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(7) A. has kerseys at 41. 5s. a piece ready money; in barter they are charged by him at 5l. 6s. each, and of that required down; B. has flax at 3d per lb. How ought he to rate it not to be hurt by the extortion of A.?

(8) A. has 50 broad cloths, at 111. 10s. a piece, but in change required 131. taking wool at 2s. 6d. per stone, of B. in return, that was really worth but 4s. 2d. a tod. The question is, how many sacks of wool will pay for the cloth, and which of the dealers has the advantage in the bargain.

(9) A. with an intention to clear 30 guineas on a bargain with B. rates hops at 16d. per lb. that stood him in 10d. B. apprised of that, set down malt which cost 20s. a quarter at an adequate price. How much malt did they contract for?

(10) A. in order to put off to B. 720 ells of damaged Holland, worth 5s. an ell, at 6s. 8d. proposes, in case he has half the value in money, to allow B. a discount of 10 per cent. The rest A. is to take out in saffron, which B. apprised of the whole management, rates in justice at 30s. per pound. What was it really worth in ready money, and what quantity of saffron was he to deliver on the change?

(11) A. has 100 reams of paper, at 8s. ready money, which in barter he sets down at 10s. B. sensible of this, has pamphlets at 6d. a piece ready money, which he adequately charges, and insists, besides, on of the price of those he parts with in specie: what number of the books is he to deliver in lieu of A.'s paper? What cash will make good the difference? and how much is B. the gainer by this affair ?

(12) A. and B. barter; A. has 140 lb. 11 oz. of plate, at 6s. 4d. the ounce, which in barter he rates at 7s. 2d. an ounce, and allows a discount on his part to have of that in ready specie; B. has tea worth 9s. 6d. the lb. which he rates at 11s. 2d. When they come to strike the balance, A. received but 7 cwt. 2 qrs. 18 lb. of tea. What discount did A. allow B., which of them had the advantage, and how much, in an article of trade thus circumstanced?

(13) A. and B. barter; A. has 14 cwt. 2 qrs. 25 lb. of Farnham hops, at 21. 19s. per cwt. but in barter insists on

3 guineas; B. has wine worth 6s. per gallon, which he raises in proportion to A.'s demand: on the balance, A. received but a hogshead and a half of wine. What had he in ready money?

XXV. LOSS AND GAIN

IS a rule by which we discover the gain or loss by any parcel of goods, and so instructs us how to raise or fall the price of any commodity in such proportions, that neither our gain may be so exorbitant as to injure our customers, nor our loss so great as to impoverish ourselves; which is generally at so much per cent.

In this rule there are a great variety of examples, all of which may be easily solved, with a little consideration, bythe following proportion :

:

Case 1. When the quantity lost and gained of the whole is given, to find the value of any part thereof.

RULE.

Say, As the whole quantity of goods : is to the sum of the whole cost and proposed gain :: so is any part of said goods : to the price they must be sold for.

Case 2. When the proposed gain or loss is at so much per cent., make 100l. with the gain or loss added to it, your second

term.

EXAMPLES.

(1) Bought 240 yards of cloth, at 14s. 6d. per yard, and sold it again at 18s. per yard. What did I gain by the whole?

(2) Suppose I give 46l. for 9 cwt. 2 qrs. 18 lb. of sugar, at what rate must I sell it per lb. to gain 12 guineas by the whole?

(3) If I buy tea at 8s. 6d. per lb. and sell it again for 10s. 6d. what is the gain per cent.?

(4) If by selling cloth at 5s. per ell, I gain 81. per cent, what shall I gain per cent. if I sell the ell at 6s. 3d. (5) At 5s. per dozen, I gain 71. 10s. per cent. how much shall I gain per cent. if I sell the dozen at 5s. 9d.

(6) A Manchester tradesman going to a fair, sold fustians for 11s. 6d. the end, wherein was gained 151. per. cent. but, seeing no other tradesman had so good, raised them at the latter end of the fair to 12s. the end. I demand what he gained per cent, by this last sale.

(7) Suppose I sell 500 deals at 15d. per piece, and 9l. per cent. loss, what do I lose by the whole quantity ? (8) Suppose I sell 1 cwt. of hops, for 61. 15s. and gain 251. per cent. what would have been the gain per cent. if I had sold them for 81. per cent. ?

