EXAMPLES. 1. A merchant sold a parcel of goods for 63£, and by so doing lost 17 per cent., whereas he ought to have gained 20£ per cent. by the transaction; how much under their just value were they sold? 100£ As 83 : 91 100£ 120 :: 63£ to 91£ 1s. 8d. and 2. A merchant sold a quantity of goods for $600, and by so doing lost $20 per cent., whereas he ought to have gained $25 per cent. by trading fairly; how much under their just value were the goods sold? Ans. $337.50cts. CASE 12. To find the quantity of any thing contained in a box or bag, &c. when the buying and selling prices are both given, and a certain rate per cent. is gained or lost by the transaction. RULE. As the selling price is to the quantity for which it paid, so is the buying price per box or bag, &c. with the gain per cent. added, or the loss per cent. subtracted, to the quantity contained in the said box or bag, &c. EXAMPLES. 1. A grocer bought 100 boxes of prunes, at $2.10cts. per box, and sold them at $3.50cts per cwt., and by doing so he gained $25 per cent.; how many pounds were contained in each box, one with another? Ans. 84lbs. or 3qrs. of a cwt. p.c. Scts. 2. A merchant bought 80 bags of cotton at $37.50cts per bag, and sold it at $15 per 100lbs., and by doing so he gained $20 per cent.; how many pounds were contained in each bag, what were the buying and selling prices of each pound, what was the whole gain, and the gain on each pound? Ans. Each bag contained 300lbs.; the cotton cost 124cts. per lb. and was sold at 15cts. per lb.; the whole gain was $600, and the gain on each pound 2 cts. FELLOWSHIP. Fellowship is a rule by which the accounts of merchants and other persons trading in partnership are so adjusted, that each man may have his equitable share of the profit, or sustain his proportional part of the loss, in a just ratio to his share of the joint stock, together with the time of its continuance in trade. Legacies are adjusted by this rule, when there is a deficiency of assets, and the effects of bankrupts divided among their creditors. CASE 1. When the several shares composing the joint stock of the whole company are continued in trade an equal term of time. RULE. As the whole sum of the joint stock So is each man's share in the stock Add the several shares of the gain or loss together, and the total sum will be equivalent to the whole gain or loss, if the operation is right. EXAMPLES. 1. Three merchants, namely, A, B, and C, join in company; A put in $140, B $300, and C $160; their clear gain is $120. What is each partner's share of it, in proportion to his share in the joint stock? Ans. A must have $28, B $60, and C $32. Examine the work carefully. 2. Divide the number 360 into four parts, which shall be in proportion to each other, as 3, 4, 5, 6. Ans: 60, 80, 100, and 120. 3+4+5+6=18. As 18:360:3 As 18:360 :: 4 As 18:360 :: 5 As 18: 360 :: 6 3. It is required to divide $120 between A and B, so that A may and B of the whole sum; what is each man's part in the above proportion? have Wherefore, I say-1st. As 100: 120 :: 6072 A's part. 2d. As 100 120 :: 40.48 B's part. $120=proof. 4. Three men, namely, A, B, and C, joined in partnership; A put in $1200, B $4800, and C $2000; they gained $800. Please to inform me how much each partner must receive of the gain?. Ans. A must receive $120, B 480, and C 200. 5. Three men, namely, D, E, and F, joined in company; D put in $2880, E $11520, and F $4800, and by misfortune lost $1920, What sum must each man sustain of the loss? Ans. D must lose $288, E 1152, and F 480. 6. A, B, and C freighted a ship with 108 tuns of wine, of which A had 48, B 36, and C 24, and by reason of bad weather they were obliged to cast 45 tuns overboard; how much must each man sustain of the loss? A must lose 20 tuns, B 15, and C 10. 7. P, Q, and R have rented a pasture containing 360 acres at $140 per annum, of which P holds 90, Q 120, and R 150 acres; please to tell me how much each tenant must pay in proportion to the land he holds? Ans. P must pay $60, Q 80, and R 100. 8. Four men, namely, D, E, F, and G, traded together with a stock of $800, and in two years time they gained twice as much and $40 more-D's stock was $140, E's $260, and F's $300; I demand G's stock, and what each man gained by trading? Ans. G's stock was $100; D gained $287, E $533, F $300, and G $205. 9. Three neighbors, namely, X, Y, and Z, bought a grindlestone in partnership for $4.50cts. of which X agreed to pay 1, Y and Z 1; please to tell me how much each one had to pay of the debt in the said proportion? Ans. X had to pay $2.07cts. 6m,+900 rem. Y $1.38cts. 4m.+600 rem. and Z $1.03cts. 8m,+450 rem. 10. A merchant is indebted to S $169, to T $960, to V $337.50 cents, but upon his decease his estate is found to be worth only $983.28 cents; how must it be divided among his creditors? When the several shares composing the joint stock of the whole company are continued in trade an unequal term of time. RULE. 1. Multiply each man's share in the joint stock of the whole company by the time of its continuance in trade. 2. Say-As the sum of the several products So is each particular product To its share of the gain or loss. The operation may be proved as in case the first. 1. Three merchants, namely, A, B, and C, traded together; A put in $120 for 9 months, B $100 for 16 months, and C $100 for 14mo., and they gained $150; what is each man's share in proportion to. his stock and time? 2. Three merchants namely, D, E, and F, joined in partnership for 12 months; D put in at first $873.60cts. and 4 months after that time he put in $96 more; E put in at first $979.20cts. and at the end of 7 months he took out $206.40cts.; F put in at first $355.. 20cts. and 3 months afterwards he put in $206.40cts. and 5 months after that time he put in $240 more, and at the termination of 12mo. their clear gain is found to be $3446.40 cents; what is each part-ner's share thereof, in proportion to his stock, and the time of its 'continuance in trade? $ c. m. products. 1st. D put in 873.60×4=3494.40 $ C. $ c. m. remainders. As 29049.60: 3446.40 :: 11251.20..1334.82,6+ 336000 29049.60: 3446.40 :: 10718.40..1271.61,4+1570560 Ans... 29049.60 3446.40 :: 7080.00.. 839.96,0+ 998400 1=2904960 $3446.40,0-proof. 3. A with a capital of $400 commenced merchandising on the 1st day of January 1829, and being successful in business, he took in B as a partner on the 1st day of March following, with a capital of $500-three months afterwards they admitted C as a third partner, with capital of $600-on the 1st of January, 1830, they dissolved partnership, and found their neat gain to be $700; what is each man's share of it, in proportion to his stock and time? Ans. A must receive $240, B 250, and C 210. 4. A, B, and C traded in company, A put in $1000 for 5 months; B, $1200 for 8 months, C $1500 for 6 months, and D $2100 for 4 months-by misfortune on sea they lost goods to the amount of $1600; please to inform me how much each one must sustain of the damage? Ans. A must lose $250, B 480, C 450 and D 420. 5. B,C,and D hold a pasture in common, for which they pay $90 per annum-in this pasture B had 45 oxen for 8 weeks, C had 25 for 12 weeks, and D 34 for 10 weeks; what must each one pay of the rent? Ans. B had to pay $32.40cts. C $27 and D $30.60cts. |