5. C. bas nutmegs worth 7s. 6d. per lb. in ready money, but in barter he will have 8s.; D. has tobacco worth 9d. per lb.; how much must he rate it per lb. that his profit may be equal to C.'s? Ans. 93d.

6, A. has tea which he barters with B. at 10d. per lb. more than it cost him, against cambric which stands B. in 10s. per yard, but he puts it at 12s. 6d.; I would know the first cost of the tea? Ans. 3s. 4d. per lb.

7. A. has 240 bushels of rye, which cost him 90 cts. per bushel; this he barters with B. at 95 cts. for wheat that stands B. in 99 cts. per bushel; how many bushels of wheat is he to receive in barter, and at what price is it to be rated, that their gains may be equal?

Ans. 218,3 bushels, at 1041 cts. per bushel. 8. A. and B. barter some goods-A. put his at 30% shillings, and gains 8 per cent.; B. puts his at 24 shillings, and gains at the same rate; what was the first cost of the goods? Ans. 288. and 22s. 6d. 9. A. and B. barter-A. has cloth that cost 28d. B.'s cost him 22d. and he puts it at 25d.; how high must A. put his to gain 10 per cent. more than B.? Ans. 35d. 10. C. and D. barter-C. makes of 7s., 6s. 8d.; D. makes of 7s. 6d., 7s. 3d.; who has lost most, and by how much per cent.? Ans. C. loses 13 per cent. more than D.

LOSS AND GAIN

Is a rule that discovers what is gained or lost in buying or selling goods, and instructs merchants and traders to raise or fall the price of their goods so as to gain or lose so much per cent. &c.

EXAMPLES.

1. Bought a piece of broadcloth containing 53 yards, at 4 dols. 65 cents per yard, and sold at 5 dols. per yard; what is the profit on the whole?

2. If 1 lb. of coffee cost 28 cts. and is sold for 31 cents, what is the profit on 3 bags, weighing 293 lbs. net? Ans. 8 dols. 79 cts.

3. Bought a piece of baize of 42 yds. for £4 14 6, and soid it for 2s. 6d. per yard: what is the gain or loss on the whole piece? Ans. 10s. 6d. gain.

4. A merchant bought 59 cwt. 3 qrs. 14 lbs. of iron, at 112 dols. per ton, paid freight and charges, 24 dols.: what is the gain or loss, if he sells the whole at 37s. 4d. per cwt.

Ans. 13 dols. 26 cts. gain.

5. If a gallon of wine cost 6s. 8d. and is sold for 78. 2d. what is the gain per cent.?

;

7 2 6 8

8. d.

£

Ans. 7 per cent. gain.

If 6 8 : 6 :: 100

6. When 20 per cent. loss is made on coffee, sold at 20 lb. what was the first cost? Ans. 25 cents.

cts. per 7. At 13 cts. profit on the dollar, how much is it per ct.? Ans. 13 per ct. or 13 dols. 50 cts. per 100 dols. 8. A trader sells his goods at 24d. profit on the shilling, how much is it per cent.? Ans. 20%, or £20 16 8. 9. Which is the better bargain, in purchasing fish, 178. per quintal, and 4 months credit, or 168. 8d. cash? Ans. They are alike. PROOF. The present worth of 178. found by discount, is equal to 168. 8d.; and 16s. 8d. with 4 months interest, will

amount to 17s.

10. A. bought a piece of shalloon, containing 34 yards, at 3s. 4d. per yard, and sold it at 121 per cent. loss: how much did he sell it per yard? Ans. 2s. 11d.

11. Bought wine at 90 cts. per gallon: at what rate must it be sold to gain 20 per cent.? Ans. $1,08.

12. A trader bought 1 hhd. of brandy, of a certain proof, containing 115 gallons. at $1,10 per gallon: how many gallons of water must he put into it to gain $5, by selling it at $1 per gallon? Ans. 16 gals.

13. Bought 4 hhds. of wine, containing 450 gallons at $1 per gallon, and sold it at $1,20 per gallon, and gave 3 months credit: allowing the leakage of the wine, while in my possession, to be 10 gallons, I would know the gain or loss, discounting for the present worth of the debt at 6 per cent. per annum? Ans. $70,19 gain.

14. A vinter buys 596 gallons of wine, at 6s. 3d. per gallon, in ready money, and sells it immediately at 6s. 9d. pei gallon, payable in 3 months: how much is his gain or loss, supposing he allows the interest for the time, at 6 per cent. per annum, as discount for present payment?

Ans. £11 17s. 8d. gained. 15. What would be the gain or loss on the aforesaid wine, supposing the discount for present payment to be made at 2 per cent. without any regard to time?

Ans. £10 17 61 gain.

16. A merchant bought a parcel of cloth, at the rate of $1 for every 2 yards, of which he sold a certain quantity at the rate of $3 for every 5 yards, and then found he had gained as much as 18 yards cost: how many yards did he sell? Ans. 90 yards.

17. Bought rum at $1,25 per gallon, which not proving so good as I expected, I am content to lose 18 per cent. by it: how must I sell it per gallon? Ans. $1,02.

