PARTNERSHIP OR FELLOWSHIP.

248. PARTNERSHIP or Fellowship is the joining together of several persons in trade, with an agreement to share the losses and profits according to the amount which each one puts into the partnership. The money employed is called the Capital Stock.

The gain or loss to be shared is called the Dividend.

It is plain that the whole stock which suffers the gain or loss, must be to the gain or loss, as the stock of any individual to his part of the gain or loss. Hence,

As the whole stock is to each man's share, so is the whole gain or loss to each man's share of the gain or loss.

PROOF.

Add all the separate profits or shares together; their sum should be equal to the gross profit or stock.

EXAMPLES.

1. A and B buy certain merchandise amounting to £160, of which A pays £90, and B £70: they gain by the purchase £32: what is each one's share of the profits?

2. A and B have a joint stock of $4200, of which A owns $3600, and B $600: they gain in a year $2000: what is each one's share of the profits?

3. A, B, C, and D have £40,000 in trade: at the end of six months their profits amount to £16,000: what is each one's share, supposing A to receive £50 and D £30 out of the profits, for extra services?

QUEST. 248. What is Partnership, or Fellowship? What is the gain or loss called? What is the rule for finding each one's share?

4. Five persons, A, B, C, D, and E, have to share between them an estate of $20,000: A is to have one-fourth, B oneeighth, C one-sixth, D one-eighth, and E what is left: what will be the share of each?

DOUBLE FELLOWSHIP.

249. WHEN Several persons who are joined together in trade, employ their capital for different periods of time, the partnership is called Double Fellowship.

For example, suppose A puts $100 in trade for 5 years, B $200 for 2 years, and C $300 for 1 year: this would make a case of double fellowship.

Now it is plain that there are two circumstances which should determine each one's share of the profits: 1st, The amount of capital he puts in; and 2dly, The time which it is continued in the business.

Hence, each man's share should be proportional to the capital he puts in, multiplied by the time it is continued in trade. Therefore, to find each share,

Multiply each man's stock by the time he continues it in trade; then say, as the sum of the products is to each particular product, so is the whole gain or loss to each man's share of the gain or loss.

EXAMPLES.

1. A and B enter into partnership: A puts in £840 for 4 months, and B puts in £650 for 6 months: they gain £300 · what is each one's share of the profits?

QUEST.-249. What is Double Fellowship? What two circumstances determine each one's share of the profits? Give the rule for finding each one's share.

2. A put in trade £50 for 4 months, and B £60 for 5 months: they gained £24: how is it to be divided between them?

3. C and D hold a pasture together, for which they pay £54: C pastures 23 horses for 27 days, and D 21 horses for 39 days: how much of the rent ought each one to pay?

GENERAL EXAMPLES IN FELLOWSHIP.

1. A bankrupt is indebted $2729, viz.: to A $509,37; to B $228; to C $1291,23; and to D $709,40; but his estate is only worth $2046,75. How much can he pay on the dollar, and how much will each creditor receive?

2. A, B, and C send a ship to sea, which together with her cargo was worth $15000. A and B owned each onefifth, and C the rest. They gained $1250: how much did each pay towards the ship and cargo, and what did each receive of the profits ?

3. A man bequeathed his estate to his four sons in the following manner, viz.: to his first $5000; to his second $4500; to his third $4500; and to his fourth $4000. But on settling his estate, it was found that after paying debts, charges, &c., only $12000 remained to be divided: how much must each receive?

4. A widow and her two sons have a legacy of $4500, of which the widow is to have one-half and the sons each onefourth. Now suppose the eldest son to relinquish his share, and the whole to be divided in the above proportions between the mother and youngest son, what will each receive?

5. Suppose premiums to the value of $12 are to be distributed in a school in the following manner. The premiums are divided into three grades. The value of a premium of the first grade is twice the value of one of the second; and the value of one of the second grade twice that of the third. Now there are 6 to receive premiums of the first grade, 12 of the second, and 6 of the third: what will be the value of a single premium of each grade?

6. Four traders form a company: A puts in $300 for 5 months, B $600 for 7 months, C $960 for 8 months, D $1200 for 9 months. In the course of trade they lost $750: how much falls to the share of each?

7. A and B lay out certain sums in merchandise amounting to $320, of which A pays $180 and B $140; they gain by the purchase $64: what is each one's share ?

ALLIGATION MEDIAL.

250. A MERCHANT mixes 8lb. of tea, worth 75cts. per pound, with 167b. worth $1,02 per pound: what is the value of the mixture per pound?

The manner of finding the price of this mixture is called Alligation Medial.

Hence,

ALLIGATION MEDIAL teaches the method of finding the price of a mixture when the simples of which it is composed, and their prices, are known.

In the example above, the simples 87b. and 167b., and also their prices per pound, 75cts. and $1,02, are known.

Divide the entire cost of the whole mixture by the sum of the simples, and the quotient will be the price of the mixture.

QUEST.-250. What is Alligation Medial? How do you find the price of the mixture?

EXAMPLES.

1. A farmer mixes 30 bushels of wheat worth 5s. per bushel, with 72 bushels of rye at 3s. per bushel, and with 60 bushels of barley worth 2s. per bushel: what is the value of a bushel of the mixture?

2. A wine merchant mixes 15 gallons of wine at $1 per gallon with 25 gallons of brandy worth 75 cents per gallon: what is the value of a gallon of the compound?

3. A grocer mixes 80 gallons of whiskey worth 31cts. per gallon with 6 gallons of water, which costs nothing: what is the value of a gallon of the mixture?

4. A goldsmith melts together 2lb. of gold of 22 carats fine, 6oz. of 20 carats fine, and 6oz. of 16 carats fine: what is the fineness of the mixture?

5. On a certain day the mercury in the thermometer was observed to average the following heights from 6 in the morning to 9, 64°; from 9 to 12, 74°; from 12 to 3, 84°; and from 3 to 6, 70°: what was the mean temperature of the day?

ALLIGATION ALTERNATE.

251. A FARMER would mix oats worth 3s. per bushel with wheat worth 9s. per bushel, so that the mixture shall be worth 5s. per bushel: what proportion must be taken of each sort?

The method of finding how much of each sort must be taken is called Alligation Alternate. Hence,