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of the several partners was in the firm the same term of time: by misfortunes of various kinds, they lost 12375 dollars 20 cents. What loss did each partner sustain ?

9. A, B, and traded in partnership. A's stock was 385 dollars 50 cents; B's 297 dollars 75 cents; C's 175 dollars 25 cents: they gained 343 dollars 40 cents. What was each one's share of gain ?

When the stock of the several partners is in the firm unequal terms of time, the profit or loss must be apportioned with reference both to stock and time. Thus, A, B, and C, traded in company; A put in 200 dollars for 3 months, B 180 dollars for 5 months, and C 70 dollars for 10 months: they gained 132 dollars. Now, to · apportion this gain justly, we say that A's 200 dollars for 3 months was the same as 600 dollars for 1 month; B's 180 dollars for 5 months the same as 900 dollars for 1 inonth; and C's 70 dollars for 10 months the same as 700 dollars for 1 month; therefore it is the same as if A had put in 600 dollars, B 900 dollars, and C 700 dollars, all for an equal term of time. These sums added together make 2200 dollars; therefore, A had 2000 of the gain, B 226, and C 220: These fractions, when reduced, are

5, 5, and 7 of 132 dollars is 6 dollars; then A had 6 times 6 dollars, B 9 times 6 dollars, and C 7 times 6 dollars.

RULE. Multiply each partner's stock by the time it was in the firm; 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.

10. A, B, and C traded in company. A put in 400 dollars for 9 months, B 300 dollars for 6 months, and C 200 dollars for 5 months: they gained 320 dollars. What was the gain of each ?.

11. X, Y, and Z formed a partnership. X put into the firm 500 dollars for 18 months, Y 380 dollars for 13 months, and Z 270 dollars for 9 months; but they lost 818 dollars 50 cents. What was the loss of each?

12. R and S entered into partnership for 16 months; R put in at first $ 1200, and at the end of 9 months $200 more. S put in at first $ 1500, and after 6 months had elapsed he took out $ 500. In this partnership they gained $772.20. How must the gain be divided ?

13. On the first day of January, A began business with 380 dollars; on the first day of May following, he took B into partnership with 270 dollars; on the first day of the next August, they took in C with 400 dollars: at the end of the year, they found there was a gain of 436 dollars. What share of the gain had each ?

14. Gould and Davis entered into partnership for one year. Gould's stock, at first, was only 500 dollars, but at the end of 5 months he put in 150 dollars more. Davis's stock, at first, was 600 dollars, but at the end of 9 months he took out 200 dollars: at the end of the year, it was found they had gained 682 dollars 50 cents. What was the gain of each partner?

15. Three farmers hired a pasture at 60 dollars 50 cents for the season. A put in 5 cows 4 months, B 8 cows 5 months, and C 9 cows 6 months. What rent did each pay?

16. A and B hired a coach in the city, to go 40 miles for $20, with liberty to take in two more passengers. When they had ridden 15 miles they admitted C; and on their return, within 25 miles of the city, they admitted D. As each person is to pay in proportion to the distance he rode, it is now required to settle the coach hire justly between them.

17. Messrs. Howard, Bender, Dorr, and Tremere were partners for 2 years, under the firm of Joseph Howard and Co. When the firm commenced business, Howard's stock was 6000 dollars, Bender's 3500 dollars, Dorr's 2800 dollars, and Tremere's 1700 dollars. At the end of 8 months, Howard withdrew 3000 dollars from the firm; after trading 10 months, Tremere added 1300 dollars to his former stock; at the end of the first year, Bender withdrew 800 dollars. At the close of the two years, they had gained 3608 dollars 40 cents. How much was each partner's share of the gain ?

XXI.

BANKRUPTCY. In the course of mercantile business, it happens not unfrequently, that a merchant, either from misfortune or imprudence, becomes insolvent, and what property he has, is distributed among his creditors in proportion to their respective dues.

Questions in bankruptcy are performed on the same principle with those in partnership: we first ascertain the amount of the bankrupt's property, then the amount of his debts, next what per cent. he pays, and then multiply the sum due to each creditor by the decimal expressing the per cent. which the debtor pays.

