Art. 158.

When goods are purchased at different times, and on different terms of credit, find the time when each amount will become due, then find what will be the average or mean time for the payment of the whole amount.

11. A merchant purchased the following bills of goods : Feb. 1, a bill of $120 on a credit of 120 days, due June 1. Feb. 15, a bill of $150 on a credit of 90 days, due May 16. May 7, a bill of $ 70 on a credit of 60 days, due July 6. Aug. 12, a bill of $ 90 on a credit of 80 days, due Oct. 31.

What will be the average or mean time of payment for the

2029041049 days, from May 16, which will carry the average or mean time of payment to July 4.

12. A merchant sold the following bills of goods:

Jan. 16th, sold a bill amounting to $350, on a credit of 4 months.

March 11th, sold a bill amounting to $475, on a credit of 6 months.

June 21st, sold a bill amounting to $500, on a credit of 8 months.

What was the average or mean time of payment?

Art. 159. When partial payments are made before the expiration of the term of credit, to find the time when the balance should be paid, so that no loss of interest shall be sustained by either debtor or creditor.

RULE. Multiply the whole debt by the term of credit. Then multiply each payment by the time it was paid after the date of purchase, and subtract the sum of the products from the product of the whole debt multiplied by the whole term of credit. Divide the remainder by the balance due at the expiration of the term of credit; the quotient will be the time when this balance should be paid.

13. A merchant purchased goods to the amount of $1200 on a credit of 8 months; but he offers to pay $400 in 4 months, on condition that the balance shall remain unpaid until it shall cancel the interest of the $400. When will the balance of $800 become due ? Ans. 10 months.

PARTNERSHIP.

Art. 160. A PARTNERSHIP is an association of two or more persons for the transaction of business. Such an association is called a firm or house; and each individual of the association is called a partner.

The whole amount of money contributed by the firm is its capital or joint stock; and the sum contributed by each partner is his part of the joint stock.

A and B formed a partnership with a capital of $25000, of which A furnished $15000, and B $10000; at the expiration of three years they had gained $7500. What was each partner's share of the gain?

=

Since A furnished 15000 of the whole capital or joint stock, he must have of the gain, and $7500 × $4500, A's gain. B furnished 19888 of the whole capital or joint stock, and he must have of the whole gain, and $7500 X = $3000, B's gain. &

When the stock of each of the several partners is employed the same length of time, it is plain that each partner's share of the gain or loss must be in proportion to his share of the joint stock; hence, we have the following rule.

RULE. Make each partner's stock the numerator of a fraction, and the whole capital or joint stock the denominator; the several fractions thus formed will express each partner's part of the joint stock; then multiply the whole gain or loss by each partner's fractional part of the joint stock; the product will be his share of the gain or loss.

1. William and James bought a sheep. William paid $3, and James paid $2; they afterwards sold the sheep, and gained $1. What was the share of each?

2. A and B entered into partnership. A contributed $500, and B $300; at the end of one year, they had gained $160. What was the share of each?

3. A, B, and C, formed a partnership. A furnished $1200, B $1000, and C $800; they gained $360. What was each partner's share of the gain?

Ans. A's share $144. B's share $120. C's share $96.

4. A, B, C, and D, traded in partnership. A furnished $800, B $500, C $300, and D $150; by misfortune they lost $350. What must each partner sustain of the loss?

Ans. A's loss $160. B's loss $100. C's loss $60. D's loss $30.

5. Three men trade in company. The first furnishes $750, the second $600, and the third $525; they gain $325. What is each partner's share?

Ans. The first $130. The second $104. The third $91. 6. A, B, and C, purchased a ship, for which they paid $7500. A paid $2750, B paid $2500, and C the rest; in her first voyage she cleared $3500. What was each partner's share?

Art. 161. When the stock of each of the several partners is employed for different periods of time, it is plain that each partner's share of the gain or loss must be in proportion to his share of the joint stock multiplied by the time it is employed.

ILLUSTRATION. A and B traded in company. A furnished $500 for 8 months; B furnished $600 for 5 months; they gained $280. What was each partner's share of the gain?

The use of $500 for 8 months is equal to the use of 8 times $500 for 1 month, or $4000 for 1 month. The use of $600 for 5 months is equal to the use of 5 times $600 for 1 month, or $3000 for 1 month. $4000+ $3000 = $7000, the whole amount of capital employed for 1 month. A furnished 888 of the joint stock, and he must have of the gain. B furnished 888 of the joint stock, and he must have of the gain. $280 × = $160, A's gain. $280 - $120, B's gain.

=

=

Hence, we have the following rule.

