Queft. 3. What Principal or Stock will gain 207. in 8 Months at 6 per Cent. per Annum? Prin. 100 Time. Gain. 12. 6 Terms in the Suppofition. 8 20 In this Queftion the Blank falls under the firft Place, therefore it muft be found by the fecond Rule. Thus 100 x 12 x 20 24000 the Dividend. And 8x648 the Divifor. Then 48) 24000 (500l. the Answer required. The Proof of all Queftions in this Double Rule of five Numbers, is beft performed by varying the Question; viz. by ftating it in another Order, as in the last Example: Thus, If rool. gain 67. in 12 Months, what will 500l. gain in 8 Months? The Answer to this Queftion must be 207. if the Work of the laft Example be true. 500 500 x 8 X 6 =24000. And 100 x 12 1 200. Then 1200) 24000 (207. the Answer, &c. Quest. 4. If two Men can do 12 Rods of Ditching in 6 Days, How many Rods may be done by 8 Men in 24 Days, at the fame Rate of working? Anfw. 192 Rods. Queft. 5. If the Carriage of 5 C. 3 qrs. Weight, 150 Miles, coft 3 1. 7 s. 4 d. What must be paid for the Carriage of 7 C. 2 qrs. 25 lb Weight, 64 Miles, at the fame Rate? Anfw. 1. 18 s. 7 d. Quest. 6. If 8 Men deserve 2 1. Wages for 5 Days Work, How much will 32 Men deferve for 24 Days, at the fame Rate? Anfw. 381. 8s. Queft. 7. Suppofe a Hundred Pounds would defray the Expences of five Men for Twenty-two Weeks and fix Days, How long would twelve Men be in fpending of one Hundred and Fifty Pounds, at the fame Rate? Anfw. 14 Weeks and 2 Days., СНАР. CHAP. VIII. Of Trading in Company, ufually called the Rule of Fellowhip; alfo Battering, and Exchanging of Coins, &c. THE 'HE Rule of Fellowship is that by which the Accompts of several Partners trading in a Company, are fo adjusted or made up, that every Partner may have his juft Part of the Gain, or fuftain his juft Part of the Lofs; according to the Proportion or Share of Money he hath in the Joint-Stock: Now this falls under two Confiderations, called the Single and Double Rules of Fellowship. Sect. 1. The Single Rule of Fellowship; viz. That without Time. BY Y the Single Rule of Fellowship is adjusted the Accompts of thofe Partners that put all their feveral and perhaps different Sums of Money, into a common Stock at one and the fame Time; and therefore it is ufually called the Rule of Fellowship without Time: Now all Queftions of this Nature are answered by fo many feveral Operations in the Rule of Three Direct, as there are Partners in the Stock. For, as the Total Sum of Money in the Stock is in Proportion to the whole Gain,, or Lofs: fo is every Man's particular Part of that Stack; to his particular Share of that Gain, or Lofs. Queft. 1. Three Partners, fuppofe A, B, and C, make a JointStock of 961. in this manner. 4, puts in 241. B, puts in 32 1. and C, puts in 40%, with this 961. they trade and gain 12. It is required to find each Man's true Part of that Gain. The Operation will ftand, thus 241. 31. = A's 961: 121:32 1.: 41. B's Part of the Gain. = (401.: 51.=C's) Proof 3+4+5 l. 127. the whole Gain. That is, if the Sum of each Man's particular Gain, amount to the whole Gain, the Work is true; if not, fome Error is committed which must be found out, Note, Thefe Operations will be very much abbreviated, if you work them by Theorem 2. page 87. For here 96 is a common Antecedent, and 12 is the common Confequent in all the three Proportions. 0 2 There Now this Method is more readily performed than the other, efpecially when the Partners are many; because one Single Divifion ferves for all the Work. Queft. 2. Three Merchants, A, B, and C, freight a Ship with 248 Tun of Wine: Thus, A, loaded 98 Tun, B, 86 Tun, and C, 64 Tun. By Extremity of Weather the Seamen were forced to caft or throw 93 Tun of it over-board. How much of this Lofs muft each Merchant fuftain? Now if the Queftion were to find how much of the remaining Wine that was faved, belongs to A, to B, and to C. That is, A, ought to have 61 Tun and 63 Gallons. B, ought to have 53 Tun and 189 Gallons. And C, ought to have 40 Tun of what was left. Queft. 3 Suppofe fix Men, viz. A, B, C, D, E, and F, make a Joint-Stock of 25581. The whole Stock 2558. 00=2558,00 according to the Quest With this Stock of 25581. they trade eighteen Months, and gain 8311. 75. It is required to find every Man's Part or Share of that Gain. Note, Although the Time of Trading, viz. eighteen Months, be mentioned in the Queftion, yet it is no Way concerned in answering of it; as you may observe in the following Work.. First, 25581. 831,35l. :: 1 l. : 0,325 Decimal Parts. Confequently, 17.: 0,325 :: 654,5 212,7125. That is, I have omitted refolving this Queftion according to the ufual Method (as before directed) of finding every Man's particular Part of the Gain by the Golden Rule, as in the first Work of Example 1. leaving that for the Learner's Practice. Sect. 2. The Double Rule of Fellowship; or that with Time. THIS is ufually called the Double Rule of Fellowship, because every particular Man's Money is to be confidered with Relation to the Time of it's Continuance in the Joint-Stock. Question 1. A, and B, join in Partnership upon these Terms, viz. A, agrees to lay down 1001. and to employ it in Trade 3 Months: Then B, is to lay down his 100%, and with the whole Stock of 2007. they are to trade 3 Months more. Now at the End of that Time, they find their whole Gain to be 21. It is required to know what each Man's Part of the Gain ought to be, according to his Stock, and the Time of employing it. Here Here it is but reasonable to conclude, that A, ought to gain more than B, notwithstanding their Stocks of Money are equal; because A employed his Money a longer Time than B. Now for folving of this Queftion, let us fuppofe A's 108 l. employed the first three Months to gain Z= a Sum as yet unknown; then it muft gain 2 Z in 6 Months; and to find what B, muft gain, it will be, But A's Gain added to B's Gain muft 21 7. the whole Gain by the Question. ThereforeZ+ 100 x 3 x 2 Z 100x6 =21% That is, 100 x 6 x 2 Z + 100 x 3 x 2 Z 21 x 100 x 6. Confequently, 2 Z= 21 × 600 which gives the following 900 Analogy, Viz. 900: 21: 600: 2 Z 14 1. for A's Gain. Now this way of arguing hath not only refolved the prefent Queftion, but it alfo affords (and demonftrates) a general Rule for refolving all Queftions of this Nature, be the Partners never fo many. Rule. Multiply every particular Man's Stock, with the Time it is employed, then it will be, As the Sum of all thofe Products Is to the whole Gain (or Lofs), So is every one of thofe Products to it's proportional Part of that whole Gain (or Lofs). Question 2. Three Merchants A, B, and C, enter into Partnerfhip, thus; A puts into the Stock 65 1. for 8 Months; B puts in 78%. for 12 Months; and C puts in 84 7. for 6 Months. With these they traffick, and gain 1661. 12 s. It is required to find each Man's Share of the Gain, proportionable to the Stock and Time of employing it, |