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 D100 more: 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?

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 B.'s D100, and their oss or gain D37.50, which is at the rate of 12 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 continues 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.

REVIEW.

What is partnership? When is it used? When time is not considered, what is the rule? How will you prepare the 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.? 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?

When

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. D3751; F. D1871; G. D15613-D720 proof. 27. A. put in for of a year, B. 2 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 15; B.'s 27; C.'s 7271

PERCENTAGE.

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

EXAMPLES.

1. What is the difference between D500 at 7.5 per cent., and D500 at 8 per cent.?

Thus: D500×7.5=D37.50; D500 × 8=D40.00; difference 2.50. Ans.

2. Two men had each D240; one of them spends 14 per cent., and the other 18 per cent.; how much more did one spend than the other?

D240 x 14 = D33.60; D240+18 x D44.40; difference D10.80. Ans.

To find the rate per cent.

RULE I.

1. Bring the number to hundreds by annexing two ciphers, or removing the decimal point two places to the right.

2. Divide the numbers so formed by the sum on which the percentage is estimated; the quotient will express the per cent.

3. A merchant goes to New York with D1500; he first lays out 20 per cent., after which he expends D660; what per cent. was his last purchase of the money that remained after his first? Thus: D1500×20 per ct.= D300: 1500-300=1200)66000(55. per cent. Ans.

4. If I pay D679.84 for 750 bushels of wheat, and sell the same for D874.50; how much do I make per cent. on what I paid, and on the sum received?

5. If I contract a debt of D500 and make a payment of D350, what per cent. of the debt do I pay?

When the per cent. of loss or gain is given, and the amount received, to find the principal cost.

6. I sell a quantity of goods for D170, by which I lose 15 per cent.; what did they cost?

Ans. D100-15=85)170 × 100(200 D. cost. 7. Sold goods to the amount of D225, and made 20 per cent.; what did they cost?

To find the percentage on lands, or allowance for roads, &c.

It is customary in Pennsylvania, and probably in many other states, to deduct 6 acres out of 106, for roads, &c.; the land before the deduction is made may be termed the gross, and that remaining after each deduction, the net or strict measure.

RULE 1.

Reduce the gross to perches, and divide by 1.06, and the quotient will be the answer in perches, strict measure.

Multiply the net or strict measure by 1.06, and the product will give the gross measure or quantity; or work decimally.

EXAMPLES.

1. How much net land or strict measure is there in a tract of 901 A. 2 R. 26 po. gross?

Thus, 901 A. 2 R. 26 po. 850 A., 2 R., 20 po. Ans.

901.6625÷1.06=850.625 A.=

2. How much land must I enclose to have 850 A. 2 R. 20 po., net? Thus 850.625 × 1.06=901.6625 A.=901 A. 2 R. 26 po., gross. Ans.

NOTE. These two operations prove each other.

RULE II.

Divide the content in perches by 169.6, which will give the net in all cases, where the given quantity is 106 A., and ratio 6. Thus: 901 Å. 2 R. 26 po.=144266 po.÷169.6=850.625 A. =850 A. 2 R. 20 po.

Ans.

Or: 850.625 x 169.6=144266 po.=901 A. 2 R. 26 po. as above.

Again: 106 A.=16960 po.÷169.6=100 A.; or 16960÷1.06 =16000 po.100 A.

NOTE. The deduction to be made on every 106 A. is 9.6 perches; this added to 160 po.=169.6 po., hence the divisor.

GROSS, TARE, AND NET WEIGHT.

THE following questions are usually denominated under the rule or appellation of Tare and Tret. The use and application of the several rules are for deducting certain allowances which are made by merchants and tradesmen in selling their goods by weight, for the purpose of making the proper deduction to ascertain the net weight. In England these rules are in constant use, but a better system is being introduced into this country, that of taking 100 pounds as the true weight, in place of 112 lb. gross; then all that will be required will be to ascertain the weight of the box, cask, bag, &c., containing the article, and

the remainder will be the net or true weight. The collections at the customhouse, or United States duties, are connected with gross weight.

Gross weight is the whole weight of the goods, together with the weight of the cask, bag, &c., which contains them.

Tare is an allowance made to the buyer, or the deduction of the weight of the cask, box, bag, &c., containing the articles sold.

Net weight is what remains after all the deductions are made NOTE. The following questions are only the application of the rules of proportion and practice.

When the tare is so much on a given quantity.

RULE I.

Subtract the given tare from the given quantity, and the re mainder will be the net weight.

1. What is the net weight of a cask of sugar, weighing 7 cwt 1 qr. 16 lb. gross, tare 3 qrs. 18 lb. ?

2. What is the net weight of a cask of rice, weighing 5 cwt. gross; tare 2 qrs. 13 lb. ? Ans. 4 cwt. 1 qr. 15 lb. 3. Required the net weight of a hogshead of sugar, weighing gross, 8 cwt. 1 qr. 22 lb.; tare 3 qrs. 9 lb. ?

Ans. 7 cwt. 2 qrs. 13 lb. 4. What is the net weight of 175 cwt. 2 qrs. 20 lb. ; tare

6 cwt. 2 qrs. 25 lb. ?

Ans. 168 cwt. 3 qrs. 23 lb. casks of sugar, each weigh

5. What is the net weight of 4 ing 5 cwt. 2 qrs. 12 lb. gross; tare per cask, 2 qrs. 18 lb.

Ans. 19 cwt. 3 qrs. 4 lb.

When the tare is so much per cask, box, bag, &c.

RULE II.

Multiply the given tare per bag, box, &c., by the number of bags, boxes, &c., and subtract the product from the gross weight, and the remainder is the net weight.

6. A sold 5 casks of rice, which weighed 1137 lbs. each, and each cask weighed 75 lbs.; required the net weight and value of the tobacco at 14 cents per pound?

Ans. Net weight, 5310 lb.; value, D743.40.