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CASE V.

When a certain loss per cent. has to be sustained on the first

cost to find the retail price. RULE.—Multiply the first cost by the given per centage, and divide by 100 for the amount of loss sustained, the amount subtracted from the first cost will give the result; or, as 100 : 84 : : 840 : $705.60 as required.

Suppose I purchase a lot of goods for $840, at auction, and owing to their being damaged, have to sustain a loss of 16 per cent below the first cost, how much will they be sold for?

Ans. $705.60.

CASE VI.

To find the profit per pound, per yard, &c. when the first

cost and sales of a certain number of yards, pounds, cwts. &c., are given.

RULE.—Find the whole gain, and divide it by the number of yards, pounds, or cwts., &c.

Ex. 5. Bought a chest of tea, containing 340 lbs. for $289, and sold it for $408, what was the profit on each pound?

Ans. 35 cts.

per

lb.

CASE VIL

When there is a loss per cent. sustained by the sale and the

first cost is required. RULE.—Subtract the rate per cent. from 100, then say as 100 less the rate per cent. is to 100, so is the amount of the sale to the first cost.

Ex. 6. Sold a lot of dry goods for $540, and had to :sustain a loss of 10 per cent., what did they cost me?

Ans. $600.

CASE VIII.

When you purchase goods and wish to gain a certain sum

on the whole purchase, so as to be able to sell them at a certain per centage.

Rule.-Add the sum you wish to gain to the amount of the purchase, then divide that amount by the number of yards, pounds, and cwts. for the answer required.

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Ex. 7. A merchant tailor bought 100 yards of cloth for $256, how much must he sell it per yard to gain $44 on the whole?

Ans. $3 per yard. 1. Bought knives at 20 cents each, and sold them for 25 cents, how much is gained per cent.? Ans. 25 pr. ct.

2. Suppose I buy cloth for $5 per yard, and sell it for $6, how much is the gain per cent.? Ans. 20

pr.

ct. 3. A store-keeper sold 100 yards of silk at $1.50 per yard, which cost him $1.25 per yard, how much did he gain by the sale?

Ans. $20 on the whole. 4. George Brown, merchant, Baltimore, purchased the following bill of goods, viz: 10 pieces domestic muslin, each 29 yards at 10 cents per yard, and 16 pieces calico, each 271 yards at 20 cents per yard, how much is the retail price per yard on the muslin and calico, and the whole gain allowing a gain of 25 per cent for the sale of the goods?

A. The retail price of the muslin is 124 cts. per yard, and the calico 25 cts. per yard—whole gain $29.25.

5. Sold a yard of cloth for $1.55, by which was gained at the rate of 15 per cent., what would have been the gain per cent. if it was sold for $1.72? Ans. $27.61 +

6. A. sold cloth at 84 cents per yard, and gained 10 per cent., should it be sold for $1.20, what would be the gain?

Ans. $574 7. Richard Rich purchased of D, Draper, 18 pieces of broad cloth at $8 per piece, of which he sold 10 at $9.60 per piece, 5 pieces at $9 per piece, and the balance he wishes to dispose of, on terms to gain 12 per cent. on the whole, at what rate must the remainder be sold at per yard?

Ans. $6.76. 8. Sold a lot of dry goods for $5.50, and gained 10 per cent., how much was the first cost? Ans. $5.00.

9. Bought at auction a hhd. of molasses for $50, and having found, that there was a leakage of 5 gallons, I sold it immediately, at 10 per cent. loss, how much did I receive for it?

Ans. $45. 10. Bought rum at $1.25 per gallon, and by accident, so much leaked out, that I am willing to lose 20 per cent., at what price must I sell it per gallon? Ans. $1.00.

11. Bought for cash $1740 worth of hardware, and sold the lot for $2000 on a credit of 3 months, what is the gain per cent. per annum?

Ans. 5987. 12. Bought goods to the amount of $1400 cash, and sold them at 4 months credit for $1600, what is the gain per cent. per annum?

Ans. 424c. 13. Bought 3000 gallons of molasses at a credit of 2 months, for 30 cents per gallon, and sold it again at 35 cents per gallon, on a credit of 3 months, required the gain per cent?

Ans. 644c. EXERCISE QUESTIONS. 1. I purchased 100 boxes of prunes at $2.10 each, and by selling them at $3.50 per cwt. the gain is 25 per cent, the weight of each box is required? Ans. 84 lbs.

2. If I sell linen for 75 cents per yard, and gain 121 per cent., what would the prime cost of 30 pieces, each 33į yards, stand me in the whole?

Ans. $670. 3. Bought a quantity of leather at 22 cents per lb., how should I sell it to gain 10 per cent profit?

Ans. 24c. 2m. 4. Admitting that a yard of muslin was sold for 32 cents, which cost 37į cents, what is the loss

per

cent.?

Ans. 143. 5. Sold 500 penknives at 17 cents a piece, and by so doing lost 9 per cent, what is the loss on the whole?

Ans. $8.40 + 6. Bought a hhd. of wine for a certain sum, but 15 gals. having leaked out, I sell the remainder for $2.21.63 per gal., and thereby lose 5 per cent. on the cost, what was the cost?

Ans. $112.

COMPANY ACCOUNTS.

Partnership or Company transactions, in an Arithmetical sense) is a Rule by which merchants in partnership adjust their accounts in proportion to stock and time.

CASE I.

The gain or loss, with the several sums at hazard given, to find each partners share.

Rule.—Multiply the whole gain by each man's fraction part of the stock—or, agreeably to the Old Method; say, as the whole stock is to the whole gain, so is each man's share of the stock, to each man's share of the gain.

1. Three men, A, B and C, entered into partnership for 2 years, with a capital of $6000, A put in $2500, B $1500 and C $2000, they gain $1080; required, each man's share of the gain?

Solution. As the whole stock in trade is $6000, A's share would be 50%

B's 150%

= 1, and C's 4888 = { Again, it of $1080 = $450, A's share, and of $1080 $270, B's share, and C's į of $1080 $360. Proof.-A's share of gain is $450.00 · B's

do. do. 270.00 C's do. do. 360.00

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Whole gain $1080.00 2. A and B enter into partnership; A has in goods at cash price $3400 worth, and cash $1300: B puts in $1200, and agrees to pay for A, a debt of $1100, for which A gives B a title to that amount of his goods. Now suppose A, ágrees to take B's note for what B's funds want, of being equal to his own, (say the note bears legal interest, and is not reckoned in the partnership,)

what amount should the note be drawn for, to make them equal? Solution.-Amount of A's goods $3400.00

Cash

1300.00

66

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$1300.00 difference. A's stock in trade then would be $3600-650 $2950. A and B's equivalent composed of

Goods $1100.00
Cash

1200.00
Note

650 00

$2950.00 proof.

CASE II.

Apportioning the effects of a Bankrupt. In apportioning the effects of a Bankrupt amongst his creditors, it is more convenient to find the proportion for one dollar, &c. Which will be a constant multiplier for each debt.

1. A Bankrupt owes $5000, his effects sold at auction, amounting to $4000, what will his creditors receive on a dollar?

Ans. 80 cents. 2. A merchant having sustained many losses is obliged to become a bankrupt, his effects are valued at $1728, with which he can pay only 15 cents on the dollar, what did he owe?

Ans. $11520. 3. A, B and C, freighted a ship with 108 tuns of wine, of which A had 48 tuns, B 36, and C 24, but by reason of stormy weather were obliged to cast 45 tuns overboard; how much must each man sustain of the loss?

Ans. A 20 tuns, B 15 and C 10.

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