 Proof, $ 1500, entire proc'ds.

$ 1500.00, 6000 = $ 0.25, or 25 cents on $ 1.

Rule. Divide the net proceeds of the insolvent estate by the number denoting the total amount of its indebtedness, to find the sum it pays on each dollar of the debts.

Multiply each man's claim by the sum the estate pays on a dollar, to obtain each man's dividend.

Examples.

2. Clarke, Soule, & Co. have failed. Their liabilities are $ 63500, their assets have a cash value of $ 52384, and the expenses of settling are $ 1584. How much can they pay on a dollar, and what dividend should John Dayton receive, whose claim is $8361.55? Ans. 80 cents on a dollar; $0689.24.

3. A merchant failing in trade owes A $ 600, B $ 760, C $840, and D $800. The net proceeds of his effects are $ 2275. What dividend does each of his creditors receive?

Ans. A, $ 455; B, $ 576.33$; C, $ 637; D, $ 606.662.

4. J. Bonney owes A $ 400, B $ 300, and C $ 1000. His effects are worth $ 600. What sum can he pay each of his creditors?

5. A manufacturing company becomes insolvent. Its indebtedness amounts to $ 300000. Its assets consist of factory buildings and machinery worth $ 180000, stock worth $ 40000, and bills receivable good for $ 12875. The charges of the court of insolvency and the assignee will amount to 3£ per cent. on the amount distributed to the creditors. How much will the company pay on a dollar, and what will be Amos Henderson's dividend on a claim of $ 1360.60?

Ans. 75 cents on a dollar; $ 1020.45.

TAXES.

421. A Tax is a sum of money assessed on individuals by goverpment, corporations, societies, districts, &c.

Taxes for government purposes are imposed on property, and in most States on persons.

A poll or capitation tax is one without regard to property, on the person of each male citizen liable by law to assessment. A person thus liable is termed a poll.

422. Immovable property, such as lands, mills, houses, &c, is called real estate. All other property, such as money, notes, mortgages, cattle, shipping, furniture', &c, is called personal property.

423. In assessing taxes, it is necessary to have an inventory of taxable property; and, if a levy on the polls is to be included, there should be also a complete list of taxable polls.

424^ The method of assessing taxes, though not precisely the same in all the States, is yet in most of them virtually the same.

In some of the States, however, the public schools are supported in whole or in part by rate bills; that is, the expenses of the schools, in whole or in part, are apportioned among the inhabitants patronizing the same, according to the number of days of each pupil's attendance.

Note. — Tn Massachusetts one sixth part of the whole sum to be raised is assessed upou the polls; provided the whole |r,11 tax assessed in any one year upon any individual for town, county, and State purposes, except highway taxes, shall not exceed two dollars.

425. To assess a state, county, town, or other tax.

Ex. 1. The inhabitants of a certain town are to be taxed $ 4109. The real estate of the town is valued at $ 493000, and the personal property at $ 177000. There tire 506 polls, each of which is to be taxed $ 1.50. "What is the tax on each dollar of property? What is J. B. Tewksbury's tax, whose real estate is valued at $ 3700, and his personal at $ 2300, he paying for 2 polls?

OPERATION.

$ 1.50 X 506 = $759, amount assessed on the polls.

$ 493000 + $177000 = $ 670000, amount of taxable property.

$ 4109 — $ 759 = $ 3350, amount to be assessed on property.

$3350 H- 670000 = $ .005, tax to be assessed on each dollar.

$ 3700 -f- $ 2300 = $ 6000, Tewksbury's taxable property.

$ 6000 X -005 = $ 30, Tewksbury's property tax.

$1.50 X 2 = $3, Tewksbury's poll tax.

$ 30 -f- 3 = $ 33, amount of Tewksbury's tax.

Rule. Multiply the tax on each poll by the number of taxalde polls; and the product, subtracted from the whole sum to be raised, will (jice the sum to be raised on the property.

The sum to be raised on properly, divided by the whole taxable property, will give the sum to be paid on each dollar of property tared.

Kach man's taxable property, multiplied by the number denoting the sum to be paid on SI, with his poll tax added to the product, will <jivc the amount of his tax.

Note. — The operation of assessing taxes may be facilitated by finding the tax on 82, $3, &c. at the rate of taxation on $ 1, before making the assessment on the inhabitants of the town, &c., and arranging the numbers as in the following

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