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3. How much tea at 9s. per lb. can I have in barter for 4 crot. 2 grs. of chocolate, at 4.s. per lb. ?

Ans. 2 cut. s. Two merchants barter; A hath 20 cwt. of clieese at 21% 6d. per cut. B hath 8 pieces of Irish cloth, at £3. 14 per piece; I desire to know who must receive the difference, and how much?

Ans. B must receive of A £8.2. 5. A and B barter; A hath 31 lb. of pepper at 13fd. per lb. B hath ginger at 154d. per lb. how much ginger must he deliver in barter for the pepper?

Ans. 3 lb. 1 0%. * 6. How many dozen of candles, at 5s. 2d. per dozen, must be delivered in barter for 3 cwt. 2 qr. 16 lb. of tallow at 37s. 4d. per ewt.?

Ans. 26 doz. 3 lb. 1. A hath 608 yards of cloth, worth 14s. per yard, for which B gives him £125. 12 in ready money, and 85 cut. 2 grs. 24 lb. of bees wax. The question is, what did B reckon his bees wax at per cwt. ?

Ans. £3.10. 8. A and B barter ; A hath 320 dozen of candles, at 45. 6d. per dozen ; for which B giveth him £30 in money, and the rest in cotton, at 8d. per lb. I desire to know how much cotton B gave A besides the money ?

Ans. 11 cwt. I go 9. If B hath cotton at 1s. 2d. per lb. how much must he give A for 114 lb. of tobacco at 6d. per 16. ?

Ans. 48 lo. ?? 10. Chath nutmegs worth 7s. 6d. per lb. ready money, but in barter will have 8s. per lb, and D hath leaf tobacco worth 9d. per Ib. ready money, how much must D rate his tobacco at per 10. that his profit may be equivalent with Cs?

Ans. 9ļd.o.

EXAMPI ES.

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PROFIT AND LOSS S a rule that discovers what is got or lost in the buying or

selling of goods, and instructs us to rise and fall the price, so as to gain so much per cent. or otherwise.

The questions in this rule are performed by the Rule of Three,

1. If a yard of cloth is bought 2. If 60 ells of Holland cost for 11s. and sold for 128. 6d. £18. what must 1 ell be sold for what is the gain per cent. ? to gain 8 per cent. ?

d. £

£ £ £
As 11 : 1...6 :: 100 As 100: 18 :: 108
12
20

108

12x5=60; 18 2000 1100)19/44 18

20 12)19...8...97 12...0 11...0 11)36000

8/80 5f1... 12...44

12 1...6 12)3272

Ars, 6...63 2|0\27|2..8,1

9160 Ans, £13..12 811

240

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3. 11 iib, of tobacco cost 16d. and is sold for 20d. what is the gain per cent. ?

Ans. 25. 4. If a parcel of cloth be sold for £560 and at £12 per cent. gain, what was the prime cost ?

Ans. £500. 55. If a yard of cloth is bought for 13s. 4d. and sold again for 16s. what is the gain per cent. ?

dns. 20. 6. If 112 lb. of iron cost 27s. 6d. what must 1 cwt. be soli for to gain 15 per cent. ?

Ans, £1.11.7%. 7. If 375 yards of broad cloth be sold for £490 and 20 per cent. profit, what did it cost per yard ? Ans, £1.1.

8. Sold i cwt. of hops at £6.15 at the rate of 25 per cent. profit, what would have been the gain per cent. if I had sold them for £8 per cwt. ?

Ans. £48.2. 114. 9. If 90 ells of cambrick cost £60 how must I sell it per yaru to gain 18 per cent. ?

Ans. 128. 7d. . 10. A plumber sold 10 fother of lead for £205. 15 (the fother being, 19 cwt. 2) and gained after the rate of £12. 10 per cent. what did it cost him per cwt. ?

Ans. 18s. 8d. 11. Bought 436 yards of cloth, at the rate of Rs. 6d. per yard, and sold it for 10s. 4d. per yard, what was the gain of the whole ?

Ans. £39. 19.4. 12 Paid £69. for one ton of steel, which is retailed at 6d. per P. what is the profit or loss by the sale of 14 tons ?

