CASE III.

To find the RATE PER CENT. of profit or loss, the cost and selling price being given.

16. If a merchant buys a quantity of butter for $75, and sells it for $90, what per cent. profit will he make?

Analysis. Subtracting the cost from the selling price, shows that he gained $15. Now 15 dollars are 4 of 75 dollars; therefore he gained 45 of his outlay, or the purchase price of the goods. And reduced to a decimal, is equal to 20 hundredths, or 20 per cent. (Art. 387. Obs. 3.)

Or, we may reason thus: If $75 (outlay) gain 15 dollars, $1 will gain of $15. And $15÷75=.20, the same as before.

446. Hence, to find the rate per cent. of profit or loss, when the cost and selling prices are given.

First find the amount gained or lost by subtraction; then make the gain or loss the numerator and the purchase price the denominator of a common fraction; reduce this fraction to a decimal, and the result will be the per cent. required. (Art. 337.)

Or, simply annex ciphers to the profit or loss, and divide it by the cost; the quotient will be the per cent.

OBS. 1. As per cent. signifies hundredths, the first two decimal figures which occupy the place of hundredths, are properly the per cent.; the other decimals are parts of 1 per cent. After obtaining two decimal figures, there is sometimes an advantage in placing the remainder over the divisor, and annexing it to the decimals thus obtained. (Art. 387. Obs. 3.)

2. It should be remembered that the percentage which is gained or lost, is always calculated on the purchase price, or the sum paid for the article, and not on the selling price, or sum received, as it is often supposed.

17. Bought a quantity of cotton at 64 cents per yard, and sold it at 8 cents: what per cent. was the profit?

18. Bought a quantity of calico, at 12 cents per yard, and sold it at 12 cents: what per cent. was the profit?

19. Bought a lot of corn, at 45 cents per bushel, and sold it at 38 cents what per cent. was the loss?

QUEST. -Obs. What figures properly signify the per cent.? What do the other decimal figures on the right of hundredths denote? On what is the per cent. gained or lost calcu lated?

20. A grocer bought a pipe of wine for $252, and ret at 12 cents per gill: what per cent. did he make?

21. A man bought a house for $4325, and sold it for what per cent. did he make?

22. A speculator invested $75000 in stocks, which he s $77225: what per cent. did he make by the operation?

CASE IV.

To find the cost, the selling price and per cent. gained being given.

23. A man sold a lot of salt for $360, which was 20 p more than cost: what did he pay for the salt?

20

100

Analysis. The cost is 100 of itself, and the gain is cost. (Art. 386.) Now 100+1=128; hence, the selling is 128 of the cost. The question then is this: $360 is what sum? If $360 is 120 of a certain sum, Th of that Now $360-120-$3, and 180-$3×100,

120 of $360.

is $300. Ans.

Or, if we divide $360, the selling price, by the fractio the quotient $300, will be the cost. (Art. 234.) PROOF. $300X.20 $60.00 the gain; (Art. 388;) and $300+$60-$360, the selling price.

24. A miller sold a lot of flour for $170, which was cent. less than cost: how much did the flour cost him?

85

Analysis. Reasoning as before, the cost is 100 of itse the loss is of the cost. Now 1991; conse the selling price is of the cost. The question ther this: $170 is of what sum? If $170 is of a certa T is of $170. Now $170-85-$2, and 100-$2 which is $200. Ans.

Or, thus: Since he lost 15 per cent., he realized only 8 on $1 outlay. Therefore, if 85 cents, selling price, requi outlay, $170, selling price, will require as many dollars ou 85 cents are contained times in $170; and $170÷.85=$; PROOF.-$200X.15 $30.00, the loss; (Art. 388;)

and $200-$30-$170, the selling price. Hence,

447. To find the cost when the selling price and the per cent. gained or lost are given.

Divide the selling price by $1, increased or diminished by the per cent. gained or lost, as the case may be, and the quotient will be the cost required.

Or, make the given per cent. added to or subtracted from 100, as the case may be, the numerator, and 100 the denominator of a common fraction; then divide the selling price by this fraction, and the quotient will be the cost.

OBS. 1. It is not unfrequently supposed that if we find the percentage on the selling price at the given rate, and add the percentage thus found to, or subtract it from, the selling price, as the case may be, the sum or remainder I will be the cost. This is a mistake, and leads to serious errors in the result. It will easily be avoided by remembering, that the basis on which profit and loss are calculated, is always the purchase price or sum paid for the articles under consideration. (Art. 446. Obs. 2.)

