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1. If I sell cloth at 5s. per yd. and thereby gain 15 per cent. what shall I gain per cent. if I sell it at Os. per yard?
£. As 5 : 115 :: 6 : 138 Ans. gained S8 per cent.
2. If I retail rulli at 1 dollar 50 cents per gallon and thereby gain 25 per cent. what shall I gain or lose per cent. if I sell it at 1 dol. 8cts. per gallon?
$ cts. $ $ cts. S 1,50 : 125 : : 1,08 : 90 Ans. I shall lose 10 per cent.
3. If I sell a cwt. of sugar for 8 dollars, and thereby lose 12 per cent. what shall I gain or lose per cent. if I sell 4 cwt. of the same sugar for 36 dollars ?
Ans. I lose only i per cent. 4. I sold a watch for 171. Is. 5d. and by su doing lost 15 per cent. whereas I ought in trding to have cleared 20 per cent.; how mucli was it sold under its real value ? As 85 : 17 1 5 : : 100 : 20 1 8 the prime costo 100 : 20 1 8:: 120 : 24 20 the real value,
Sold for 17 1 5
f. s. d.
67 0 Answer.
a rule by which the accompts of several merchants or other persons, trading in partnership, are so adjusted, that each may have his share of the gain, or sustain his share of the loss, in proportion to his share of the joint stock.--Also by this Rale a bankrupt's estate may be divided among his creditors, &c.
SINGLE FELLOWSHIP, Is when the several shares of stock are continued in trade an equal term of time.
RULE. As the whole stock is to the whole gain or loss : sa iş each man's particular stock, to his particular share of the in or loss.
PROOF.-Add all the particular shares of the gain or loss together, and if it be right, the sum will be equal to the whole gain or loss.
1. Two partners, A and B, join their stock and buy a quantity of merchandize, to the amount of 820 dollars; in the purchase of which A laid out 350 dollars, and B 470 dollars; the commodity being sold, they find their clear gain amounts to 250 dols. What is each person's share of the gain : A put in 350 B 470
S 350 : 106,7073+A's share.
Proof 249,9999+ -8250 2. Three merchants make a joint stock of 12001. of which A put in 2401. B S601. and C 6001.-and by trading they gain 325l. what is each one's part of the gain?
Ans. A's part 665. B's & 97 10s. C's £162 10s. 3. Three partners, A, B, and C, shipped 108 mules for the West-Indies; of which A owned 48, B 36, and C 24. But in stress of weather the mariners were obliged to throw 45 of them overboard; I demand how much of the loss each owner must sustain ?
Ans. A 20, B 15, and C 10. 4. Four men traded with a stock of 800 dollars, by which they gained 307 dols. A's stock was 140 dols. B's 260 dols. C's 500 dols. I demand D's stock and what each man gained by trading ? Ans. D's stock was $100, and A gaired $53, 72cts. 5m. B 899, 77fcts. C 8115, 12fcts, and D $38, 374cts. 5. A bankrupt is indebted to A 2111. to B 3001. and to C 3911. and his whole estate amounts only to 675l. 10s. which he gives up to these creditors ; how much must each have in proportion to his debt?
Ans. I must have £158 Os. 520. BL-84 15s. 47 ano C£292 169 5:
6. A captain, inate and 20 seamen, took a prize worth 3501 dols. of which the captain takes 11 shares, and the mate 5 shares; the remainder of the prize is equally divided among the sailurs; how much did cach man reccive?
97, 25 7. Divide the number of 360 into s parts, which shall be to each other as 2, 3, and 4. fls. 80, 120, and 160.
8. Two merchants have gained 4501. of which A is to fiave 3 times as much as B ; low much is each to have:
Ans. A £337 105. 00:1 B £ 112 105.--1-4-3=1:
450 :: 3 : £957 106. A's share. 9. Thice persons are to share cool. A is to have a certain sum, B as much again as A, and C three times as muc!) as B. I demand each man's part?
ins. A 1992, B £133), anıl C 6400 10. A and B trailed together anul gainel 100 ilois. putin 640 dols. B put in so much that he inust receive Gu dols. of the gain ; I demand B's stock! ins. 9960
11. A, B, and C, traded in company: A putin 140 dols. B 250 dols. and C putin 120 yds. of cloth, at cash price; they gained 250 dos. of which C took 100 dols. for his share of the sain ; how did C value his cloth per yard in common stock, and what was A and B's part of the gain?
Ins. C pit in the cloth at $2% per jare. I gainet
$46, 67cis. 6.2. to und B S83, 33cts. Sm.
COMPOUND FELLOWSHIP, Or Fellowship with time, is occasioned by several shares of partners being continued in trade an unequal term of time.
RULE. Multiply each man's stock or share by the tiinc it was continued in trade: then,
As the sum of the several products,
1. A, B and C hold a pasture in common, for which
per annum. A put in 8 oxen for 6 weeks; B12 oxen for 8 weeks; and ( 12 oxen for 12 weeks; what must each pay of the rent?
£. $. d. 8x 6= 489
48 : 3 3 4 A's pt. 12x 8= 96
96 : 6 6 8 B's 12x12=144 SAS 289 : 191. :: 144 : 9 10 O C's
Proof 19 0 0 2. Two merchants traded in company ; A put in 215 dols. for 6 months, and B 390 dols. for 9 months, but by misfortune they lose 200 dols. ; how must they share the
; loss : Ans. A's loss S53, 75cts. B's $146, 25cts. 5. Threc
persons had received 665 dois. interest: A had 4000 dols. for 12 months, B 3000 dols. for 15 months, and C 5000 dóls.for 8 inonths; how much is each man's part of the interest?
Ans. A 8240, B $225 and C $200 4. Two partners gained by trading 1101. 128.: A's stock was 120l. 10s. for 4 months, and B's 2001. for 61 months; what is each man's part of the gain ? Ans. A's part £, 29 18s. 31d.1356. B’s 6,80 135. 8.11.4203
5. Two merchants enter into partnership for 18 inonths. A at first put into stock 500 dollars, and at the end of 8 months he put in 100 dollars more; B at first put in 800 dollars, and at 4 month's end took out 200 dols. At the expiration of the time they find they have gained 700 dol. Jars; what is each man's share of the gain?
S $324, 07 4-+ I's share.
$375, 92 5+ B's. do 6. A and B companied ; A put in the first of January, 1000 «lols.; but B could not put in any till the first of May; what did he then put in to have an equal share with A at the year's end ?
DOUBLE RULE OF THREE. THE Double Rule of 'Three tenches to resolve at once such questions as require two or more statings in simple proportion, whether direct or inverse.
In this rule there are always five terms given to find a sixth; the three first terms of which are a supposition, the two last a demand.
RULE. In stating the question, place the terms of the supposition so that the principal cause of loss, gain or action possess the first place; that which signifies time, distance of place, &c. in the second place; and the remaining tering in the third place. Place the terms of domand, under those of the same kind in the supposition. If the blank place or term sought, fall under the third terin, the priportion is direct; then multiply the first and second terms together for a divisor, and the other three for at dividend: but if the blank fall under the first or second term, the proportion is inverse; then multiply the third and fourth terms together for a divisor, and the other three for a dividend, and the quotient will be the answer.
1. If 7 men can build 36 rods of wall in S days; how many rods can 20 men build in 14 days ?
7: 3 : : 36 Terms of supposition. 20 : 14 Terins of deinand.
7x3=21) 10080(480 rods Ans. 2. If 1001. principal will gain 61. interest in 12 months, what will 4001. gain in 7 months ? Principal 1001. : 12n1o. : : 61. Int. 400