Ans. £182 loss. 13. Bought 194 yards of linen for £32 how should the same be retailed per yard to gain £15 per cent. ? Ans. 6s. 11d. mi:

14. Bought 219 yards of cloth, at 38. 4d. per yard, retailed the same at 45. 2d. per yard, what is the profit in the whole, and how much per cent. ? Ans. £10.7.6 profit, and 25 per cent.

FELLOWSHIP 1$ when two or more join their stock and trade together, so to

determine each person's particular share of the gain or loss in proportion to his principal in joint stock.

By this rule a bankrupt's estate may be divided amongst his creditors; as also legacies may be adjusted when there is a deficiency of assets or effects.

FELLOWSHIP is either with or without Time.

FELLOWSHIP WITHOUT TIME. RULE. As the whole stock : is to the whole gain or loss :: 80 is each man's share in stock : to his share of the gain or loss.

PROOF. Add all the shares together, and the sum will be equal to the given gain or loss :-but the surest way is, as the whole gain or loss : is to the whole stock :: so is each man's share of the gain or loss to his share in stock.

EXAMPLES.

1. Two merchants trade together; A put in stok £20 and B £40. they gained £50. what is each person's share thereof?

£ £ £ 20+40=60 £ As 60 : 50 :: 20 As 60: 50 :: 40 33... 6...8 B's share 20

40 16...13...4 A's

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60)1000 60)20010 £50... 0...0

£16... 13...4 £33...6...8 2. Three merchants trade together, A, B, and C; A put ir £20 B £30 and C £40 they gained £180 what is each man's part of the gain?

Ans. # £40 B £69 C £80. 3. A, B, anů C, enter into partnership; A puts in £364 B £482 and C £500 and they gained £867, what is each man's share in proportion to his stock? Ans. A £234...9...31.-rem 70. B £310...9...5-rem. 248.

C £322...1...31-rem. 1028. 4. Four merchants, B, C, D, and E, make a stock; B put in £227 C £349 D £115 and E £439 in trading they gained £ 128. I demand each merchant's share of the gain.

Ans. B £85...19...61–690. C £132...3...9—120.

E £43...11...15-250. E £166...5...6-70. 5. Three persons D, E, and F, join in company ; D's stock was£750 E's £460 and F's £500, and at the end of 12 nionths they ained £684, what is each man's particular share of the gain?

Ans. D £300 E £184 and F £200. 6. A merchant is indebted to B £275...14...0 to C £304.. 7...O to D £152 and to E £104...6...O but upon his decease, his estate is found to be worth but £675...15...0 how must it be divided among his creditors ?

Ans. B's £222... 1,5...2–6584. C's £245...18...14—15750.

D's £122...16...21–12927. and E's £81...5...5—15620 7. Four persons trading together in a joint stock, of which A has }, B }, C }, and D the remainder, and at the end of six months they gain £100, what is each man'sshare of the said gain?

Ans. A £33...6...8. B £25...0...0. C £20...0...0. and

D £21...13...4. 8. Two persons purchased an estate of £1700 per annum freehold for £27,200 when money was at 6 per cent. interest, and 4s. per pound land tax, whereof D paid' £15,000 and E the rest; some time after the interest of the money falling to 5 per cent, and 8s. per pound land tax, they sell the said estate for 24 years purchase. I desire to know each person's share ?

Ans. D £22,500. E £18,300. 9. D, E, and F join their stocks in trade, the amount of their stock is £647, and are in proportion as 4 6 and 8, are to

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one another, and the annount of their gain is equal to D's stock, what is each man's stock and gain ?

D's stock, £143...15...64 $ gain, £31...19...0,
E's............215... 13...4

47...18...6
Fs....... ..287...11...11

63...18...O 10. D, E, and F join stocks in trade; the amount of their stocks was £100 D's gain £3 E’s £5 and F's £8, what was each man's stock? Ans. D's stock £18...15...0 E's £31...5...0 and F's £50.

FELLOWSHIP WITH TIME. Rue. As the sum of the product of each man's money and time : is to the whole gain or loss :: so is each man's product": to his share of the gain or loss. Proof. As in Fellowship without time.