25. A grocer sold a quantity of cheese for $530, which was 15 per cent. more than cost: what was the cost?

26. A man sold a carriage for $175, which was 15 per cent. less than cost: what was the cost?

27. A man sold a farm for $2360, which was 10 per cent. less than cost: what did he give for it?

28. An importer sold a library for $3078, which was 12 per cent. advance on the cost: how much did it cost him?

29. A merchant sold a cargo of crockery for $12000, which was 8 per cent. less than cost: what was the cost?

30. A commission merchant sold a lot of cloths for $7265, which was 15 per cent. more than cost: how much did they cost?

31. A builder sold a house for $17450, which was 2 per cent. less than cost: what was the cost?

32. A broker sold stocks to the amount of $45000, which was 5 per cent. advance: what was the cost?

33. A manufacturer sold a quantity of carpeting for $63240, which was 50 per cent. more than the cost of the materials: what did the materials cost?

QUEST. 447. How is the cost found, when the selling price and the rate per cent. gained or lost, are given? Obs. What mistake is sometimes made in finding the cost? How may it be avoided?

DUTIES.

448. DUTIES, in commerce, signify a sum of money required by Government to be paid on imported goods.

OBS. 1. In every port of entry in the United States, the Government has an establishment, called a Custom House, at which the duties on all for ign gools entered at that port, are to be pail.

2. The persons appointed to inspect the cargoes of vess: Is engaged in foreign commerce, to examine the invoices of goods, collect the duties, &c., are called custom house oficers.

449. Duties are of two kinds, specific and ad valorem. A specific duty is a certain sum imposed on a ton, hundred weight, hogshead, gallon, square yard, foot, &c., without regard to the value of the article.

Ad valorem duties are those which are imposed on goods, at a certain per cent. on their value or purchase price.

Note. The term ad valorem is a Latin phrase, signifying according to, or upon the value.

450. Before specific duties are imposed, it is customary to make certain deductions called tare, draft or tret, leakage, &c.

Ture is an allowance of a certain number of pounds made for the box, cask, &c., which contains the article under consideration. Draft or Tret is an allowance of a certain per cent. (usually 4 per cent.) on the weight of goods for waste, or refuse matter. Leakage is an allowance of a certain per cent. (usually 2 per cent.) for the waste of liquors contained in casks, &c.

OBS. 1. All duties, both specific and ad valorem, are regulated by the Government, and have been different at different times and in different countries. 2. The allowances or deductions for draft, tare, leakage, &c., are different on different articles, and are also regulated by law.

3. In buying and selling groceries in large quantities, allowances are sometimes made for draft, tare, leakage, &c., similar to those in reckoning duties.

QUEST.-448. What are duties in commerce? 440. Of how many kinds are they? What are specific dute? Ad valorem duties? N te. What is the meaning of the term ad valorem? 450. What deductions are made before specific duties are imposed? What is tare? Draft or tret? Leakage? Obs. How are duties regulated? Are allowances for draft, &c., ever made in buying and selling groceries?

290

DUTIES.

CASE I. Calculation of Specific Duties.

[S

Ex. 1. What is the specific duty on 15 hhds. of mo 10 cents per gallon, allowing 2 per cent. for leakage?

Analysis. Since there are 63 gallons in one hhd., in there are 15 times as many, and 63 gals. ×15=945 gals. I cent. of 945 gals. is equal to 945 ×.02, or 18.9 gals.; (A and 945 gals.-18.9 gals.=926.1 gals., the net gallons. the duty on 1 gallon is 10 cents, on 926.1 gals. it is 926.1 $92.61, the duty required. Hence,

451. To find the specific duty on any given merchand First deduct the legal draft, tare, leakage, &c., from th quantity of goods; then multiply the remainder by the give per gallon, pound, yard, &c., and the product will be the d quired.

2. If the specific duty on tea is 12 cents a pound, how will it be on 30 chests, each weighing 115 lbs., allowing 1 per chest for draft?

3. At 4 cents a pound, what is the specific duty on 160 d of figs, weighing 28 lbs. apiece, allowing 24 lbs. a drum for

4. At 15 cents a pound, what is the specific duty on 63 ches opium, each weighing 150 lbs., allowing 10 lbs. per chest for d

5. At 3 cents a pound, what is the specific duty on 250 of coffee, weighing 65 lbs. apiece, allowing 4 per cent. for tr 6. What is the specific duty, at 6 cents a pound, on 173 keg tobacco, each weighing 125 lbs., allowing 6 lbs. per keg for ta

7. At 5 cents a pound, what is the specific duty on 430 bo of paints, weighing 175 lbs. a box, reckoning the tare at 15 per box?

8. At 8 cents per gallon, what is the specific duty on 140 1 of olive oil, allowing 2 per cent. for leakage?

9. At 22 cents per gallon, what is the specific duty on 50 hh of wine, allowing 2 per cent. for leakage?

10. At 7 cents per pound, what is the duty on 345 sacks almonds, weighing 75 lbs. apiece, allowing 3 per cent. for tare?

QUEST.-451. How are specific duties calculated?