joint stock of 8247. and in three years' time they gained as much, and 70l. over; C.'s stock was 3201. D.'s 340l. I demand E.'s stock, and what each person gained by trading.

(3) Suppose four merchants, A. B. C. and D. join their stocks and trade together, of which A. puts in, B., C., and D.; but at the expiration of 12 months, they had the misfortune to lose 120l. What must each person suffer of the said loss?

(4) Three merchants. D. E. and F. in partnership together, with one common stock of 400l. gained as follows, viz, D. 30l. E. 481. and F. 42l. What was each man's stock?

(5) Suppose the money and effects of a bankrupt amount to 2420l. 17s. 6d. and he is indebted as follows, viz. to A. 1000l. to B. 640l. to C. 900l. and to D. 8421. 16s. How must his effects be divided amongst them? or what share must each have?

QUESTIONS for Exercise at leisure Hours.

(6) A father ordered 500l. to be divided amongst his five sons, thus. Give A. said he,, B., C., D., and E.. Part this equitably amongst them, according to the father's intentions.

(7) Three persons purchase together a West-India sloop, towards which A. advanced, B., and C. 140l. How much paid A. and B. and what part of the vessel had C.?

(8) A. and B. clear by an adventure at sea 50 guineas, with which they agree to buy a horse and chaise; whereof they were to have the use in proportion to the sums adventured, which was found to be A. 10; B. 7: they cleared 45 per cent. What money did each send abroad?

(9) A. and B. join their stocks, and vest them in brandy. A.'s stock was 191. 19s. 8d. more than that of B. Now by selling out their commodity at 55s. per anker, A. cleared 741. 11s. and B. just 50 guineas. The quantity of brandy dealt for is required, and the gain upon the anker.

(10) In an article of trade A. gains 14s. 6d. and his adventure was 35s. more than B.'s, whose share of the

profit is but 8s. 6d. What are the particulars of their stock?

(11) Three persons, A. B. and C. entered into joint trade; to which A. contributed 210l. B. 3121. They cleared 140l. whereof 371. 10s. belongs of right to C. That person's stock and the several gains of the other two are required.

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(12) A. and B. venturing equal sums of money, clear by joint trade 1541. By agreement A. was to have 8 per cent. because he spent time in execution of the project, and B. was only to have 5. What was allotted A. for his trouble?

(13) A. B. and C. are three horses belonging to different men, and are employed as a team to draw a load of wheat from Hertford for 30s. A. and B. are deemed to do of the work, A. and C., and B. and C. of it: they are to be paid proportionably. Do you know how to divide it as it should be ?

(14) Bought 100 quarters of malt, meal, and oatmeal, together, for 142l. For every 5 bushels of malt I had 3 of meal; for every 8 of meal I had 7 of oatmeal. What did these cost me severally per bushel, the malt being half as dear again as the meal, and the meal being double the price of the oatmeal?

(15) In raising a joint stock of 400l. A. advanced,

B.

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of, C. more the difference between A.'s adventure and B.'s; and D. the rest of the money. What did every one subscribe ?

XXIII. DOUBLE FELLOWSHIP,

OR,

Fellowship with Time,

IS when each person's stock continues unequal time in company, so that a consideration must be made of the time, as well as of the stock.

RULE.

Multiply each person's stock by the time it has continued in trade, and proceed with the products, as with the particular stocks in Single Fellowship.

PROOF.

As in Single Fellowship.

EXAMPLES.

(1) Three merchants, A. B. and C. enter into partnership, thus: A. puts into the stock 240l. for 4 months, B. 120l. for 6 months, and C. 2002. for 8 months; with this joint stock they traffic, and gain 260l. It is required to find each person's share of the gain, proportionable 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 40l. 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 400l. and at 6 months' end withdraws 200l.; B. puts in 360l. and at 7 months' end 100l. more, but at the end of 9 months he takes out 120l.; C. puts in 190l. and at 8 months' end 110l. more, but at the end of 10 months he takes out 100l. They gain 460l. 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. 12s. 6d. lay for 19 months, and B.'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 640l. What then were the particulars?

(7) A. clears 13l. in 6 months, B. 18l. in 5 months, and C. 23l. 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 Z.'s 9 months; they gained 420l. which was to be divided in the following manner, viz. of X.'s gain to be equal to of Y.'s, and 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 400l. for 7 months, and required on the balance 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 June following: B. on the 2d of August took him into Scotland, and staid till Nov. 13, and thus 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 11. 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 før 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 71⁄2d. per lb. 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 lh. ready money, but in barter will have 10s. per lb. 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 20l., how much will A. have gained of B.?

(6) 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?