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EXAMPLES.

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

per

cent. ? Thus: D500 x7.5=D37.50; D500 X 8=D40.00; difference 2.50. Ans.

2. Two men had each D240; one of them spends 14 per cent., and the other 181 per cent. ; how much more did one spend than the other?

D240 x 14 = D33.60; D240+184 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, oi 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 x 20 per ct.=D300: 1500—300=1200)66000(55.

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 ?

per cent.

When the per cent. of loss or gain is given, and the amount re

ceived, 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 x 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, fc.

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 reasure.

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.=901.6625=-1.06=850.625 Ai= 850 A., 2 R., 20 po. Ans.

2. How much land must I enclose to have 850 A. 2 R. 20 po., net ? Thus 850.625 X1.06=901.6625 A.=901 A.2 R. 26 po., gross.

Ans.
Note.-These two operations prove each other.

RULE 11.

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 sor 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. ?

7 cwt. 1 qr. 16 lb.

3 18

6 1 26 Ans. 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. 5. What is the net weight of 4 casks of sugar, each weighing 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, fc.

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.

7. Received per ship Napoleon, from South America, 55 bagg of coffee, the gross weight of which is 220lbs. each, and the weight of each sack is 5lbs.; required the net weight and valuo of the coffee at 16 cents per pound?

Ans. net weight 11825lbs.; value D1892. 8. Received from Salina 72 bags of salt, the weight of each bag is 210lb. gross, and each sack weighs 7lbs.; what is the net weight, and what does it come to at 4 cts. per pound ?

Ans. weight 14616lbs. ; value D584.64. 9. Bouy it 110 hogsheads of sugar, gross 723lbs. each, weight of each hogshead 62 lbs.; what is the net weight, and what will it come to at 12.5 cts. per pound ?

Ans. 72710lbs.; amount D9088.75. 10. Bought 5 casks of rice, which weighed gross 18 cwt., 2 qrs., 12 lbs., tare per cask 45 lbs., for which I paid D5.50 per cwt., and sold the same for D6.25 per cwt.; required the net weight, cost, amount it sold for, and profit?

Ans. net eight 1859 lbs.; cost D91.29; sold for D103.74 ; profit D12.45.

REVIEW.

What is net weight?

What is gross weight? What is tare? Repeat rule Ist. Repeat rule 2d.

UNITED STATES DUTIES.

In all civilized countries, where merchandise or goods are imported, importers are required to pay a certain amount of their value, at a certain rate per pound, hundred, yard, or gallon; this is called duty, which is established and collected by the laws of the country where the goods are landed; for this purpose, customhouses are erected in the seaport towns to collect the custom or duties, tonnage of vessels, port duties, &c., which together are called the revenue. An ad-valorem duty is such a per cent. on the actual cost of the goods in the country from which they are imported; thus an ad-valorem duty of 20 per cent. on tea from China, is a duty of 20 per cent. on the cost of the tea in China; the duties are computed on the net weight.

EXAMPLES.

1. What is the duty on 1400 lbs. of coffee at 2} cts. per lb.?

Ans. 1400x21=D3.50

2. If the duty on molasses is 5 cents on a gallon when im ported in an American vessel, and 10 per cent. more in a foreigr vessel; what is the duty on 3950 gallons in both vessels ?

Ans. D197.50 and D217.25 3. What is the duty on goods which cost in Calcutta D2780.50, at 124 per cent. ad valorem ? Ans. D347.561

POSITION.

Position is a rule founded on the principles of proportion, and by working with one or more supposed numbers, as real numbers, we can discover the true number or answer to the question. It is of two kinds, termed single and double. Single Position is when only one supposed number is necessary for the operation. Such questions as are usually given in arithmetic for solution, by working with supposed improperly called false) numbers, are equations in algebra, by which they are more conveniently and readily solved by those who are acquainted with that science. (For an illustration of the rule, see Double Position.)

SINGLE POSITION.

RULE.

Suppose a number, and work with it as though it was tho true number, according to the nature of the question ; then, as the result of that operation : is to the given number :: so is the number supposed : to the number required. Proof, add the several results together.

QUESTION.

1. A. owes a certain sum of money : 1, ļ, , is D500; what is the amount of the debt ? Suppose debt D1200 1=300 ) then, 650 : 500 :: 1200 = 150

1200 b=200

D

650)600000(923.07.7 A Sum of shares, - D650

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