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There is, indeed, great variety in questions in this rule; but they may be all easily solved by a little consideration, and the following proportion, viz.-That the gains or losses, are in proportion as the quantities of goods.

EXAMPLES.

1. Bought 30 hogsheads of molasses for 600 dollars ; paid in duties 20 dollars 66 cents, freight 40 dollars 78 cents, for storage 6 dollars 5 cents, and for insurance 30 dollars 84 cents: If I sell it at 26 dollars per hogshead, how much shall I gain per cent. ?

$. cts. 600

$26
20 66

30 hhds.
40 78
6 05

$780 00 Sold for.
30 84

698 33 Cost.

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698 33

81 67 Gain. $. cts. $. cts.

$. cts. 693 33 : 81 67

100 11 69+Ans. 2. At 3s. 6d. profit on the pound, how much per cent. ?

Ans. £17 10s. 3. If it. of coffee coșt 12cts, and it sold for 15 cents, what is the profit on 293lb. neat ? Ans. 8dolls. 79cts.

4. If a gallon of wine cost 6s. 8d. and is sold for 7s. 2d. what is the gain per cent. ? Ans. 74 per cent.

5. Sold a repeating watch for 175 dollars, upon which I lost 17 per cent. whereas I ought to have gained 20 per cent. ; how much was it sold for under its just value ?

Ans. 78dolls. Ict. + 6. If I buy broadcloth for 13s. 5d. per yard, how must I sell it to gain at the rate of 25 per cent. ? £. £.

s. d. 100 125

13 5 16 91 Ans. Or thus, 4)13 5

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341

16s. 944. 7. Bought oil for 90 cents per gallon ; at what rate must it be sold to gain 20 per cent. ?

Ans. 108cts.

8. Bought 115 gallons of wine at 1 dollar 10 cents per gallon ; how many gallons of water must be put in, so as to gain 5 dollars by selling it at 1 dollar per gallon!

Ans. 161 gallons. 9. Bought a hhd. of molasses containing 119 gallons, at 52cts. ger gallon; paid for carting the same $1,25cts.; and by accident 9 gallons leaked out ;-at what rate per gallon must I sell the remainder, so as to gain $13 in the whole ?

Ans. 69cts. 2m. + 10. Bought 11cwt. of sugar, at 6 d. per th. but could not sell it again for any more than £2 16s. per cwt.; did I gain or lose by.my bargain ! Ans. Lost £2 118. 4d.

11. Bought cloth at 17s. 6d. per yard, which on examination, I find to be much damaged; and am, therefore, content to lose 15 per cent. by it;-bow must I sell it

Ans. 14s. 102d. 12. By selling broadcloth at $3,25cts. per yard, I lose at the rate of 20 per cent. ; what is the prime cost of said cloth per yard ?

Ans. $4,6 cents, 2fm. 13. If, when I sell cloth at $7 per yard, I gain $10 per cent. ; what will be the gain per cent. when it is sold for $8 per yard ?

Ans. 825,71 cents, 4m. + 14. If I sell a cwt. of sugar for $8, and thereby lose 12 per cent. ; what shall I gain or lose per cent., if I sell 4cwt. of the same sugar for $36 ?

Ans. I lose only 1 per cent.

per yard?

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

By this rule a bankrupt's estate may be divided among bis creditors; as also legacies adjusted when there is a deficiency of assets or effects.

SINGLE FELLOWSHIP. Single Fellowship is when different stocks are employed for any certain equal time.

RULE.*--As the whole stock is to the whole gain or loss, so is each man's particular stock to his particular share of the gain or losset

PROOF.-Add all the shares together, and the sum will be equal to the gain or loss, when the work is right.

EXAMPLES.

1. A and B gained by trade £182. A put into stock

A $300 and B £100; what is each person's share of the profit? £ £ £ £

£. 300+400=700 : 182 : : 300 : 78 A's share.

700 : 182 : : 400 : 104 B's share.

£182 Proof.

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2. A man dying, bequeathed his estate to his three sons in the following manner, viz. to the eldest he gave 1840 dollars, to the second 1550 dollars; and to the third 960 dollars ; but it was found his whole estate was no more than 1840 dollars; what is each one's proportion ?

$778,2977 the first. Ans. 655,63), the second.