RULE. Multiply each partner's stock by the time it was employed; make each product the numerator of a fraction, and the sum of the several products the denominator; the several fractions thus formed will express each partner's part of the joint stock. Then multiply the whole gain or loss by each partner's fractional part of the joint stock; the product will be his share of the gain or loss.

7. A and B hired a pasture for 6 months, for which they paid $24. A had 5 cows pastured 6 months, B had 6 cows pastured 3 months. How much should each pay?

8. C and D traded in company. C furnished $500 for 6 months, D furnished $1000 for 2 months; they gained $300. What was each partner's share of the gain?

9. A commenced business January 1, with a capital of $4500. April 1, he took B into partnership, with a capital of $5000; at the expiration of one year they had gained $660. What was each partner's share of the gain?

Ans. A's share $360. B's share $300.

10. Charles Adams, John Brown, and William Eaton formed a partnership, under the firm of Adams, Brown & Co., with a capital of $15000; of which Adams furnished $6000, Brown $5000, and Eaton $4000. At the expiration of 6 months, Adams furnished $1500 more; at the expiration of 9 months, Brown furnished $2000 more; and at the expiration of 12 months, Eaton withdrew $2000. At the end of 2 years, they found their profits amounted to $6500. What was each partner's share?

Art. 162.

METHOD OF DIVIDING A BANKRUPT'S EFFECTS

AMONG HIS CREDITORS.

A bankrupt is a trader, or other person, who is unable to pay his just debts.

1. A bankrupt owes A $500, B $650, and C $850; the whole amount of his property is $1500. How much can he pay on a dollar, and how much will each creditor receive?

$500+$650+ $850 = $2000, the amount of his debts. And $1500 $2000 = $.75 the number of cents he can pay on a dollar. $.75 X $500 = $375.00, the number of dollars A will receive. $.75 × $650 = $487.50, the number of dollars B will receive. $.75 X $850 $637.50, the number of dollars C will receive. Hence, the following

rule.

RULE. Divide the amount of the bankrupt's property by the amount of his debts; the quotient will be the per cent., or what he can pay on a dollar. Then multiply the per cent., or what he pays on a dollar, by the amount due each creditor; the several products will express the several shares.

2. A merchant died insolvent, and it was found that his debts amounted to $25000; his property was sold for $6250. How much can he pay on a dollar, and how much will D receive, to whom he owed $4000 ?

Ans. 25 cents on a dollar.

D will receive $1000.

3. A trader failing in business, owes E $1250, F $940, G $1575, and H $1885; his effects amount to $875. much will each of his creditors receive?

How

4. If the money and other property of a bankrupt amount to $3750.75, and he owes A $2650.25, B $1975.50, and C $1250.75, what per cent. can he pay, and what will each creditor receive?

ASSESSMENT OF TAXES.

Art. 163. TAXES are sums of money assessed upon the persons and property of citizens, to defray the expenses of the state, county, city, or town. Each individual, liable to be taxed, is usually assessed a specific sum, called a poll tax, also a specified per centage on his property.

When any required amount of taxes is to be assessed by any city or town, it will be necessary to ascertain the name of each individual liable to be taxed, and the amount of his property; also the number of individuals who pay a poll tax, and the total amount of taxable property in the city or

town.

1. Suppose the city of Boston should assess a tax to the amount of $790000, and the whole amount of taxable property in the city to be valued at $130000000, the number of individuals who pay a poll tax to be 8000, and each of them to be assessed a poll tax of $1.25; what is the amount of poll tax, what per centage is the tax upon the whole amount of property in the city, and what is the amount of A's tax, who pays a poll tax, and whose property is valued at $125000?

$1.25 X 8000 = $10000, the whole amount of poll tax. $790000 $10000 $780000, to be assessed on the whole amount of property. $780000 $130000000= .006 tenths of 1 per cent., or 6 mills on a dollar.

=

$.006 × $125000, the value of A's property $750.00, A's tax on his property, and $750.00 +$1.25, his poll tax, $751.25 the whole amount of A's tax. Hence, the following rule.

RULE. Find the whole amount of poll tax by multiplying the poll tax that each individual is assessed by the number of individuals; the product will be the whole amount of poll tax.

Subtract this amount of poll tax from the whole amount of tax to be assessed; the remainder will be the amount to be assessed on the property.

Divide this amount by the whole amount of taxable property; the quotient will be the per cent. or tax on 1 dollar. Multiply the tax on 1 dollar by the amount of each individual's taxable property; the product will be the tax on his property. Add each individual's poll tax to the tax on his property; the sum will be his whole tax.

2. B, an inhabitant of Boston, pays a poll tax for himself and son; his taxable property is valued at $25675. What is the whole amount of his tax? Ans. $156.55.