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2. Hats manufactured, or bought, at $2.50, and sold at 3 dollars, what is gained per cent. ? Ans. 20 per cent.

3. If corn is bought at 50cts. per bushel, and sold at 45cts. per bushel, what is the loss per cent.? Ans. 10 per cent. loss.

4. Bought a horse for 40 dollars, and sold the same immediately for $50.50, at two months' credit*--required the gain per cent.

Ans. 25 per cent. gain. 5. If I buy cloth at 13s. per yard, on 8 months' credit, and sell it again at 12s. ready money, do I gain or lose, and how much per cent. ?

Ans. 4 per cent. loss. 6. If by selling ilb. of pepper for 105 mills, there is 2 cents loss, what is the loss per cent. ? Anş. 16 per cent.

7. If a merchant gain 24d. on a shilling, what is that per cent. ?

Ans. 18.75. 8. If for ready money I could purchase tobacco at 6 dol. lars per 100lbs., and sell it on three months' credit, at $7.308 per 100lbs., what would be my gain per cent.? Ans. 20.

CASE 2.

The prime cost and the loss or gain per cent. given, to find the price sold at. (That is, when you have the prime cost, to calculate how goods must be sold so as to gain or lose any proposed rate per cent.)

RULE.

As $100
Is to the prime price, (the given price,)
So is $100, with the gain added, or the loss subtracted,
To the selling price.

Or, without a statement, add the gain per cent. to 100, or subtract the loss per cent. from 100, then multiply by the prime, and point off two right hand figures of the product.

EXAMPLES.

1. Wheat bought at 75 cents per bushel-at what price must it be sold per bushel, to gain 20 per cent. ?

* When goods are bought or sold on credit, the present worth of the value of the goods (for the time) must be found, in order to find the true gain or loss.

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Ans. 90.00cts. 90cts. Ans. 2. Bought muslin at 8 cents per yard—what must it be sold for per yard, to gain 25 per cent. ? Ans. 10cts.

3. Bought cloth at 50 cents per yard, which I find on examination to be of inferior quality to what I expected, and I must lose 10 per cent. by it—what will then be the price per yard ?

Ans. 45cts. 4. If a trader buy Glauber's salts, at 4 cents per lb. and by retailing them by the ounce, clears 1100 per cent.-re. quired the price per ounce and pound,

Ans. 3cts. per oz. and 48cts. per lb. 5. Bought a cask of brandy, containing 50 gallons, at 75 cents per gallon, but by accident 10 gallons leaked out-at what must I sell the remainder per gallon, to gain upon the whole prime cost, at the rate of 10 per cent. ?

Ans. $1.03,125.

CASE 3. When the gain or loss per cent. is given, with the selling price of the commodity, to find the prime cost.

RULE.

As $100, with the gain per cento added, or the loss per cent. subtracted,

Is to the selling price,
So is $100
To the prime cost.

EXAMPLES

1. If by selling hats at $3, there is 20 per cent. gainrequired the prime value.

Ans. $2.50. As 100 20

$ c. 120 : 3 :: 100 : 2.50 Ans. 2. If by selling tea at 875 mills per pound, there is a loss of $12.5 per cent., what did it cost per pound? Ans. $1.

3. Suppose corn şold at 45 cents per bushel, at a loss of 10 per cent.-required the prime cost.

Ans. 50cts. 4. Suppose a trader sells a lot of muslins for $50.5, at 2 months' credit, and gains 25 per cent.-required the prime cost; discount of six per cent per annum.

Ans. $40. 5. A store-keeper was asked what his coffee cost him ; he answered that he was losing 5 per cent. by selling it at 19 cents per pound-required the prime cost. Ans. 20cts.

CASE 4. The selling price and the gain or loss per cent. being given, to find what would be the gain or loss per cent. if sold at any other price.

RULE.

As the first price
Is to the second price,

So is $100 with the gain per cent. added, or the loss per cent. subtracted,

To the proceeds of $100, at the second price.

