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PROOF.

As in Single Fellowship.

EXAMPLES (1) Three merchants, A. B. and C. enter into partnership,

thus: A. puts into the stock 2401. for 4 months, B, 1201. for 6 months, and C. 2001. for 8 months; with this joint stock they traffic, and gain 260l. It is required to find each person's share of the gain, propor

tionable to his stock and time of employing it. (2) A ship’s company take a prize, value 4000l. which they

agree to divide amongst them according to their pay and time they have been on board ; now the officers and midshipmen have been on board 4 months, and the sailors 3; the officers have 50s. a month; the midshipmen 40s. and the sailors 28s. There are also 4 officers, 8 midshipmen, and 120 sailors. I demand what

is each person's share of the said prize? (3) A. B. and C. rent a piece of land, for which they pay 401.

per annum; A. puts in 60 oxen for 4 months, B. 40 oxen for 5 months, and C. 30 oxen for the remainder of the year; what must each person pay of the said

rent? (4) Three merchants, A. B. and C. in partnership together for

a year, put into one common stock as follows, viz. A. puts in 4001. and at 6 months' end withdraws 2001.; B. puts in 360l. and at 7 months' end 100l. more, but at ihe end of 9 months he takes out 1201. ; C. puis in 1901. and at 8 months' end 1101. more, but at the end of 10 months he takes out 100l. They gain 4601. What is each man's share?

QUESTIONS for Exercise at leisure Hours. (5) A. and B. in partnership equally divide the gain: A.'s

money, which was 84l. 128. 6. jay for 19 months, and Bi's for no more than 7 : the adventure of the latter is

sought. (6) A. for 9 months' adventure received 20l. B. for one of

7 months received 25 guineas, and C. for lying out

of his contributions 5 months had a title to 321. The total of their adventures, multiplied into their respective times, was 6401. What then were the par

ticulars ? (7) A. clears 131. in 6 months, B. 181. in 5 months, and C.

231. in 9 months, with a stock of 721. 10s. What then

did the general stock amount to? (8) X. Y. and Z. in company, make one common stock of

42621. X.'s money was in 4 months, Y.'s 6 months, and Zi's 9 months; they gained 4201. which was to be divided in the following manner, viz. Ź of X.'s gain to be equal to į of Y.'s, and į of Y.'s gain to be equal to

of Z.'s. Quere, what each person gained and put

in ? (9) A. B. and C. in company; A. put in his share of the.

stock for 5 months, and laid claim to of the profits; B. put in his for 8 months; C. advanced 4001. for 3 months, and required on the balance s of the gain :

the stock of the other two adventurers is sought. (10) A. and B. paid equally for a horse, Feb. 7, 1805; A. on

the 10th took him a journey to the west, and returned on the 10th of Jure following: B. on the 2d of August took him into Scotland, and staid till Nov. 13, and inus concluded his service for this year. From Jan. 17th following, A. used him ten days; and, in six weeks. after his return, employed him till April 30th. B. then rode him from May-day to Midsummer : A. had him from the 14th of July to 14 days after St. James's tide ; B. on Sept. 30th, took him into Norfolk, and came back Oct. 19th: he then was sold for 71. 10s. and they would have the money parted equally between them, viz. in proportion to the use each made of their steed.

XXIV. BARTER

IS the changing of one commodity for another, and informs us how to proportion the value of any goods, so that neither party may sustain loss. And if the commodities exchanged. are not of equal value, the defect is supplied with money.

RULE. • 1. Find the value of that commodity, whose quantity is given : then find what quantity of the other, at the given rate, you can have for the aforesaid value; which quantity will be the answer.

2. When one has goods at a certain price ready money, but in barter advances it to something more, say, As the ready money price of the one ; is to its bartering price :: so is the ready money price of the other to its bartering price: then the quantity of the latter commodity may be found, either from the ready money or bartering price.

EXAMPLES.

(1) How much sugar at 1l. 10s. per cwt. must be given in

barter, for 4 cwt. of tea, at 12s. per pound? (2) How many yards of cloth, at 18s. per yard, must I give

for 45 yards of shalloon, at 16d. per yard? (3) A. and B. barter: A. has 30 cwt. of prunes at 6d. per lb.

ready money, but in barter will have 7d. per ib. B. has hops worth 36s, per cwt. ready money. What ought B. to rate his hops in barter, and what quantity

must be given for the 30 cwt, of prunes ? (4) A. has tea at 8s. 6d. per lb. ready money, but in barter

will have Jos. per Ib. B. has tobacco worth 18d. per Ib. ready money. How must B. rate his tobacco per lb, that his profit may be equivalent with A.'s?

QUESTIONS for Exercise at leisure Hours. (5) A. has currants worth 4d. per lb. but in barter charges

6d. and also requires one half of that in ready money; B. has candles worth 6s. 8d. the dozen, and he, in barter, charges but 7s. Should these persons deal together for the value of 201., how much will A. have

gained of B.? (0) A. lets B. have a hogshead of sugar, weight 18 cwt.

worth 31s. for 42s. per cwt. one-third of which he is to pay in cash; B. has paper worth 14s. per ream, which it is agreed shall bear no more than 15s. 6d. At that rate, and barter for the rest, how stood the account?

per cent.

(7) A. has kerseys at 4l. 55. a piece ready money ; in barter

they are charged by him at 51. 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 11l. 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 Ib. 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 6ș. 8d. proposes, in case he has half the value in money, to allow B. a discount of 10

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 88. ready money,

which in barter he sets down at 10s. B. sensible of this, has pamphlets at 6d. a piece ready money, which he adea quately 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 1 of that in ready specie ; B. has tea worth Is. 6d. the Ib. which too ratés 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 Faru

ham hops, at 21. 195. 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, by the 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 ihe 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 148. 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 Ib. 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.?

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