the receipt of the goods, and had been allowed 4 per cent. discount? Ans. $803.92.+

12. Sold goods to the amount of $1200, one half of which is to be paid in 6 months, and the other half in 8 months. What is the discount for the present payment of the whole, discounting at 6 per cent. per annum ? Ans. $40.553.

13. A person having a legacy of $1450 left him, payable in 6 years, requests present payment, and proposes to allow 6 per cent. discount. What must he receive? Ans. $1066.

176.+

14. What is the discount of $458 for 8 months, discounting at 8 per cent. per annum? Ans. $23.188.+

QUESTIONS.-What is discount? What is the present worth of any sum of money, payable at some future time, without interest? Is discount a deduction of a given per cent. from a hundred cents, or a hundred dollars? Why? What numbers express the ratio which any sum due a year hence, at 6 per cent. bears to its present worth? What is the rule for discount? How is the discount obtained? How is discount proved? Ans. Cast the interest on the present worth, for the time and rate per cent. of discount, and add it to the present worth.

PROFIT AND LOSS.

Profit and Loss is the rule by which merchants and others engaged in trade, determine how much is gained or lost by any transaction. It also enables them so to regulate the price of their goods as to gain or loose a certain per cent. on the first

cost.

1st. To FIND HOW MUCH IS GAINED OR LOST ON A QUANTITY OF GOODS SOLD AT RETAIL, THE PURCHASE PRICE OF THE WHOLE QUANTITY BEING GIVEN.

RULE. Find the value of the whole quantity at the retail price; then, if there be a gain, subtract the purchase price from the same, and the remainder will be the sum gained; but if there be a loss, subtract the amount received from the purchase price, and the remainder will be the sum lost.

Ex. 1. Bought 40

yards of cloth for $160, and sold the How much did I gain? $5.20×40

same for $5.20 per yard?

= $208.00; and $208.00

$160 $48.00, Ans.

2. Bought a hogshead of melasses for $25, and sold the same for 8 cents a pint. How much did I gain? Ans. $15.32. 3. Bought 12 cwt. of sugar at 8 d. per pound, and sold it at 3 £. New York currency, per cwt. Did I gain or lose, and

how much? Ans. Lost $22.

4. Purchased 2 hogsheads of wine for $94.50, and retailed the same at 2 s. New York currency, per quart. How much did I gain? Ans. $31.50.

5. Paid $57 for 456 yards of cloth, and sold the same at the rate of 4 s. 6d. New York currency, for 3 yards. What did I gain? Ans. $28.50.

6. Bought 12 rolls of ribbon, each containing 50 yards, for $18.75, and sold the same at 6 d. New York currency, per yard. How much did I gain by the operation? Ans. $18.75.

7. Bought 44 lb. of tea for $16.50, and sold it for 3 s. 6 d. New England currency, per pound. What did I gain? Ans. $9.166.+

8. What do I gain on 15 cwt. of rice, which cost me $50, by retailing the same at 4 d. New York currency, per pound? Ans. $20.

2d. TO FIND WHAT IS GAINED OR LOST PER CENT

RULE. Find the whole gain or loss by the preceding rule, and, having multiplied it by one hundred, divide the product by the first cost. Or say, as the first cost is to the whole gain or loss, so is $100 or 100£. to the gain per cent.

Ex. 1. If I buy broadcloth at $5.50 per yard, and sell the same for $6.00 per yard, what do I gain per cent.?

$6.00-$5.50=$0.50, the gain on $5.50. Therefore, .50 ×100=50.00, and 50.00÷$5.50=9.09+, the gain on $100. Or, $5.50 .50: 100: the gain on $100.

Or, the operation may be canceled, by placing first above the horizontal line, the whole gain or loss found by subtraction, and $100 or 100£. at the right of this, on the same side, and the whole cost below the same. Cancel, &c.

2. What do I gain per cent. if I buy wheat at 12 s. a bushel, and sell the same for 15 s. a bushel? Ans. 25 per cent.

3. Purchased pepper for 8d. per pound, and sold the same for 9 d. per pound. What per cent. did I gain? Ans. 12. 4. Bought 650 lb. of sugar for 10 cents a lb., and sold the same for 12 cents per lb. What was my whole gain, and what my gain per cent.? Ans. Whole gain $13.00; gain per cent. $20.

5. Bought goods to the amount of $325, and sold the same for $370. What was the per cent. gained? Ans. $13.846.+ 6. If I lose $2 on $25, at what rate per cent. do I lose? Ans. 8 per cent.

7. Purchased a hogshead of wine for $50, and sold the same for $75, on six months' credit. What was s my gain per cent., allowing 4 per cent. discount for the 6 months' credit? Ans. $44.23.