NOTE.-If the result exceeds 100, the excess is the gain per cent., but if less than 100, the deficiency is the loss per cent.

EXAMPLES.

1. If molasses sold at 48 cents per gallon, produce $10 per 100 gain ; what will be the gain or loss per cent., if it is sold at 42 cents per gallon?

Ans. $32. If 48 : 42 :: 110 110

100. 48)46200 96.25 100+10=110 third term

Ans. $3.75 loss 2. If a merchant gains $123 per cent. by selling salt at 1 dollar per bushel; afterwards becoming scarce, he advances the price 125 mills per bushel-what then will be his gain

Ans. $26.56,2,5. 3. A man, by selling a yard of cloth for $2.23, gained 10 per cent.—if he had sold it for $2.75, what would have been his gain per cent. ?

Ans. $35.65+ 4. If I sell lcwt. of sugar for $8, and thereby lose 10 per cent., what shall I gain or lose per cent. if I sell 4cwt. of the same sugar for $36 ?

Ans. I gain $14 or $1.25 per cent.

per cent. ?

2

102

EQUATION OF PAYMENTS.

EQUATION OF PAYMENTS Is the finding a time to pay at once several debts due at different times, so that no loss shall be sustained by either party.

RULE 1. Multiply the several payments by the number of months each has to run; then divide the sum of their products by the sum of the several payments, and the quotient will be the equated time, or that required.

EXAMPLES.

1. A owes B $330, to be paid as follows: $100 in six months, $120 in 7 months, and $160 in 10 months—what is the equated time for the payment of the whole debt?

100 x 6= 600
120 x 7 = 840
160 x 10=1600

38,0 )304,0(8 months, Ans. 2. F owes H $1000, of which $200 are to be paid at the present time, $400 at five months, and the rest at ten months; but they agree to make one payment of the whole, and wish to know the time.

Ans. 6 months. 3. P owes Q $420, which will be due 6 months hence, but P is willing to pay him $60 cash, provided he can have the remainder forborne a longer time, to which Q agreesthe time of payment is required.

Ans. 7 months.

RULE 2. See, by rule 1st, at what time the first man mentioned ought to pay in his whole money ; then, as the other's money is to his money, so is the time that the first-mentioned man

ought to pay in his money, to his time; which, when found, must be added to, or subtracted from, the time at which the second ouş't to have paid in his money, as the case may require, and the sum or remainder (as the case may be) will be the true time of the second's payment.

EXAMPLE,

A is indebted to B 150 dollars, to be paid 50 dollars at 4 months, and 100 dollars at 8 months: B owes A 250 dollars, to be paid at 10 months. It is agreed between them that A shall make immediate payment of his whole debt, and that

B shall pay his so much the sooner, as to balance that favor. I demand the time at which В must pay the $250, reckon. ing simple interest.

50 X4=200
100 X 8=800
15,0 100,0(63 months, A's equated time

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BARTER. BARTER is the exchanging of one commodity for another, and teaches to proportion their quantities without loss.

CASE 1. When the quantity of one commodity is given, with its value, and the value of some other commodity to be given for it, to find the quantity; or having the quantity given, to find the price or rate of selling it.

RULE.

Find the amount of that commodity of which the price und quantity are given, by the most concise method.

Then find what quantity of the other, at the rate proposed, you may have for the same money.

If the quantity be given, find the rate of selling it.

Or,

EXAMPLES.

P

25

1. A has 350 yards of linen, at 25cts. per yard, which he will barter with B for sugar, at 5 dollars per cwt.-how much sugar will the linen come to? 35,0

Or,
4)350

cut.
If 5 : 87.5 :: 1
$87.5

1
1750
70

5)87.5
$87.50 A's linen

17.5=17fcwt. 2. A has 35 pieces of broadcloth, at $44 per piece, and B has indigo at $1.42 per pound-how many pounds of indigo must B give A for the cloth? Ans. 10843lb.

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