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11. A., B., and C., put their money into joint stock; A. put in D40, B. and C. together D170; they gained D126, of which B. took D42 ; what did A. and C. gain, and B. and C. put in respectively ?
Ans. A.'s gain D24, B.'s stock D70, C.'s stock D100, and C.'s gain D60.
12. A. and B. companied; A. put in D45, and took of the gain; what did B. put in ?
Ans. D30. 13. A. and B. venture equal stocks in trade, and clear D164; by agreeinent A. was to have 5 per cent. of the profits, because he managed the concerns ; B. was to have but 2 per cent. ; what was each one's gain? how much did A receive for his trouble ?
Ans. A.'s gain was D117.1429, and B.'s D46.857}, and A. received 170.285, for his trouble.
A tax is a sum required to be paid to the government for its support, or for other purposes, and is generally collected from each individual in proportion to his property ; this, however, is different in some states, where every white male eitizen over the age of 21 years is required to pay a certain tax, called a polls tax; in this case each person is called a poll: hence the expressions,“ polling votes,"." attending the polls,” &c. In the assessment of taxes, we must first make an inventory of all the property, both real and personal, of the whole town or district to be taxed, and also of each individual who is to be taxed; and as the number of polls are rated at so much each, the tax on all the polls must be taken out from the whole tax, and the remainder is to be assessed on the property.
Then to find how much any individual must be taxed for his property, we need only find how much the remainder of the whole tax is on D1, and multiply his inventory by it.
14. If a town raise a tax of D1920, and all the property in town be valued at 164000, what will that be on Di, and what will be A.'s tax whose property is valued at D1200 ?
Ans. DO 03c. on a dollar; or 1 36.00 : for D1920-64000= 3c. x D1200=36.00 A's tax.
15. A certain town, valued a D64530, raises a tax of 12259.90 ; there are. 540 polls which are taxed 160 each; what is the tax on a dollar, and what will be A.'s tax, whose real estate is valued at D1340, his personal property at D874, and who pays for 2.polls ?
Thus, D540 x.60=D324 amount of the poll-taxes ; D2259.90 - D324=D1935.90, to be assessed on property ; then 64530 : 1935 :: 1:.03, or 1935.90-64530=.03, er 3c., tax Di.
Tax on Di is .03 Tax on D10 is .30 Tax on D100 is D3 2 .06 20 .60
200 6 3 .09 30 .90
300 9 4 .12 40 1.20
400 12 5 .15 50 1.50
500 15 6 .18 60 1.80
600 18 .21 70 2.10
700 21 8 .24 80 2.40
800 24 9 .27 90 2.70
900 27 1000 30
Now, to find A.'s tax, his real estate being D1340; I find by the table, that the tax on D1000 is D30 The tax on 300 is
9 The tax on 40 iş
Tax on his real estate D40.20 In like manner, I find the tax on
D26.22 his personal property to be
2 polls at .60 each are 1.20
Amount, D67.62 Ans.
When the stocks are considered with regard to time.
1. Multiply each man's stock by its time, and add the products together.
2. Then, as the sum of the whole stock, multiplied by the time, is to the product of each individual share, multiplied by its time, so is the whole gain or loss of each individual.
16. Three merchants traded together for 12 months ; A.
put in D120 for 4 months, B. put in D25.0 for 9 months, and C. put in D300 for 12 months, they gained D175; what will each man receive for the gain? A. 120 x 4 mo.= 480 ) A. 6330 : 480 :: 175g. D13.27 Ans B. 250 x 9" =2250 B. 6330 : 2250 :: 175" 62.20.4 C. 300 x 12 =3600 C. 6330 : 3600 :: 175" 99.52.6
1st. Multiply each man's stock by the time it was in trade, for its product.
2d. Divide the gain or loss by the sum of the products for their gain or loss per dollar.
3d. Multiply the gain or loss per dollar, by each product, for each man's proportional gain or loss, and the product is the
17. A. and B. traded 12 months; A. put in D300 for 12 months, B. put in D600 for 6 months, their gain is D288; required the share of each.
A. D300 x12=3600 72)288(.04c. per D.
18. A. and B. formed a partnership for 18 months ; A. put in D2750 for 15 months, and B. D3500 for 10 months ; at the expiration of that time he took out D2000; at the close of their business they find their gain to be D1500 ; what.is each man's share of the gain ?