KXAMPLES 1. D and E enter into partnership; D puts in £10 for three months, and E £75 for four months, and they gained £70. What is each man's share of the gain ? Ans. D £20 E £50. JOX3=120 As 420) : 70 :: 120

As 420 : 70 ;: 300 15 X4=300 120

300

.

.

420 4210)81010(20

420)21000(50 840

2100 2. Three merchants join in company ; D puts in stock £195 14.0 for 3 months, E £169. 18.3 for 5 months, ani F £59 14. 10 for 11 months, they gained £361. 18.0 what is each mau's part of the gain? Ans. D's. £102 6. 4-5003. E's £148.1. 11-182802.

und F's £111. 10.64--14707. 3. Three merchants, join in company for '18 months: D put in 2500 and at 5 months end took ont £200 ; at 10 months end put in £300 and at the end of 14 mouths takes out £130, E

puls in £100 and at the end of 3 months £270 more; at 9 months he takes out £140 but puts in 100 at the end of 12 months ; and withdraws £99 at the end of 15 months. in £900 and at 6 months took out £200; at the end of 11 months put in £500 but takes out that and £100 more at the end of 13 months. They gained £200. I desire to know each man's share of the gain? Ans. D £50...7...6–21720. E £62...18...54-29859, and

F £87...0...01–14167. 4. D, E, and F, hold a piece of ground in common, for which they are to pay £36...10...6. D puts in 23 oxen 27 days; E 21 oxen 30 days; and F 16 oxen 23 days. What is each man to pay of the said rent? dris. D £13...3...11-624. E £15..,11...5-1688 anil

27...15...1l..,1136.

F put

ALLIGATION 13 EITHER MEDIAL OR ALTERNATE.

80

ALLIGATION MEDIAL IS when the price and quantities of several simples are given

to be , Rule. As the whole composition: is to its total value :: 80 is any part of the composition : to its mean price.

Proof. Find the value of the whole mixture at the mean rate; and if it agrees with the total value of the several quantities at their respective prices, the work is right.

EXAMPLES. 1. A farmer m·sed 20 bushels of wheat at 5s. per bushel, and 36 bushels of rye, at 3s. per bushel, with 40 bushels of barley, at 23. per bushel.' I desire to know the worth of a bushel of this mixture? 20 x 5 = 100

As 96 : 288::1:3
36 X 3 - 108
40 X 2 =

Ans. 3s.
96

288 2. A vintner mingles 15 gallons of Canary at 8s. per gallon, with 20 gallons at 7s. 4d. per gallon, 10 gallons of sherry, at 6s. 8d. per gallon, and 24 gallons of white wine, at 45. per gale lon. What is the worth of a galion of this mixture?

Ans. 68. 2 d. 3. A grocer mingled 4 cwt. of sugar, at 568. per cut. 7 cwt. at 43s. per cwt. and 5 cwt. at 37s. per cwi. I demand the price of 2 cwt. of this mixture?

Ans. £4.8.9. 4. A maltster mingles 30 quarters of brown malt, at 28s. per quarter, with 46 quarters of pale, at 30s. per quarter, and 24 quarters of high-dried ditto, at 26s. per quarter. What is the value of 8 bushels of this mixture? Ans, £1.8.21.18

5. If I mix 27 bushels of wheat, at 5s. 6d. per bushel, with the same quantity of rye, at 45. per bushel, and 14 bushels of barley at 2s. 8d. per bushel, whai is the worth of a bushel of this mixture ?

Ans. 45. 3.2 6. A vintner mixes 20 gallons of port, at 5s. 4d. per gallon, with 12 gallons of white wine, at 5s. per gallon, 30 gallons of Lisbon, at 6s, per gallon, and 20 gallons of mountain, at 4s. Odi per gallon. What is a gallon of this mixture worth?

Ans. 55. 31.5.2 5. A refiner having 12 th, of silver bullion, of 6 oz. fine, would melt it with 8 lb. of 70%. fine, and 10 lb. of 80%. fine; required the fineness of 1 lb. of that mixture? Ans. 60%. 18 dwt. 16 gr.

8. A tobacconist would mix 50 lb. of tobacco at 11d. per lb. with 3016. at 14d. per ib. 25lb. at 22d. per lb. and 37 lb.ʻat 2s. per 多, What will 1 lb. of this mixture he worth? Ans. 16 d.145

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