The whole gain .72-C's gain .32 .40. A's and B's gain : Then, As.100, A's and B's stock : £.40 their gain :: £.40 A's stock: £.16, his gain. Again, As £.16 A's gain : £.40, his stock :: £.32, C's gain: £.80, his stock. 12. A, B and C put in D.720, and gained D.540, of which, so often as A took up D.3, B took 5, and C 7: What did each put in and gain? D. D. D. D. D. D. D. And, as 3+ 5 + 7 : 720 :: S3: 108 A's gain. 5 180 B's ditto. Or, you may find a common multiplier to multiply the proportions by, or multiplicand to be multiplied by the given proportions, thus, 15)720(48 multiplicand to find the stocks.-And 15)540(36 multiplicand to find the gains. D. 48x3=144 A's stock. 48x5=240 B's ditto. 48x7=336 C's ditto. } And 36x3=108 A's gain. 36x7=252 C's dittto. as before. 13. A, B, C and D companied ; and gained a sum of money of which A, B and C took .120, B, C and D, L.180, C, D, and A,160, and D, A and B, £.140; What distinct gain had each ? The sum of these 4 numbers is £.600, and as each man's money is named 3 times, therefore, viz. .200 is the whole gainTherefore £.200-.120 A's, B's and C's gain=.80 D's gain ;— And £200-£.180 B's, C's and D's gain=.20 A's gain..200-160 C's, D's and A's gain=.40 B's gain. And L.200-.140 D's, A's and B's gain=.60 C's gain. 14. Two merchants companied; A put in ducats. They gained .135, of which A took the value of a ducat? As £.60, A's gain: .40, and B 288 60. What was 40, his stock :: .135 the whole gain L.60, A's gain: .50, B's stock. Duc. L. Duc. s. d. And, as 288: 50 :: 1 : 3 5 Ans. 15. Four men spent, at a reckoning, 20 shillings, of which they agreed that A should pay 4, B, 1, C, 4, and D, . What must each pay in that proportion? s. d. DOUBLE FELLOWSHIP,* Or, Fellowship with Time, is occasioned by the shares of partners being continued unequal times. RULE. Multiply each man's stock, or share, by the time it was continued in trade. Then, As the whole sum of the products, is to the whole gain or loss, so is each man's particular product, to his particular share of the gain or loss. EXAMPLES. 1. A, B and C hold a pasture in common, for which they pay 401 per annum. A put in 9 oxen for 5 weeks; B, 12 oxen for 7 weeks, and C 8 oxen for 16 weeks. What must each pay of the rent ? 9x5=45. 12x7=84, and 8x16-128, then 128+84+45=257 As 257: 40 :: 45 As 257 40 :: 84 As 257: 40 :: 128 When times are equal, the fhares of the gain or lofs are evidently as the ftocks, as in Single Fellowship; and when the stocks are equal, the fhares are as the times; wherefore, when neither are equal, the fhares must be as their preducts. T 2. Four merchants traded in company; A put in D.400 for five months, B, D.600 for 7 months, C, D.960 for 8 months, and D, D. 1200 for 9 months; but by misfortunes at sea, they lost D.750. What must each man sustain of the loss? 3. A, with a capital of 1001. began trade January 1st 1787, and meeting with success in his business, he took in B as a partner, on the 1st day of March following, with a capital of 1501. Three months after that, they admit C as a third partner, who brought into stock 1801. and after trading together until the 1st of January 1788, they found there had been gained since A's commencing business, 1771. 13s. How must this be divided among the partners ? Ans. A, 531. 16s. 8d. B, 671. 5s. 10d. C, 56l. 10s. 6d 4. Two merchants entered into partnership for 18 months; A, at first, put into stock D 400, and at the end of 8 months he put in D.200 more; B, at first, put in D.1100, and at 4 months' end took out D.280. Now at the expiration of the time, they found they had gained, D.1052. What is each man's just share? Ans. A, D.385 90c. B, D.666 10c. 5. A and B companied; A put in the 1st of January, 1501.; but B could not put in any until the 1st of May: What did he then put in, to have an equal share with A at the year's end? 6. A, B and C companied; A put in, the first of March, 301. B, the 1st of May, put in 80 yards of broadcloth; and on the 1st of June C put in 120 dollars. On the 1st of January following, they reckoned their gains, of which A and B took 2281. B and C 2151. 10s. and C and A 1871. 10s. What was the whole gain, and the gain of each? What did they value a yard of cloth at? and, what was C's dollar worth? 2281. + 2151. 10s + 1871. 10s. = 6311. and 631 ÷ 2 = 3151. 10s. the whole gain; then, 3151. 10s.-228 = 871. 10s. C's gain. 3151. 10s.-2151. 10s. = 1001. A's gain, and 3151. 10s.-1871. 10s. = 1281. B's gain. To find the value of one yard of cloth, say, As 1001. A's gain: 301. his stock :: 1281. B's gain : 381. 8s. ; then, inversely, As 10 months: 381. 8s. :: 8 months: 481. the value of the whole cloth. As 80yds. 481. :: lyd.: 12s. answer. Now, to find the value of a dollar. As 1001. A's gain: 301. his stock :: 871. 10s. C's gain : 261. 5s. ; then, inversely, As 10 months: 261. 5s :: 7 months: 371. 10s. 120 dollars. Lastly: As 120 dollars: 371. 10s. :: 1 dollar : 6s. 3d. Answer. FELLOWSHIP FELLOWSHIP BY DECIMALS. RULE.* Divide the whole gain, or loss, by the whole stock, or sum of all the products, as the case requires, and the quotient multiplied severally, by each man's stock, or product, will give the gain or loss of each. Proof. A's gain 171. 2s. 10d. + B's gain 341. 5s. 81d. + C's gain 681. 11s. 44d. 1191. 19s. 11d. 2. A, B and C companied; A put in D.400 for 8 months; B D.300 for 9 months; and C D.175 for 12 months; with which they gained D.720. Required the share of each? 3. A, B, C and D trade, and gain 2001. which is to be divided in the following manner, viz. so often as A has 61. B must have 101. C, 141. and D, 201. What is the share of each ? = 6+10+14 + 20 50, and 200 4, quotient; then 6 x 4 = 241. A's gain; 10 × 4 = 401. B's gain; 14 x 4 = 561 C's; and 20 × 4 = 801. D's gain. 4. An insolvent estate amounting to D.633 60c. is indebted to A D.312 75c. to B D.297, to C D.50 25c. to D 25c. to ED.200, to F D.142 50c. and to G D.21 25c.; what proportion will each oreditor receive? 633.6 312-75+297 + 50·25 +25 + 200+ 142.5+ 21.25 61c. 84m. on a dollar. And, D. c. m. 45 [193·51 4 = A's proportion. 3 31.09 26 D. C. 312.75 297. 3 50.25 D's ditto. E's ditto. IS a contraction of the Rule of Three Direct, when the first term happens to be an unit, or one; and has its name from its daily use among merchants and tradesmen, being an easy and concise method of working most questions which occur in trade and business. The method of proof is by the Rule of Three, Compound Multiplication, or by varying the order of them. GENERAL RULE. 1. Suppose the price of the given quantity to be 11. or Is. &c. then will the quantity itself be the answer at the supposed price. 2. Divide the given price into aliquot parts, either of the supposed price, or of one another, and the sum of the quotients belonging to each will be the true answer required. EXAMPLE. What is the value of 468 yards, at 2s. 91d. per yard? |