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month ; and $ 350 for 8 months is the same as 8 x $ 350 = $ 2800 for 1 month. The question, therefore, is the same as if A had put in $ 2100 and B $ 2800 for 1 month each. The whole stock would then be $ 4900. A's share of the gains, therefore, will be 2188 = of $ 84 = $ 36. And B's share will be =of $ 84 = $ 48.
RULE. - Multiply each man's stock by the time it continued in trade, and consider each product a numerator to be written over the sum of all the numerators, as a common denominator ; then multiply the whole gain or loss by each fraction, and the several products will be the gain or loss of each man,
Note. - It might be well for the student to be acquainted with the “old way” of performing these questions. The following is the
RULE. — Multiply each man's stock by the time it was continued in trade ; then, as the sum of all the products is to the whole gain or loss, so is each man's particular product to his share of the gain or loss.
The first question would be performed thus : $ 420 x 5=2100 4900 : 84 :: 2100 : $ 36 A's gain. $350 X 8=2800 4900 : 84 :: 2800 : $ 48 B’s gain.
4900 Proof, $36 + $ 48 = $ 84 = A and B's gain. 2. A commenced business, January 1, with a capital of $3200; May 1, he took B into partnership, with a capital of $ 4200 ; and at the end of the year they had gained $240. What was each man's share of the gain?
$128, A's gain.
$112, B's gain. 3. A, B, and C traded in company. A put in $ 300 for 5 months, B put in $ 400 for 8 months, and C put in $ 500 for 3 months ; they gain $100. What is the gain of each ?
$ 24.1911, A's gain. $ 51.61,9, B's gain.
$ 24.1911, C's gain. 4. Three men hire a pasture in common, for which they are to pay $26.40. A put in 24 oxen for 8 weeks, B put in 18 oxen for 12 weeks, and C put in 12 oxen for 10 weeks. What ought each to pay ?
A should pay $ 9.60.
C should pay $ 6.00. 5. Two men in Boston hire a carriage for $25, to go to Concord, N. H., the distance being 72 miles, with the privilege of taking in three more persons. Having gone 20 miles, they
take in A ; at Concord, they take in B; and when within 30 miles of the city, they take in C. How much shall each man
First man pays $ 7.60,918].
$ 5.87,3%. B pays
$ 2.86,412 C pays
$ 25.00,0 6. Three men engage in partnership for 20 months. A at first put into the firm $ 4000, and at the end of four months he put in $ 500 more, but at the end of 16 months he took out $1000; B at first put in $ 3000, but at the end of 10 months he took out $1500, and at the end of 14 months he put in $ 3000; C at first put in $ 2000, and at the end of 6 months he put in $ 2000 more, and at the end of 14 months he put in $2000 more, but at the end of 16 months he took out $1500 ; they had gained by trade $ 4420. What is each man's share of the gain ?
A's gain, $1680. B's gain, $1260.
C's gain, $1480. 7. John Jones, Samuel Eaton, and Joseph Brown formed a partnership, under the firm of Jones, Eaton, & Co., with a capital of $10,000 ; of which Jones put in $ 4000, Eaton put in $ 3500, and Brown put in $ 2500; but at the end of 6 months Jones withdrew $ 2000 of his stock, and at the end of 8 months Eaton withdrew $1500 from the firm ; but at the end of 10 months Brown added $ 2000 to his stock. At the end of 2 years they found their gains to be $1041.80. What was the share of each man ?
Jones's gain, $ 300.5114.
GENERAL AVERAGE is in mercantile law whatever damage or loss is incurred by any part of a ship and cargo for the preservation of the rest.
When real damage occurs, the several persons interested in the ship, freight, and cargo contribute their respective proportions to indemnify the owners of the part in question against the damage or necessary expense which has been incurred for the good of all.
No general average takes place unless the danger was immi- '. nent, and absolutely necessary for the safety of the ship.
Particular Average signifies a partial loss of the ship and cargo, arising from accidents at sea, and the loss must be borne by the owners of the property, who have sustained damage. Underwriters must pay such proportion of the prime cost as corresponds with the proportion of diminution in value occasioned by the damage.
