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1. If I sell cloth at 55. per yd. and thereby gain 15 por cent. what shall I gain per cent. if I sell it at 6s. per yard £.
£. As 5 : 115 :: 6 : 138 Ans. gained 38 per cent.
2. If I retail rum 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. 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 1 per
cent. 4. I sold a watch for 171. Is. 5d. and by so doing lost 15
per cent. whereas I ought in trading to have cleared 20 per cent. ; how much was it sold under its real value ? .. £. s. d.
£. s. d. As 85 : 17 1 5 : : 100 : 20 1 8 the prime cost, 100 : 20 1 8:: 120 : 24 2 0 the real value.
Sold for 17 1 5.
£7 on Answer.
S 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 Rule a bankrupt's estate may be divided among his creditors, &c.
SINGLE FELLOWSHI 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 : so is cach man's particular stock, to his particular share of the main or loss.
Proor. Add all the particular shares of the gain or loss together, and if it bé 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 dollars. What is each person's share of the gain?
A put in 350
As 820 : 250 : :
350 : 106,7073+A's share.
Proof 249,9999+$250 2. Three merchants make a joint stock of 12001, of which A put in 2401. B 360l. and C 6001.; and by trading they gain 3252. what is each one's part of the gain ?
Ans. A's part £65, 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 300 dols. I demand D's stock and what each man gained by trading ?
Ans. D's stock was $100, and A gained $53, 72cts. 511. B $99.77.cts.. C 115, 12 cts. and D $38, 37 cts.
5. A bankrupt is indebted to A 2111. to B 3001. and to C 3911. and his whole estate amounts only to 6751. 103. which he gives up to these creditors ; how much must, each have in proportion to his debt?
Ans. A must have £158 08. 31d. B £224 138. 410.. and C £292 163. 3:1d.
6. A captain, mate and 20 séamen, 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 sailors ; how much did each man receive.
$ cts. Ans. The captain received 1069,75 I'he mate
486,25 Each sailor
97,25 7. Divide the number of 360 into 3 parts, which shall be to each other as 2, 3 and 4. Ans. 80, 120 and 160.
8. Two merchants have gained 450l. of which A is tờ have three times as much as B ; how much is each to have.
Ans. A £337 10s. and B £112 10s.-1+3=4:
450 : :3: £337, 108. A's share. 9. Three persons are to share 6001. A is to have a cerlain sum, B as much again as A, and C three times as much as B. I demand each man's part?
Ans. A £669, B £133), and C£400. 10. A and B traded together and gained 100 dols. A put in 640 dols. B put in so much that he must receive 60 dols"
. of the gain ; I demand B's stock ? Ans. $960.
11. A, B and C traded in company: A put in 140 dols. B 250 dols. and C put in 120 yds. of cloth, at cash price; they gained 230 dols. of which C took 100 dols. for his share of the gain : how did C value his cloth per yard in tómmon stock, and what was A and B's part of the gain? Ans.. C put in the cloth at $2} per yard. A gained
$46, 67 cts. 6m.+and B $83, 33cts. 3m.+ 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 time it was tontinued in trade : then,
As the sum of the several products,
ti á, B and C hold a pasture in common, for which
A put in 8 oxen for 6 weeks; B i2 oxen for 8 weeks; and C 12 oxen for 12 weeks; wnat must each pay of the rent?
£. 8. d. 8 x 6= 48
[ 48 : 3 3 4. A's pt. 12 X 85 96
96 : 6 6 8 B's 12x12=144 ŞAs 288: 191, ; ; 144 : 9 10 O C's
Proof 1900 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 $53, 75cts. B's $146, 25cts.
3. Three persons had received 665 dols. interest: A had put in 4000 dols. for 12 months, B 3000 dols. for 15 months, and C 5000 dolş. for 8 months ; how much is each man's part of the interest?
Ans. A $240, B $225 and C $200, 4. Two partners gained by trading 1101. 128. : A's stock was 1201. 10s. for 4 months, and B's 2001. for 64 months; what is each man's part of the gain ? Ars. A's part £29 185. 3}d.}**. B's £80 138. 81d.. MG
5. Two merchants enter into partnership for 18 months. 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 dollars; what is each man's share of the gain ?
$324, 07 4+ A's share.
37592 5+B's do. 6. A and B companied ; A put in the first of January, 1000 dols. ; 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 ? Mo. 8 Mo.
9 As 18 : 1000 : : 8 : 1000 x 12--1500 ans.
DOUBLE RULE OF THREE. THE
HE Double Rule of Three teaches 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.
KULE. 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 term in the third place. Place the terms of demand, under those of the same kind in the supposition. If the blank place or term sought, fall under the third term, the proportion is direct ; then multiply the first and second terms together for a divisor, and the other three for a 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.
EXAMPLES. 1. If 7 men can build 36 rods of wall in 3 days; how many rods can 20 men build in 14 days ?
7: 3 ; : 36 Terms of supposition. 20 : 14 Terms of demand.
7x321)10080(480 rods. Ans. 2. If 1001. principal will gain 6l. interest in 12 month. what will 4001. gain in 7 months ? Principal 1001. : 12mo. : : 6l. Int. 400 : on