8. Bought 6 cwt. of cheese for $48, but it being damaged, I am willing to sell it for the same on a year's credit. What is loss per cent. discounting at 6 per cent. per annum? Ans. $5.66.+

my

3d. TO FIND HOW A COMMODITY MUST BE SOLD TO GAIN OR LOSE A CERTAIN PER CENT. ON THE WHOLE COST.

RULE.-If the purchase price of the quantity for which the retail price is required, be not given, it must first be found, and then multiplied by $100 increased by the per cent. to be gained, or diminished by the per cent. to be lost. The last product divided by 100, or, what is the same thing, with two figures cut off from the right, will be the answer required. Or the operation may be reduced to the following statement: As $100 is to $100 increased by the per cent. to be gained, or diminished by the per cent. to be lost, so is the purchase price of the commodity to the retail price.

Ex. 1. Bought 300 yards of cloth for $550; how must I sell the same per yard, to gain 25 per cent. ?

$550÷300=$1.83, the price of one yard; and $1.831 × 125 $229.16; and $229.16--100=$2.29,+ Ans. Or 100: 125: 1.83: Ans. or $2.29.+

Or the operation may be canceled by the following rule:

RULE. Write the given price above a horizontal line, and the quantity which cost that price directly below it. Then place

$100 increased by the per cent. to be gained or diminished by the per cent. to be lost, above the same line, and 100 below, and proceed to cancel, &c.

2. How must I retail melasses by the gallon, for which I paid $30 per hogshead, to gain 124 per cent.? Ans. $0.535.+ 3. Purchased 100 gallons of wine for $130, but by accident 15 gallons leaked out. How must I sell the remainder per galjon, to gain 15 per cent. ? Ans. $1.758.+

4. Paid $1.10 per gallonfor melasses; how must I sell the same per quart, to gain 30 per cent.? Ans. 35 cents.

5. Received from Lisbon 180 casks of raisins, which cost me $2.13 per cask. How shall I sell them per cask, to gain 25 per cent.? Ans. $2.66.

6. Bought 2 cwt. of pepper at 1 s. New York currency, per pound, but it being damaged, I am cent.; how must I sell it by the lb. ?

willing to lose 10 per Ans. 11 cents 2 mills. how must I sell the Ans. 8 cents 6 mills.

7. Bought one ton of steel for $184; same per pound, to gain 5 per cent. ? 8. A merchant bought 160 yards of cloth for $240; how must he sell the same per yard to gain 12 per cent.? Ans. $1.68.

9. Bought 8 pieces of cloth, each containing 15 yards, at 3 s. New England currency, per yard; how must I retail the same, to gain 8 per cent., and how much must I receive for the whole ? Ans. 54 cents retail price; whole value, $64.80.

10. If I buy 6 cwt. of sugar at 10 d. New York currency, per pound, and am allowed 4 per cent. discount for ready money, and sell the same so as to gain 15 per cent. on the money advanced, how much money do I receive? $77.28.

Ans.

11. Bought 12 chests of tea, each weighing 56 pounds, at 4s. 6 d. New England currency, per lb. For ready money was allowed 2 per cent. discount; how much must I receive

for the whole to realize a profit of 10 per cent. on the money paid out? Ans. $543.312.

12. Bought 700 yards of ribbon, at 6 d. New York currency, per yard; how must I sell the same to gain 12 per cent. and what shall I receive for the whole quantity? Ans. 63 d. per yard, nearly; and for the whole, $49.218.+

13. How must cloth which costs 13 s. 4 d. be sold to gain 20 per cent.? Ans. At 16 s. per yard.

QUESTIONS.-What is profit and loss? What is Case 1st? What is the rule? What is Case 2d? What is the rule? How is the statement made for canceling? What is Case 3d? What is the rule ? What is the rule for canceling?

Ᏼ Ꭺ Ꭱ Ꭲ Ꭼ Ꭱ.

Barter is a rule by which those engaged in trade exchange commodities so that neither party suffer loss.

Take the following illustration:

Ex. 1. How much sugar at 10 d. per lb. must be given in exchange for 12 cwt. of butter at 15 d. per pound?

12. 15

It is obvious that the 12 cwt. of butter bears the same ratio to the number of cwt. of sugar required, as 10 d. bears to 15 d. Therefore, as 10:15::12: the answer, viz. 18 cwt. Or, 10 the statement for canceling :

6 3

is

The scholar will perceive that the principle here involved is the same as in the rule of proportion, which has already been fully explained.

2. How much tea at 8 s. per lb. must be given for 2 cwt. of chocolate at 4 s. 6 d. per lb. ? Ans. 1 cwt. 14 lb.