1. A man failing, owed the following sums: to A 120 dollars 68 cents, to B 150 dollars 75 cents, to C 310 dollars 32 cents, to D 208 dollars 25 cents; and his whole property amounted to only 632 dollars, which was divided among them in proportion to their respective demands. How much did each receive?

2. If the money and effects of a bankrupt amount to 3361 dollars 74 cents, and he is indebted to A in the sum of 1782 dollars 24 cents, to B 1540 dollars 76 cents, and to C2371 dollars 17 cents, how much will each of them receive ?

3. A person failing in trade, owed A 539 dollars, B 756 dollars 30 cents, C 854 dollars 16 cents, and D 1200 dollars; his property amounted to 837 dollars 49 cents, which was distributed among them in proportion to their several demands. How much did each creditor lose by the failure ?

4. A bankrupt owes A 813 dollars 74 cents, B 3673 dollars 46 cents, C 1840 dollars 40 cents, D 117 dollars 80 cents, and E 814 dollars 60 cents, his whole property, worth 4029 dollars 30 cents, he gives up to his creditors. What per cent. does he pay, and how much does each creditor receive ?

XXII.

ASSESSMENT OF TAXES. Taxes are imposts paid by the people for the support of government. They are assessed on the citizens in proportion to their property; except the poll tax, which is assessed by the head without regard to property.

An accurate inventory of all the taxable property of every citizen is indispensable to a just assessment of taxes, and is the first thing to be obtained.

When a tax is to be assessed on property and polls, we first ascertain the amount which the polls pay, and deduct it from the sum to be raised; then apportion the remainder according to each man's property.

To effect the apportionment, we find what per cent. of the whole property to be taxed, the sum to be raised is; then multiply each man's inventory by that per cent. expressed in decimals, and the product is his tax.

1. A tax of four hundred and fifty dollars is to be assessed on a parish, in which there are 40 rateable polls. Of this tax, that to be assessed on the polls amounts to 50 dollars; leaving 400 dollars to be assessed on the real and personal property of the parish, which by inventory is 40000 dollars. What must a parishioner pay, whose real estate in the inventory is 700 dollars, personal property 150 dollars, and who pays for one poll ? 400 dollars is one per cent. (.01) of 40000 dollars.

Real estate 700
Personal estate 150
Total property 850

01
Tax on property 8.50

Poll tax 1.25

Total tax $9.75 Ans. : 2. An incorporated town, in which the rēal and personal property was valued in the inventory at 72856 dollars, and

in which there were 154 rateable polls, voted to raise 1285 dollars 34 cents by taxation. The tax on each poll was 1 dollar 25 cents. How much did A pay, whose real estate stood in the inventory at 2146 dollars, personal property at 224 dollars, and who paid for 1 poll? How much did B pay, whose real estate in the inventory was 1000 dollars, his personal property 140 dollars, and who paid for 2 polls? How much did C pay, whose real estate was valued at 785 dollars, personal property at 103 dollars, and who paid for 3 polls ? How much did D pay, whose real estate in the inventory was 4000 dollars, personal property 478 dollars, and who paid for 1 poll? How much did E pay, who had no real estate, whose personal property was valued at 250 dollars, and who paid for 4 polls ? How much did a single woman pay, whose real estate was valued at 500 dollars, and her personal property at 120 dollars ?

Assessors find it most expedient to make a table, which shall exhibit at once, the tax on all sums, from $1 up to any amount required. The table is made by multiplying the per cent. which the tax amounts to, by the several numbers, 1, 2, 3, 4, and so on.

The following is a table of taxes to be made when 11 per cent. is to be raised on the valuation of property. $ 1 pays .015 | $ 20 pay .30 $ 200 pay $3.00

30°65 .45 300 *4.50 3 66 .045 40 66.60 400 66 6.00 4 66 .06 - 50 66 75

500 66 7.50 5 " .075

.90

600 66 9.00 6 16.09 70 66 1.05

700 66 10.50 .105 80 66 1.20 800 66 12.00 8 " .12

90 66 1.35 900 66 13.50 9 66.135

100 66 1.50 1000 66 15.00 10 " .15 |

3. By the above table, what would be the tax on $ 6425 real estate, and $2346 personal estate ? . 4. By the above table, what would be the tax of a freeholder, whose real estate is valued at $ 9842, and personal estate, at $ 15066; poll tax $1.25 ?"

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