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2. A is indebted to B £.120, whereof one half is to be paid in 3 months, one quarter in 6 months, and the remainder in 9 months, what is the equated time for the payment of the whole ?

Anf. 5 months and 71 days. 3. Cowes D 1400 dollars, to be paid in 3 months, but D being in want of money, C pays him, at the expiration of 2 months, 1000 . dollars, how much longer than 3 months ought C, in equity, defer the payment of the rest ?

Anf. 24 months. Those who are exact in these calculations, find the present worth of each particular sum, then find on what time these present worths will be increased to the total of the particular sums payable at the particu

lar times to come ; and that is the true equated time for payment of the whole.


Is the exchanging one commodity for another on such terms as may be agreed on.


1. How many quintals of fish, at 2 dols. per quintal, will pay for 140 hhds. of salt, at 4

70 cts. per


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2. A buys of B 4 hhds. of rum containing 410 gallons, at 1 dol. 17 cts. per gallon; and 253 lb. of coffee, at 21 cts. per lb. in of which he pays 21 dollars in cash, and the balance in boards, at 4 dols. per thousand; how many feet of boards did the balance require ?

Anf. 1279571 feet. 3. B has C's note for 250 dols. with 6 months interest due on it, and to redeem it C delivers him 60 bushels of wheat at 75. 6d. per bushel, 50 bushels of corn at 55. 3d. per bushel, and the balance



thousand ; what number of staves did B receive ?

Ans. 5550 staves, or 4 m. 6 hun, and casts.

in staves at 30

4. B bought of D the hull of a schooner of 70 tons, at 16 dołs. per ton, and paid him in cash 500 dols. 3 hhds. of molasses containing 350 gallons, at 64 cts. and is to pay the balance in New-En. gland rum at 74 cts. per gallon ; how many gallons is D to receive?

Anf. 535 i gallons. 5. A buys of B 250 quintals of fish, at 255. per quintal ; in payment B takes 100 dols. in cash, 2 hhds. of molasses containing 87 and 92 gals. at 35. 8d. per gallon, 1 pipe of brandy containing 120 gals. at 75. 6d. per gallon, and gives 3 months credit for the remainder; required the balance due, and what cash would pay it, allowing the interest of it for the time at 6 per cent. per annum, as discount for prompt payment ?

Anf. the balance is 672 dols. 4 cts. 2 m. 6. C lells to D 28,674 feet of boards at 8 dols. 50 cts. per thousand, and takes in payment of cash, 4 barrels N. E. rum containing 128 gallons at 78 cents per gallon, I barrel of sugar weighing neat 2 cwt. 2 qrs. 4 lb. at 10 dollars per cwt. and the balance in coffee at 25 cts. per lb.; how much money and coffee is C to receive ?

Ans. 37 dols. 28 cts. 9 mills, and 1497 lb. of Coffee. 7. C has nutmegs worth 7s. 6d. per lb. in ready money, but in barier he will have 8s.; D has tobacco worth od. per lb.; -how much must he rate it per lb. that his profit may be equal to C's ?

Anf. 9 d.

9. A has


8. A has tea, which he barters with B at 10d.


'b. more than it cost him, against cambrick which stands B in 1os. per yard, but he puts it at 125. 6d. ; I would know the first cost of ihe iea.

Ans. 35. 4d. per

bushels of

which cost him

90 per

bushel ; this he barters with B at 95 cts. for wheat that stands B in 99 cents per bushel; how


bushels of wheat is he to receive in barter, and at what price is it to be rated, that their gains may be equal ?

Anf. 21820 bushels, at 1041 cts. per bushel. 10. A and B barter some goods—A put his ar 30,5 shillings, and gains 8 per cent. B puts his at 247's shillings, and gains at the fame rate ; what was the first cost of the goods ?

Anf. 28s, and 225, 60, A and B barter; A has cloth that cost 28d. B's cost him 22d. and he puts it at 25d. ; how high must A put his to gain 10 per cent more than B ?

Anf. 35d. C and D barter-C makes of 75. 6s. 8d. D makes of 75.

6d. 95. 3d. ; wo has lost most, and by how much per cent ?

Anf. Closes 1 per cent. more than D.


I 2.


Is a rule that discovers what is gained or lost in buying or selling goods, and instructs merchants and traders to raise or fall the price of their goods so as to gain or lose so much per cent, &c.


1. Bought a piece of broadcloth containing 53 yds. at 4 dols. 65 cts. per yd. and sold at 5 dols. per yd. what is the prosit on the whole ?

dols, cts.


4,65 yd.

yds. 935 53


If 1


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2. If 1 lb. of coffee cost 28 cts, and is sold for 31 cts. what is the profit on 3 bags, weighing 293 lbs. neat?

Ans. 8 dols. 79 cts. 3. Bought a piece of baize of 42 yds. for £ .4 14 6 and fold it at 25, 6d. per yd. what is the gain or loss on the whole piece ?