Ans. A.'s D701.13.3+; B.'s D798.86.7+. 19. A. put in stock to the amount of D1800, B. advanced 4 mo. after ; what sum must he put in to receive equal profit with A. at the end of the year ?
Ans. D2700. 20. A. and B. formed a partnership; A. put in, the 1st of January, D1000, but B. could not put in till the 1st of May; what sum did he then put in, to have an equal share with A. at the expiration of the year?
Ans. D1500, 21. A., B., and C., entered into partnership for 12 months ; A. put in at first D873.60, and 4 months after he put in D96 more ; B. put in at first 1979.20, and at the end of 7 months he took out D206.40; C. put in at first D355.20, and 3 months after he put in D206.40, and 5 months after that he put in D240 more; at the end of 12 months their gain is D3446:40; what is each man's share of the gain ? Ans. A. D1334.82.5, B. D1271.61.4, C. D839.96.
22. Two merchants entered into company for 18 months ; A. at first put in D500, and at the end of 8 months he put in 1100 niore: B. at first put in D800, and at the end of 4 months he took out D200; at the expiration of the time they find their gain to be D700; what is each man's share of the gain?
Ans. A. D324.07.4, B. D375.92.5+ 23. Three persons, A., B., and C., made a stock for 12 months; A. put in at first D580, 3 months after he put in D100 more; B. put in at first. D1000, and after 9 months he put in D200; C. put in at first D486, 3 months after he took out D300, and 2 months after he put in D500; 3 months after this he took out D400, and 1 month after he put in D1000; at the end of 12 months their gain was D2108.44; what is each man's share ? A. D580x3=1740 C. 1486 x3=1458
7860 A. 680 X 9=6020+ - 300
8032 C. 7860A. +186 X2x 372 500
24. A gentleman left an estate at his death of D30000, to be divided among his 5 children, in such a' manner that their shares should be to each other as their ages, which are 7, 10, 12, 15, 16; required the share of each.
Ans. D3500, 5000, 6000, 75000, 8000. 25. A. and B. entered into partnership for 16 months; A. put in D1200 at first, and 9 months after D200 more; B. put in at first D1500, at the end of 6 months he took out D500; their gain was D772.20; what is the share of each?
Ans. A.'s D401.70, B.'s D370.50. Note.-As an evidence of the correctness of the rules of partnership, and that their loss or gain is in proportion to their stocks in trade, let A.'s stock be 200, and Bi's D100, and their oss or gain D37.50, which is at the rate of 123 per cent.; A. will gain or lose D25, and B. D12.50, because A.'s stock is just twice as much as B.'s, consequently his loss or gain must be twice as much ; and the same principle will hold good in partnership with or without time, that is, the gain or loss must be in proportion to the stock, and time that the partnership continued. If A. and B. enter into partnership for one year, and A. puts in D200, and B. D100, but at the expiration of 6 months, A. finds it convenient to withdraw his D200, and the partnership con. tinues to the end of the year, and their gain is D37.50, it must be divided equally. Again : If A. commence trade with a capital of D500, and at the expiration of 6 months he shall receive B. into partnership with a capital of D1000, their loss or gain at the end of 12 months will be equal; if at 6 per cent. (D60) it will be D30 each.
What is partnership? When is it used ? When time is not considered, what is the rule? How will you prepare
question for solution? What can you say of the assessment of taxes ? What is the first thing to be done? How will you proceed to find the amount of taxes to be paid by A., B., C., &c. ? When time is considered in partnership, what is the rule ? Repeat the 2d and 4th rules. Method of proof. What is capital or stock? On what principles are the rules of partnership founded ?
26. E., F., and G., formed a partnership; E. put in D400 for .75 of a year, F. D300 for .5 of a year, and G. D500 for .25 of a year, with which they gained D720; required the share of each.
Ans. E. D37511 ; F. D18739; G. D15613=D720 proof. 27. A. put in for of a year, B. } for } a year, and C. the rest for 1 year; their joint stock was 1, and their gain 1; what is each man's share ? Ans. A.'s is jj ; B.'s C.'s =1=1
When we speak of per cent., it generally has reference to interest or discount on money, and means the hundredth part of the thing spoken of; for we can say so much per cent. of a bushel, yard, &c., as well as money ; when we say 10 per cent., we mean D10 on the hundred, or the 10th part of 100; as B. spends 10 per ct. of his D100, he would have but D90 remaining