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19. If I buy 28 pieces of stuffs at 4 L. per piece, and sell 10 of the pieces at 6L. per piece, and 8 at 5L. per piece; at what rate per piece must I sell the rest, to gain 20 per cent. by the whole ?

Ans. 3L. 8s. 9 d. 20. Having bought a parcel of goods for 18 L. and sold the same immediately for 25 L. with 4 months credit, what is gained per cent. per annum? Ans. 116L. 138. 4d:

FELLOWSHIP.

Fellowship is a rule, by which merchants, &c. trading in company with a joint stock, are enabled to ascertain each person's particular share of the gain or loss, in proportion to his share in the joint stock.

By this rule also legacies are adjusted, and the effects of bankrupts divided, &c.

CASE 1. When the several stocks in company are considered without regard to time.

RULE.
As the whole sum, or stock,
Is to the whole gain or loss;
So is each person's share in stock, &c.
To his share of the gain or loss.

PROOF. The sum of the several shares must equal the gain or loss.

EXAMPLES 1. Three merchants trading together, gained 800 dollars; A's. stock was 1200 dols. B's. 4800 dols. and C's, 2000 dols, : what was each man's share of the gain?

A's stock 1200 dols.
B's stock 4800 dols.
C's stock 2000 dols.

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Whole stock 8000 dollars.
dols. dols. dols. dois.
As 8000 : 800 :: 1200 : 120 A's share of gain.
As 8000 : 800 :: 4800 ; 480 B's share of gain.
As 8000 : 800 :: 2000 : 200 C's share of gain.

:

2. D. E. and F. trading together gained 120L. D's stock was 140L. E's was 300 L, and F's was 160 L.; what was each man's share of the gain?

Ans. D's share was 28L. E's 60L. F's 32L. 3. Three merchants trading together, lost goods to the value of 1920 dols. ; now suppose A's stock was 2880 dols. B's 11520 dols. and C's 4800 dols. ; what share of the loss must each man sustain?

SA's share 288 dols. Ans.

C's 480 dols. 4. A, B, and C, freighted a ship with 108 tuns of wine, of which A. had 48 tuns, B. 36, and C. 24, but by reason of stormy weather were obliged to cast 45 tuns overboard d; how much must each man sustain of the loss ?

Ans. A. 20 tuns, B. 15, and C. 10. 5. If the money and effects of a bankrupt amount to 1400L 14s. 6d. and he is indebted to M. 742L. 12s. to B. 641 L. 198. 8d. and to C. 987 L. 19s 9d.: how must the property be divided among them?

M. must have 438 L. 85. 4 d. Ans. B.

379 L. Os. 3 d. C.

583L. 5s 93d. 8. Suppose a person is indebted to $.70L. to T.400L. and to V. 140 L. 12s. 6d. but upon his decease his property is found to be worth only 409 L. 145.: how must it be divided among his creditors ?

S. must have 46L. 19s. 3 d. Ans. T.

268 L. 75. 7 d. v.

94 L. 78. old. 7. Three graziers pay among them 120 dols. for a grass, inclosure, into which they put 300 oxen, whereof L. had 80, N. 100, and C. 120; how much should each person pay?

Ans. L. 32 dols. N. 40 dols, and C. 48 dols.

CASE 2. When the respective stocks in company are considered with time.

RULE.
Multiply each man's stock by its time, then,

As the sum of the products,
Is to the whole gain, or loss;
So is each particular product,
To its share of the gain, or loss.

EXAMPLES. 1. Three merchants traded together; A. put in 120 L. for 9 months, B. 100 L. for 16 months, and C. 100 L. for 14 months, and they gained 100L. ; what is each man's share ?

L.
A's stock 120 X 9 = 1080
B's stock 100 X 16 * 1600
C's stock 100 x 14

= 1400

m.

Sum 4080 uip, L. Prod. L. 8. As 4030 : 100 :: 1080 : 26 9 4 + A's share. As. 4080 : 100 :: 1600 : 39 4. 3 + B's share. As 4080 : 100 :: 1400 : 34 6 - 31+ C's share. 2. B. C. and D. traded together; B. put in 50 dollars for 4 months, C. 100 dollars for 6 months, and D. 150 dollars for 8 months; they gained $ 126.80: what is each man's share of the gain

Ans. B's share is $12.68, C's $38.4, D's 876.8. 3. B. and C. trade in company; B. put in 950 L. for 5 months, and C. 785 L. for 6 months, and by trading they gain 275 L. 18s. 4d.: what is each man's share of the gain?

Ans. B's 138L. 10s, 10d. C's 137 L. 7s.6d. 4. Thrce merchants trade in company; A. put in 400L. for 9 months, B. 680 L. for 5 months, and C. 120 L. for 12 months; but by misfortunes lost goods to the value of 500L. : what must each man sustain of the loss ?

L. d.
ŞA. must lose 213

5 4 + Ans. B.

8 5 + C.

85 6 + Ŝ. A. B. and C. made a stock for 12 months; A. put in at first 8 873.60, and 4 months after he put in $96.00 more ;

B.

pul in at first $979 . 20, and at the end of 7 months he took out $206.40; C. put in at first $355.20,

8.

and 3 months after he put in $ 206.40, and 5 months after that he put in $240.00 more.

At the end of 12 months their gain is found to be 8 3446 . 40; what is each man's share of the gain ? SA

A's share is $1334.82
Ans. B's

$127.1.611 +
C's

$839.96

EXCHANGE.

Exchange is a rule by which the money of one state or country is reduced to that of another.

Par is equality in value ;* but the course of exchange is frequently above, or below par.

Agio is a term used to signify the difference, in some countries, between bank and current money.

DOMESTIC EXCHANGE. To change the currency of either State into that of any other, work by the Rule of Three ; or by the theorems in the following page.

EXAMPLES. 1. What is the value of 750 L. Massachusetts currency, in New-York ?

Ans. 1000 L. d. L.

Or thus: 6 : 8 : : 750

L. 20.

3750

250
15000
8

1000 L..

6)120000

210)200010

1000 L.

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* Note-A Spanish dollar is valued at 45. 6d. sterling, and at 7s.6d Pennsylvania currency: 4s. 6d. sterling is, therefore, equal to 7s. 6d. Pennsylvania currency, and 100L. of the former is equat to 166L. of the latter. When exchange between England and Penasylvania is at this rate, it is said to be ar par.

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either opposite to that state, or under it, in the table

Note.-The value of a dollar in any state is found,

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