The National Arithmetic on the Inductive System

C $480. They gain $54. What is each man's share of the gain?

As the whole stock in trade is $1080, of which $240 belongs to A, A's share of the stock, therefore, will be 24, 号 and as each man's gain is in proportion to his stock, of $54, which is $12, is A's gain. B's stock in trade is $360; therefore of $ 54, which is $18, is B's gain. C's stock is $480; therefore his part of the whole stock is

360

= ; con

sequently C's share of the gain is of $54, which is $24. Hence, to find any man's gain or loss in trade we have the following

RULE. Multiply the whole gain or loss by each man's fractional part of the stock.

NOTE. - The pupil who may be desirous of performing the questions of this rule in the "old way will adopt the following

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 loss.

The following is the statement of the first question, with the answers and proof.

As the stock $1080: $54 :: $240: $12 A's gain.
$1080 $54:: $360: $18 B's gain.
$1080 $54 :: $480: $24 C's gain.

Proof, $12+$18+ $248 54 whole gain.

2. A, B, and C enter into partnership, with a capital of $1100, of which A put in $250, B put in $ 300, and C $550; they lost by trading 5 per cent. on their capital. What was each man's share of the loss?

A's loss, $12.50.

B's loss, $ 15.00.

C's loss, $27.50.

3. Two merchants, C and D, engaged in trade; C put in $6780, and D put in $12,000; they gain $1000. What is each man's share? C's share, $361.02,2. D's share, $638.97,719.

4. M, P, and Q trade in company, with a capital of $10,000; M put in $3000, P $2000, and Q $5000; they gain $500. What is each man's share of the gain?

M's gain, $150. P's gain, $100. Q's gain, $250

5. A, B, and C enter into partnership; A put in $500, B $350, and-C put in 320 yards of broadcloth; they gain $332.50,

of which C's share is $120. What were A's and B's shares of the gain, and what was the value of C's cloth per yard?

A's gain, $125.00. B's gain, $87.50. C's cloth per yd. $1.50.

6. A, B, and C trade in company; A put in $ 5000, B put in $6500, and C put in $7500; they gain 40 per cent. on their capital, but receive the whole amount of their gains in bills, for which they are obliged to allow a discount of 10 per cent. How much was each man's net gain?

A's gain, $1800.

7. A merchant, failing in trade, owes A $ 600, B $760, C $840, and D $800. His effects are sold for $2275. What will each receive of the dividend?

A, $455.00.

B, $576.33.
C, $637.00.

D, $606.66.

8. A bankrupt owes $5000. His effects, sold at auction, amount to $4000. What will his creditors receive on a dollar? Ans. $0.80.

9. A merchant, having sustained many losses, is obliged to become a bankrupt. His effects are valued at $1728, with which he can pay only fifteen cents on the dollar. What did he owe?

Ans. $11,520.

SECTION LVI.

PARTNERSHIP ON TIME.

WHEN merchants in partnership employ their stock for unequal times, it is called Partnership on Time.

EXAMPLES.

1. Two men, A and B, trade in company. A puts in $420 for 5 months, and B puts in $ 350 for 8 months; they gain $ 84. What is each man's share of the gain?

METHOD OF OPERATION BY ANALYSIS.

$420 for 5 months is the same as 5 x $420 = $2100 for 1

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 888 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 × 5=2100

$350 × 8 =2800

4900

4900: 84:: 2100: $36 A's gain.
4900: 84 :: 2800 : $48 B's gain.

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?

$24.19, A's gain. $51.61, B's gain. $24.19, 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.

B should pay $10.80.
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 pay? $7.60,9183.

First man pays

Second man pays $7.60,9103.

A pays

B pays

C pays

$5.87,3.

$2.86,472

$ 1.04,1. $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, $ 300.5113.
Eaton's gain, $300.5113.
Brown's gain, $ 440.76.

SECTION LVII.

GENERAL AVERAGE.

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 imminent, 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 furniture 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. Goods of R. S. Davis cast overboard, Damage of J. Smith's goods,