Goods, whether lost, injured, or saved, are to be valued at the price they would have brought in ready money on the ship's arriving at her destined port. The value of the vessel is also estimated in the same manner.
It is a general custom to allow in the general average two thirds of the expense incurred in procuring new masts, cables, and other furniture of the ship, the new materials being much better than the old. A deduction in the general average of from one third to one half is made from the seamen's wages while the vessel is detained in port. Goods are valued at the invoice price when the average claim is settled at the port of lading.
To find the General Average. RULE. — As the value of all the articles subject to contribution is to the whole loss, so is each person's share of that value to his average proportion of the loss; or so is $ 100 to the loss per cent.
The ship General Taylor, in her voyage from Boston to Mobile, on the night of January 10, 1847, was wrecked on Nantucket Shoals ; in consequence of which the captain was obliged to cut away her masts, and heave overboard some of the furni. ture of the ship and part of the cargo. The vessel was finally towed into New York by the steamboat Ohio. A statement of the loss and expenses is as follows:
Amount of the Loss.
. . 772
866 Amount of the freight of goods thrown overboard, 334 " " two thirds of the expense in procuring
new masts, cable, anchors, &c., . , Pilotage and port duties, . . . . . 400 Miscellaneous expenses, . . . . . 25
Contributary Articles. Value of the ship, :.
Do. of R. S. Davis's goods thrown overboard, . . 1728 Do. of J. Smith's goods at Mobile, deducting freight, 2000 Do. of C. Dana's goods do.
7000 Do. of two thirds the ship's freight, . .
$ 25,000 A Statement of what each Contributary Article pays in the General
By this rule merchants estimate their profit and loss in buying and selling goods.
The questions are to be performed by Proportion and the other preceding rules. The pupil should give an analysis of each question.
One of four things is generally required by this rule :
1. To know what per cent. is gained or lost, either in purchasing or selling goods.
2. To ascertain at what price to sell an article to gain or lose a certain per cent.
3. To ascertain the price of an article, when we know wha per cent. is gained or lost.
4. If goods be sold at a certain price, and there be gained
or lost a certain per cent., to ascertain what would be gained or lost at some other price.
The eight following examples will illustrate the above problems.
1. If I buy cloth at $4 per yard, and sell it at $ 5 per yard, what per cent do I gain?
Ans. 25 per cent. OPERATION BY PROPORTION. $5 – $4 = $1; $4:$1 :: $100 : $ 25, that is, 25 per cent.
By analysis. If $4 gain $1, it is evident that $1 will gain 1 of $1 = $0.25 ; and $100 will gain 100 times $ 0.25 = $ 25, that is, 25 per cent., answer as before.
2. When cloth is purchased at $5 per yard, and sold at $4 per yard, what per cent. is lost ?
Ans. 20 per cent. OPERATION BY PROPORTION. $5 – $4=$1. $5: $1 :: $100 : $ 20, that is, 20 per cent.
By analysis. If $1 be lost on $5, it is certain that on $1 there will be lost of $1 = $ 0.20 ; and if on $1 there be lost $0.20, on $100 there will be lost 100 times $ 0.20 = $20, that is, 20 per cent., answer as before ; therefore, when we wish to know what per cent. is gained or lost, either in purchasing or disposing of goods, we adopt the following
Rule. - As the price of the goods is to the gain or loss, so is $ 100 to the per cent. gained or lost.
3. If I buy cloth at $ 4 per yard, for how much must I sell it to gain 25 per cent. ?
Ans. $ 5. OPERATION BY PROPORTION. $100 + $ 25 = $125; $100 : $125 :: $4:$5 Ans. By analysis. If for $100 I receive $125, it is evident that for $1 I shall receive only too of $125 = $1.25, and for $4 I shall have 4 times $1.25 = $ 5, answer as before.
4. If I buy cloth at $ 5 per yard, for what must I dispose of it per yard to lose 20 per cent. ?
Ans. $ 4. OPERATION BY PROPORTION. $100 - $20=$ 80; $100 : $ 80 :: $5 : $4 Ans. By analysis. If $ 80 are to be received for $100, it is certain that for $ 1 there will be paid only 1% = of a dollar =