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day, freight $175.48, cartage $56.25, and cooperage $8.37. sold out the shipment as follows: June 3, 200 bbl. @ $6.25; June 30, 350 bbl. @ $6.50; July 29, 400 bbl. @ $6.12; Aug. 6, 50 bbl. @ $6.00. Required the net proceeds, and the date when they shall be accredited to the owner, allowing commission at 2%, and storage at 2 cents per week per bbl.

Ans. Net proceeds, $5614.28; due, July 10.

SETTLEMENT OF ACCOUNTS CURRENT.

626. To find the cash balance of an account current, at any given date.

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Required the cash value of the above account, July 1, 1860,

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ANALYSIS.

For either side of the account we write the dates at which the several items are due, and the days intervening between these dates and the day of settlement, July 1. We then compute the interest on each item for the corresponding interval of time, and add it to the item if the maturity is before July 1, and subtract it from the item if the maturity is after July 1; the results must be the cash values of the several items on July 1. Adding the two columns of cash values, and subtracting the less sum from the greater, we have $386.58, the cash balance required. Hence the

RULE. I. Find the number of days intervening between each maturity and the day of settlement.

II. Compute the interest on each item for the corresponding interval of time; add the interest to the item if the maturity is before the day of settlement, and subtract it from the item if the maturity is after the day of settlement; the results will be the cash values of the several items.

III. Add each column of cash values, and the difference of the amounts will be the cash balance required.

EXAMPLES FOR PRACTICE.

1. Find the cash balance of the following account for June 1, 1858, interest at 6 per cent.?

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$1196,67

248 79

Ans. $1202.11.

2. What is the cash balance of the following account on Dec.

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627. Partnership is a relation established between two or more persons in trade, by which they agree to share the profits and losses of business according to the amount of capital furnished by each, and the time it is employed.

628. The Partners are the individuals thus associated.

NOTE. The terms Capital or Stock, Dividend, and Assessment, have the same signification in Partnership as in Stocks.

CASE I.

629. To find each partner's share of the profit or loss, when their capital is employed for equal periods of time.

1. A and B engage in trade; A furnishes $500, and B $700 as capital; they gain $96; what is each man's share?

$ 500

$ 700

OPERATION.

ANALYSIS. The whole amount of capital em

$1200, whole stock.

500 , A's part of the stock.

1200

700 1200

$96 ×

129

=2, B's

=

66 66 66

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700

1200 $40. A's share of the gain. $96 x = $56, B's

66 66 66 66

tal.

of the capi

And since each man's share of the pro

fit or loss will have the same ratio to the whole profit or loss as his part of the capital has to the whole capital, A will have of the $96, and B1⁄2 of the $96, for their respective shares of the profits.

We may also regard the whole capital as the first cause, and each man's share of the capital as the second cause, the whole profit or loss as the first effect, and each man's share of the profit or loss as the second effect, and solve by proportion thus:

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=

:

$1200 : $500 $96 (?)= $40, A's gain,
$1200 : $700 $96: (?)= $56, B's
=

Hence we have the following

66

RULE. Multiply the whole profit or loss by the ratio of each man's share of the capital to the whole capital. Or,

The whole capital is to each man's share of the capital as the whole profit or loss is to each man's share of the profit or loss

EXAMPLES FOR PRACTICE.

1. Three men engage in trade; A puts in $6470, B $3780, and C $9860, and they gain $7890. What is each partner's share of the profit? Ans. A's, $2538.453; B's, $1483.053; C's, $3868.493.

2. B and C buy pork to the amount of $1847.50, of which B pays $739, and C the remainder. They gain $375; what is cach one's share of the gain? 31

B150, C2257

3. A, B, and C form a company for the manufacture of woolen cloths. A puts in $10000, B $12800, and C $3200. C is allowed $1500 a year for personal attention to the business; their expenses for labor, clerk hire, and other incidentals for 1 year are $3400, and their receipts during the same time are $9400. What is A's, B's, and C's income respectively from the business?

4. Four persons rent a farm of 115 A. 32 P. at $3.75 an acre. A puts on 144, B 160, C 192, and D 324 sheep; how much rent ought each to pay

y?

5. Three persons gain $2640, of which B is to have $6 as often as C $4, and as often as D $2; how much is each one's share? 6. Six persons are to share among them $6300; A is to have of it, B, C, D is to have as much as A and C together, and the remainder is to be divided between E and F in the ratio of 3 to 5. How much does each receive?

Ans. A, $900; B, $1260; .C, $1400;

D, $2300; E, $165; F, $275.

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7. Two persons find a watch worth $90, and agree to divide the value of it in the ratio of to; how much is each one's share? NOTE. If the fractions be reduced to a common denominator, they will be to each other as their numerators, (418, III).

8. A father divides his estate worth $5463.80 between his two sons giving the elder more than the younger; how much is each son's share? Ans. Elder, $2892.60; younger, $2571.20.

9. Three men trade in company. A furnishes $8000, and B $12000 Their gain is $1680, of which C's share is $840; required, C's stock, and A's and B's gain. Ans. C's stock, $20,000.

10. Four persons engage in the lumber trade, and invest jointly $22500; at the expiration of a certain time, A's share of the gain is $2000, B's $2800.75, C's $1685 25, and D's $1014; how much capital did each put in? Ans. D put in $3042.

2

11. A legacy of $30,000 was left to four heirs in the proportion of 1⁄2, 1, 1, and, respectively; how much was the share of each?

12. Three men purchase a piece of land for $1200, of which sum C pays $500. They sell it so as to gain a certain sum of

which A takes $71.27, and B $142.54; how much do A and B pay, and what is C's share of the gain? Ans. C's gain, $152.724.

13. Three persons enter into partnership for the manufacture of coal oil, with a joint capital of $18840. A puts in $3 as often as B puts in $5, and as often as C puts in $7. Their annual gain. is equal to C's stock; how much is each partner's gain?

109

14. A, B, and C are employed to do a piece of work for $26 45. A and B together are supposed to do 3 of the work, A and C % and B and C 18, and are paid proportionally; how much must each receive? Ans. A, $11.50; B, $5.75; C, $9.20.

209

CASE II.

630. To find each partner's share of the profit or loss when their capital is employed for unequal periods of time.

It is evident that the respective shares of profit and loss will depend equally upon two conditions, viz.: the amount of capital invested by each, and the time it is employed. Hence they will be proportional to the products of these two elements.

1. Two men form a partnership; A puts in $320 for 5 months, and B $100 for 6 months. They lose $140; what is each man's share of the loss?

ANALYSIS

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The use of $320 for 5 months is the same as the use of 5 times $320, or $1600, for 1 month; and the use of $400 for 6 months is the same as the use of 6 times $400, or $2400, for 1 month; hence the use of the entire capital is the same as the use of $1600 +$2400 $4000 for 1 month. A's interest in the partnership is therefore

1600 2000

, and he will suffer of the loss, or $140 × = $56: and

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