(9) If by selling hops at 31. 10s. per cwt. the planter clears 30 per cent. what was his gain per cent. when the same goods sold for 41. and a crown?

(10) Sold a repeating watch for 50 guineas, and by so doing lost 17 per cent. whereas I ought in dealing to have cleared 20 per cent. Then how much was it sold under the just value ?

QUESTIONS for Exercise at leisure Hours.

(11) If by sending pewter to Turkey, and parting with it at 354d. per lb. a merchant clears cent. per cent. what does he clear in Holland, where he disposes of the cwt. for 8l.?

(12) Bought hose in London, at 4s. 3d. per pair, and sold them afterwards in Dublin at 6s. Now, taking the charges at an average to be 2d. per pair, and considering that I must lose 12 per cent. by remitting my money home again, what do I gain per cent. by this

article of trade?

(13) If my factor at Leghorn returns me 800 barrels of anchovies, each weighing 14 lb. net, worth 121⁄2d. per Ib. in lieu of 7490 lb. of Virginia tobacco, and if I find that I have gained after the rate of 171. per cent. by the said consignment; pray how was my tobacco invoiced per lb. to the factor? or what was the prime cost?

(14) Bought comfits to the value of 411. 3s. 4d. for 3s. 1d. per lb. It happened that so many of them were damaged in carriage, that by selling what remained good at 4s. 6d. per lb. my returns were no more than 341. 2s. 6d. Pray how much of these goods were spoiled, and what did this part stand me in?

(15) A stationer sold quills at 11s. per thousand, by which he cleared of the money; but they growing scarce, he raised them to 13s. 6d. per thousand. What might he clear per cent. by the latter price?

(16) A. had 15 pipes of Malaga wine, which he parted with to B. at 4 per cent. profit, who sold them to C. for 38l. 11s. 6d. advantage; C. made them over to D. for 500l. 16s. 8d. and cleared thereby 61⁄2 per cent. What did this wine cost A. per gallon?

(17) Laid out in a lot of muslin 480l. 12s., upon examination of which two parts in seven proved damaged; so that I could make but 5s. 6d. per yard of the same; and by so doing, find I lost 487. 18s. by it. At what rate per ell am I to part with the undamaged muslin, to make up my loss?

XXVI. ALLIGATION MEDIAL

IS when the price and quantity of several commodities are given to be mixed, to find the mean price of that mix

ture.

RULE.

As the whole composition: is to its total value so is any part thereof: to its mean price.

PROOF.

Find the value of the whole mixture at the mean rate; and if it agree with the total value of the several quantities at their respective prices, the work is right.

EXAMPLES.

(1) A wine merchant mingles 14 gallons of mountain wine at 8s. per gallon, with 12 gallons at 6s, per gallon, 10 gallons of sherry at 7s. per gallon, 20 gallons of white wine at 4s. per gallon, and 8 gallons

of canary at 9s. per gallon. How may he sell this mixture per gallon?

(2) With 13 gallons of canary, at 6s. 8d. per gallon, I mingle 20 gallons of white wine, at 5s. per gallon; and to these add 10 gallons of cider, at 3s. per gallon. At what rate must I sell a quart of this mixture, so as to clear 10 per cent. ?

XXVII. ALLIGATION ALTERNATE

IS when the rates of several commodities are given, to find such quantities of them as, being mixed together, shall bear a price propounded.

RULE.

1. The rates (if not already) must all be reduced to one denomination.

2. Set down the rates, or prices, in a column under one another, and the mixed or mean rate on the left hand of these.

3. Connect or link together the several rates, so that every one less than the mean be linked with some one greater, or with as many as you please that are greater, and every great with one less, or with as many less as you please.

4. Take the difference between each price and the mean rate, and set them alternately; and if only one difference stand against any rate, it will be the quantity belonging to that said rate; but if there are several, then their sum will be the quantity; which quantities are the answer for that rate against which they stand.

EXAMPLES.

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(3) To mix gold of 18 carats fine with that of 23 carats fine, of 19, and of 16 carats fine, so that the composition. may be 20 carats fine; what quantity of each must be taken?

(4) A grocer would mix a quantity of sugar at 10d. per lb. with other sugar at 7 d. 5d. and 42d. per lb. intending to make up a commodity worth 6d. per lb. In what proportion is he to take of those sugars?

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