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(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 58. 9d. (6) A Manchester tradesman going to a fair, sold fustians

for 11s. 6d. the end, wherein was gained 15l. 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 91. 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. 108. per cwt. the planter clears

30 per cent. what was his gain per cent. when the same

goods sold for 4l, 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

35 d. per Jb. a merchant clears cent. per cent. what does he clear in Holland, where he disposes of the cwt.

for 81. ? (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 12 d. 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. 35. 4d. for 3s. Id.

per lb. 'It happened that so many of them were damaged in carriage, that by selling what remained good at 4s. 6d. per Ib. my returns were no more than 34.. 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 381. 11s. 6d. advantage; C. made them over to D. for 5001. 16s. 8d. and cleared thereby 61 per cent.

What did this wine cost A. per gallon? (17) Laid out in a lot of muslin 4801. 125., 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. 481. 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 mixture.

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 75. per gallon, 20 gallons of white wine at As. 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 38. 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 tbese,

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.

(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? (+) A grocer would mix a quantity of sugar at 10d. per

lb. with other sugar at 7d. 5d. and 4 d. per lb.intending to make up a commodity worth 6d. per lb. In what proportion is he to take of those sugars?

XXVIII. ALLIGATION PARTIAL IS when the price of each simple is given, also the quantity of one of them, and the mean rate, to find the several quantities of the rest in proportion to that given.

RULE. 1. Take the difference between each price and the mean rate as in the last rule.

2. As the difference of that simple whose quantity is given : is to the known quantity :: so is any other difference: to the quantity of its opposite name,

EXAMPLES (5) How much tea at 6s. 6d., 7s. 6d. and 9s. per Ib. must be

taken to be mixed with 36 lb. at 12s. per lb. that the mixture may

be worth 8s. per 1b. (6) A tobacconist has by him120 lb. of fine Oronoko

tobacco, worth 2s. 6d. a pound; to this he would mix York river ditto at 20d. and other inferior tobaccos at 18d. and 1511. a pound, as will make up a mixture answerable to 25. a pound. What will this parcel weigh?

XXIX. ALLIGATION TOTAL IS when the price of each simple is given, as also the mean rate, and what quantity of the compound, to find how much of each sort will make that quantity.

RULE. 1. Take the difference between each price and the mean rate, as before.

2. Say, as the sum of these differences : is to the whole quantity of the mixture :: so is each particular difference ; to its particular quantity.

EXAMPLES. (7) How much gold of 16, of 18, and 23 carats fine, must be

mixed together, to form a composition of 60 oz. of 20 carats fine?

(8) A grocer has by him 4 sorts of green tea, viz. of

5s. 6s , 8s. and 9s. per lb.; out of these he is inclined to mix up a canister, containing net, a hundred and a half, so as to make the commodity worth 7s. per pound. In what proportion must those teas be taken ?

XXX. EXCHANGE

IS the receiving in one country for the value paid in another.

The par of exchange is always fixed and certain, it being at the intrinsic value of any foreign money compared with sterling : but the course of exchange between any two countries rises and falls upon various occasions.

But as it would be both needless and endless to write of every kind of exchange, so I shall only give a few examples of the exchange of England with some of the chief countries of Europe.

Exchange is either performed by Sec. XII. or XV. and sometimes most expeditiously by the latter.

Ist. With FRANCE. They keep their accounts at Paris, Lyons, and Rouen, in livres, sols, and deniers, and exchange by the crown of three livres Tournois, or 60 sols French, and give pence sterling, more or less, for this exchange crown, which is equal to

4s. 6d. at par.

12 Deniers
20 Sols
3 Livres

make one

Sol.
Livre.
Crown.

Case 1. To change French money into sterling.

RULE.

As 1 crown : is to the given rate :: so is the given French sum: to the sterling required; or by the rules given in Practice,

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