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FELLOWSHIP.

124. FELLOWSHIP is the union of two or more individuals in trade, with an agreement to share the losses and profits in the ratio of the amount which each individual puts into the partnership. The money employed is called the capital stock.

The loss or gain to be shared is called the divide..d. What is Fellowship? What is the capital stock? What is the dividend ?

EXAMPLES.

1. A, B, and C, enter into copartnership. A put in $180, B put in $240, and C put in $480. They gained $300. What is each one's part of the gain?

$180 A's stock.
240 B's stock.
480 C's stock.

$900 whole stock.
180= =A's part of the entire stock.

40= = B's 66 66 66 66 66

489==C's 6 6 6 6 6
Hience, A must have } of $300= $60 for his gain.

B 6 " As of $300= $80 6 6 6
C6 " is of $300=$160 “ “ “

$300
From the above we may deduce the following

RULE. Make each partner's stock the numerator of a fraction, and the sum of their stock a common denominator ; then multiply the whole gain or loss by each of these fractions, for each partner's share.

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2. Five persons, A, B, C, D, and E, are to share between them $2400. A is to have ; B is to have ; C is to have }; D and E are to divide the remainder in proportion to the numbers 5 and 7. How much does each one receive ?

A receives of $2400=$400.
B 6 of 2400= 600.
C 6 of 2400= 900.

$1900.
$2400

1900

$500 sum of D's and E's part.
5 represents D's part.
7 represents E's part.

12 represents the sum.
Hence, D must receive of $500= $208.331.

E must receive 1 of 500= 291.66. 3. There are three horses belonging to three men, employed to draw a load of plaster a certain distance for $26.45. It is estimated that A's and B's horses do of the labor; A's and C's horses *; B's and C's horses i. They are to be paid proportionally according to these estimates. . What ought each man to receive ?

A's and B's horses do 75.
A's and C's horses do M=H

B's and C's horses do = .. Adding all these fractions together, we shall obtain twice what they all do, according to the above estimate; if we take half the sum, it will give the part supposed to be done by all.

Hence, A's, B's, and C's horses do 3%.

If from this fraction we subtract , which is B's and C's, we find li for the part supposed to be done by A's horse. In the same way we find X for the part done by B's horse. will represent the part done by C's horse.

Therefore, the parts which the three horses are supposed to do are 1, 2, %. These fractions, having a common denominator, must be to each other as their numerators, that is, as 10, 5, 8, whose sum is 23. Hence, A ought to have of $26.45=$11:50.

B ought to have as of 26.45= 5.75.
C ought to have any of 26-45= 9.20.

Proof, $26.45. 4. A, B, and C, agree to contribute $365 towards building a church, which is to be at the distance of 2 miles from A, 27 miles from B, and 31 from C. They agree that their shares shall be proportional to the reciprocals of their distances from the church. What ought each to contribute ?

The' reciprocals of the numbers 2, 27, 31, are 1, 2, ; these reduced to a common denominator, become 1944, 1, . Now, we must obviously divide $365 in the proportjon of these numerators; their sum is 365. Hence, A must contribute 36} of $365=$161.

of 365 = 112.
of 365= 92.

Proof $365. 5. A person wills to his two sons and a daughter, the foliowing sums: To the elder son $1200, to the younger son $1000, and to his daughter $600; but it is found that his whole estate amounts to only $800. How much ought each child to receive ?

( The elder son received $342.8577. Ans.( The younger son received 285-7144.

( The daughter received 171.4284. 6. Four persons, A, B, C and D together contribute $500 towards the erection of a school-house, which is located at the distance of 1 of a mile from A's residence, 1 of a mile from B's, of a mile from C's, and 1 mile from D's.

They contributed in the reciprocal ratio of their respective distances from the school-house. How much did each

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125. WHEN the stock of the several partners continues in trade for unequal periods of time, the profit or loss must be apportioned with reference both to the stock and time. In such cases the fellowship is called DOUBLE FELLOWSHIP. What is Double Fellowship?

EXAMPLES

1. Three partners, A, B and C, put into trade money as follows: A put in $400 for 2 months; B put in $300 for

4 months; C put in $500 for 3 months. They gained $350. How must they share of this gain ?

It is evident that $400 for 2 months is the same as $400 X 2=$800 for one month.

And $300 for 4 months is the same as $300 X4=$1200 for one month.

And $500 for 3 months is the same as $500x3=$1500 for one month. Hence, $800 A's money for one month.

1200 B's money for one month,
1500 C's money for one month.

$3500
Therefore, by Single Fellowship,

A must have 80%= of $350=$80.
B 6 6 366=of 350=120.
C " " 150= of 350= 150.

$350 Proof.

RULE.

Multiply each partner's stock by the time it was in trade ; make each product the numerator of a fraction, and the sum of the products a common denominator; then multiply the whole gain or loss by each of these fractions, for each partner's share. Repeat this Rule.

2. Three farmers hired a pasture for $55.50 for the season. A put in 6 cows for 3 months, B put in 8 cows for 2 months, C put in 10 cows for 4 months. What rent ought each to pay?

A ought to pay $13.50. Ans. < B 66 12:00.

30.00.

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