Ans. 1os. 6d. gain, 4. A merchant bought 59 cwt. 3 qr. 14 lb. of iron, at 112 dollars per ton, paid freight and charges, 24 dols. what is the gain or loss, if he sells the whole at 375. 4d. per cwt. ?

Anf. 13 dols. 26 cts. gain. 5. If a gallon of wine cost 6s. 8d. and is sold for 75. 2d. what is the gain per cent. ?

z ģ

6 8

If 6 8 6

Anf. 71 per cent. gain.


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When 20 per cent, loss is made on coffee, sold at 20 cents per lb. what was the first cost ?

Ans. 25 cents. 7 At 13į cents profit on the dollar, how much is it per cent, ? Ans. 131 per cent or 13


50 cts. per 1oo dols. 8. A trader sells his goods at 2 [d.* profit on the shilling, how nuch is it per cent, ?

Anl. 20, or £.20 16 8.




9. Which is the better bargain, in purchasing fish, 17 shillings per quintal, and 4 months credit, or 165. 8d. cash?

Ans. They are alike. Proof. The present worth of 175. found by discount, is equal to 165.8d. and 165. 8d. with 4 months interest will amount to 175.

A bought a piece of shalloon containing 34 yds, at 35. 4d. per yard, and fold it at 12į per cent. loss, how much did he sell it per yard ?


25. 11d. 11. Bought rum at 90 cts. per gallon, at what rate must it be sold to gain 20 per ?

Ans. 108 cts. A trader bought 1 hogshead of rum, at a certain proof, containing 115 gallons, at i doll. 10 cts. per gallon, how many gallons of water must he put into it to gain 5 dols. by felling it at 1 doll. per gallon?

Anf. 164 gallons. 13. Bought 4 hogsheads of rum, containing 450 gallons, at i dollar per gallon, and fold it at 1 doll. 20 cts. per gallon, and gave 3 months credit ; now allowing the leakage of the rum while in my possession to be 10 gallons, I would know the gain or loss, discount. ing for the present worth of the debt at 6

per cent. per annum.

Anf. 70 dols. 19 cts. gain. 14.

A vintner buys 596 gallons of wine, at 65. 3d. per gallon, in ready money, and fells it immediately at 6s. 9:4. per gallon, payable

3 months, how much is his gain or loss, fuppofing he allows the interest for the time at 6 per cent. per annum, as discount for present payment ?

Anf. £.11 17 8 gained. 15.

What would be the gain or loss on the aforesaid wine, supposing the discount for present payment to be made at 2 per cent. without any regard to time?

Anf. £.10 17 6į gain. 16. A merchant bought a parcel of cloth at the rate of 1 dollar for every 2 yards, of which he sold a certain quantity at the rate of 3 dollars for every 5 yards, and then found he had gained as much as 18 yards coft, how many yards did he fell?

Anf. 90 yards. 17. Bought rum at

at i dollar 25 cents per gallon, which not proving so good as I expected, I am content to lose 18 per cent. by it, how must I fell it per gallon ?

Ans. 1 dol. 2 cts. 18. H sells a quantity of corn at 1 dollar a bushel, and gains 20 per cent. some time after he sold of the same, to the amount of 37 dollars 50 cents, and gained 50 per cent. how many bushels were there in the last parcel, and at what rate did he fell it per bushel ?

Anf. 30 bushels, at i dol. 25 cts. per bushel.


19. A distiller is about purchasing 10000 gallons of molasses, which he can have at 48 cts. per gallon, in ready money, or 50 cts. with 2 months credit, it is required 10 know which is more advantageous to him, either to buy it on credit, or to borrow the money at 8 per cent. per annum to pay the cash price ?

Anf. He will gain 136 dols. by paying the cash. A tobacconist buys 4 hogiheads of tobacco weighing 38 cwt. 2 qrs. 8 lb. grofs, tare 94 ib. per hogshead, at 9 dollars per cwt. ready money, and sells it at 11 d. per lb. allowing tare at


lb. to receive two-thirds in cash, and for the remainder a note at go days credit ; his gain or loss is required, supposing the note is discounted at a bank where discount is made for 60 days ?

Anf. 283 dols. 43 cts. gain.


per cwt.


Is when the quantities and prices of several things are given, to find the mean price of the mixture compounded of those things.

RULE. As the sum of the quantities or whole composition is to their total value, so is any part of the composition to its mean price.


A grocer would mix

25 lb. of raisins, at 8 cents per lb. and 35 lb. at 10 cts. per lb. with 40 lb. at 12 cts. per lb.-what is one pound of this mixture worth?



8 35

350 40








1030 lb.

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Ans. 1o cts. 3 mills. A goldsmith mixes 8 lb. 51 oz. of gold, of 14 carats fine, with 12 lb. 8 oz. of 18 carats fine ; what is the fineness of this mixture ?

Ans. 1611' carats.


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