406,067, the third. 3. A and B companied ; A put in 450 dollars, and received of the gain ; what did B put in? Ans. $300.

4. Three merchants freight a ship with wine; A loaded 110 tuns, B 97 tuns, and C 133 tuns. In a storm the seamen were obliged to throw 85 tuns overboard; how much must each sustain of the loss ?

Ans. A 274, B 244, C 334 tuns.

C 5. Three men, A, B, and C, contract to build the hull of a vessel for 625 dollars; A works 100 days, and his work is estimated at 1 dollar 80 cents per day ; B works 1011 days, estimated at 1 dollar 60 cents per day; and C

* That the gain or loss in this rule is evidently in proportion to their stocks, may be shown from the nature of the Rule of Three.

+ The first and third contractions of note 4 of the Rule of Three, are often the best for working questions in this ruley especially in decimals.

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work 98 days, at 1 dollar 50 cents per day : how much is each man's proportion according to his work? day. $. cts. days. day. $. cts. days. day. $. cts. days. 1:1 80 ::100 1:

1 60 :: 1011 1: 1 50 :: 98 100

150

1 011

180,00 A's work. 40
162,00 B's do. 160
147,00 C's do. 160

4900 98

147,00

16

489

162,00

$. cts. 489 : 625 :: 162

: 207,0583 489 : 625 : : 147 :

187,88.563 $. 8.

$. cts. 489 : 625

180 230,06233

$230,06-29 A's share. Ans. 207,050B's do.

187,835 C's do.

: :

:

6

$625,00 Proof. 6. A ship worth 3600 dollars being entirely lost, of which belonged to A, i to B, and the rest to C;wbat loss will each sustain ? Ans. A $450. B $900. C $2250.

7. A and B gained 1260 dollars of which A is to have ten per cent. more than B: what is the share of each ?

Ans. A 660dolls. B 600dolls. 8. Three merchants made a joint stock-A put in £565 6s. 8d. B £478 5s. 4d. and C a certain sum; they gained

£373 9s. 11d. of which took £112 lls. 11d. for his part; what is A and B’s part of the gain, and how much did C put in ?

A's gain £141 6s. 8d.
Aps. / B's do. 119 11s. 4d.

C put in 150 78. 8d. 9. A, B, and C, traded in company; A put in $140; B, $250 ; and C put in 120yds. of cloth, at cash price ; they gained $230, of which took $100 for his share of the gain ;-how did C value his cloth per yard in common stock, and what was A's and B's part of the gain ! Ans.

C put in his cloth at $21 per yard; B's part of {was , .

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DOUBLE FELLOWSHIP. Double FelloWSHIP is when the stocks are employed for different times.

Rule.*-Multiply each man's stock by the time of its continuance; then say, as the sum of all the products is to the whole gain or loss, so is each man's particular product to his particular share of the gain or loss.

EXAMPLES 1. A and B hold a piece of ground in common, for which they pay £36-A put in 23 oxen for 54 days, B 21 oxen for 70 days; what part of the rent must each man pay? 23x54=1242 21x70=1470

£.
£.
2712 : 36::

19 10 32 B's.

S. d.

16 9 8913

92 A's.

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£36 Proof. 2. Two merchants enter into partnership for 16 months A put in at first 1200 dollars, and at the end of 9 months 200 dollars more; B put in at first 1500 dollars, and at the expiration of 6 months took out 500 dollars—with this stock they gained 772 dollars 20 cents; what is each man's part of it ?

Ans. A's $401 70cents-B's $370 50 cents. 3. A, B and C, enter into partnership; A put in 85 dollars for 8 months, B put in 60 dollars for 10 months, and C 120 dollars for 3 inonths; by misfortune they lost 41 dollars; what part of the loss must each man sustain?

Ans. A's part $17. B's $15. C's $9. 4. W. Thomas and N. White were joint tenants of a mill, in the building of which Thomas laid out $150, and White 8270. At the end of 7 months, Thomas sold his share to White ; and at the end of the first year White sold the mill. They then made a settlement; and, the year's profit of the mill being ascertained at $260, what was each man's share ?

Ans. Thomas's $54,16 cts. White's $205,83.4 cts. * When the times are equal, the shares of the gain or loss are evidently as the stocks, as in Single Fellowship; and when the stocks are equal the shares are as the times; but when neither are equal, the shares must be as their products.

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