18. A. sells a quantity of corn at $1 a bushel, and gains 20 per cent.; some time after he sold of the same, to the amount of $37,50, and gained 50 per cent. how many bushels were there in the last parcel, and at what rate did he sell it per bushel ?

Ans. 30 bushels, at $1,25 per bushel. 19. A distiller is about purchasing 10,000 gallons of molasses, which he can have at 48 cents per gallon in ready money, or 50 cents with 2 months credit it is required to know which is more advantageous to him, either to buy it on credit, or to borrow the money at 8 per cent. per annum to pay the cash price?

Ans. He will gain $136 by paying the cash. 20. A tobacconist buys 4 hhds. of tobacco, weighing 38 cwt. 2 qrs. 8 lb. gross, tare 94 lb. per hhd. at $9 per cwt. ready money, and sells it at 111d. per lb. allowing tare at 14 lb. per cwt; to receive two thirds in cash, and for the remainder a note at 90 days credit his gain or loss is required, supposing the interest for the time at 6 per cent. per 360 days is allowed for discount, on turning the note into cash? Ans. $283,80 gain.

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ALLIGATION MEDIAL.

ALLIGATION MEDIAL is when the quantities and prices of several things are given, to find the mean price of the mixture compounded of those things..

RULE. As the sum of the quantities or whole composition is to their total value, so is any part of the composition to its mean price.

EXAMPLES.

1. A grocer would mix 25 lb. of raisins, at 8 cts. per lb., and 35 lb. at 10 cts. per lb., with 40 lb. at 12 cts. per lb. what is 1 lb. of this mixture worth?

2. A goldsmith mixes 8 lb. 5 oz. of gold, of 14 carats fine, with 12 lb. 8 oz. of 18 carats fine what is the fineness of this mixture? Ans. 165 carats.

3. A grocer would mix 12 cwt. of sugar, at $10 per cwt. with 3 cwt. at $8 per cwt., and 8 cwt. at $7 per cwt.: what will 5 cwt. of this mixture be worth?

4. A refiner melts 2 4 lb. of 18 carats fine make it 22 carats fine?

Ans. $44 78 cts. 2 ms. lb. of gold, of 20 carats fine, with how much alloy must be put to it to

Ans. It is not fine enough by 3, carats, so that no alloy must be put to it, but more gold.

5. A maltster mingles 30 quarters of brown malt, at 28s. per quarter, with 46 quarters of pale, at 30s. per quarter, and 24 quarters of high-dried do. at 25s. per quarter: what is the value of 8 bushels of this mixture?

Ans. £1 8s. 21d.3.

6. If I mix 27 bushels of wheat, at 5s. 6d. the bushel, with the same quantity of rye, at 4s. per bushel, and 14 bushels of barley at 2s. 8d. per bushel: what is the worth of a bushel of the mixture? Ans. 4s. 3 d.38.

7. A grocer mingled 3 cwt. of sugar, cwt. at £1 17 4 per cwt., and 3 cwt. at what is 1 cwt. of this mixture worth?

at 56s. per cwt., 6 £3 14 8 per cwt. : Ans. £2 11 4.

8. A mealman has flour of several sorts, and would mix 3 bushels at 3s. 5d. per bushel, 4 bushels at 5s. 6d. per bushel, and 5 bushels at 4s. 8d. per bushel: what is the worth of a bushel of this mixture? Ans. 4s. 7d...

9. A vintner mixes 20 gallons of Port, at 5s. 4d. per gallon, with 12 gallons of white wine, at 5s. per gallon, 30 gallons of Lisbon, at 6s. per gallon, and 20 gallons of Mountain, at 4s. 6d. per gallon: what is a gallon of this mixture worth? Ans. 5s. 3 d..

10. A farmer mingled 20 bushels of wheat, at 5s. per bushel, and 36 bushels of rye, at 3s. per bushel, with 40 bushels of barley, at 2s. per bushel: I desire to know the worth of a bushel of this mixture? Ans. 3s.

11. A person mixing a quantity of oats, at 2s. 6d. per bushel, with the like quantity of beans, at 4s. 6d. per bushel, would be glad to know the value of 1 bushel of that mixture? Ans. 3s. 6d. 12. A refiner, having 12 lb. of silver bullion of 6 oz. fine, would melt it with 8 lb. of 7 oz. fine, and 10 lb. of 8 cz. fine : required the fineness of 1 lb. of that mixture?

Ans. 6 oz. 18 dwt. 16 grs.

13. If with 40 bushels of corn, at 4s. per bushel, there are mixed 10 bushels, at 6s. per bushel, 30 bushels at 5s. per bushel, and 20 bushels, at 3s. per bushel : what will 10 bushels of that mixture be worth? Ans. £2 3.

ALLIGATION ALTERNATE.

ALLIGATION ALTERNATE is the method of finding what quantity of any number of simples, whose rates are given, will compose a mixture of a given rate: so that it is the reverse of Alligation Medial, and may be proved by it.