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Or, make the gain or loss the numerator, and the prime cost the denominator of a common fraction, which, reduced to a decimal, will give the gain or loss per cent.
1. If I buy cloth at $0,80 per yard, and sell it again at $1,00 per yard, what do I gain per cent ?
Sold for $1,00
Or thus :
Prime cost 80 As 80 : 20 :: 100
to a Decimal Fraction, by 100
annexing ciphers to the nuAns.
merator and dividing by the 80)2000(25 per cent.
denominator, (see Reduction 160
of decimals,) gives ,25, or 400
25 per cent, the same as be400
fore. 2. A merchant bought goods to the amount of $845,36, and sold the same for $951,03 ; what did he gain per cent on the purchase price ? $ cts.
$ cts. As 845,36 : 105,67:: 100,00 : 12,50 or 127 per cent. Ans.
Sold for $951,03 Prime cost 845, 36 Or thus, 19597=,125=12) per ct. Whole gain $105,67
3. If I buy a hundred weight of sugar for $8,00, and sell it again at 91 cents per pound; what do I gain per cent?
Ans. 291 per cent. 4. A grocer bought a hogshead of rum for $84, and by accident so many gallons leaked out that he sold the remainder for $67,20; what did he lose per cent ?
Ans. ,20, or 20 per cent, 5. If I buy cloth at $2,00 per yard, and sell it again for $2,50 per yard, what should I gain by laying out 100 dollars ?
Ans. $25. 6. A merchant bought indigo at $1,20 per pound, and sold it again for $100,80 per hundred weight; what was lost per cent. ?
Ans. 25 per cent.
7. At 25 cents profit on a dollar, how much per cent. ? Ans. 25 per cent. At ,30 ? At ,12} ? At ,15? At ,1841 ? At ,61 ? At ,0575, or ,05% ? At ,215, or, ,211 ? &c.
Note. When goods are bought or sold on credit, we must find, by discount, the present worth of their price in order to calculate the true gain or loss.
8. Bought goods to the amount of $442, on 8 months credit, and sold the same again for $478,125, ready money; what did I gain per cent, discounting on the purchase price at 6 per cent ?
Thus, the amount of 1 dol Sold for $478,125 lar at 6 per cent, for 8 mos. Prime cost 425,000 1,04 ) 4 42,00 ( $ 4 2 5.
53,125 Therefore the present worth Then, gain 53,125
reduced of the purchase price is 425 Prime cost 425,000 dollars.
to a decimal fraction= ,125
=121 per cent. Or, As 425 : 53,125 :: 100 : 12,50, or 127 per cent. 9. A merchant bought broadcloth at $4 per yard, ready money, and sold the same again at $4,251 on 18 months credit ; did he gain or lose, and what per cent, allowing 6 per cent discount on the selling price ?
Ans. He lost ,025=2 per cent. 4. The price sold for, and gain or loss per cent given, to find the cost of any
As $100, with the gain per cent added, or loss per cent subtracted, is to the price, so is 100 to the prime cost.
1. Sold a hogshead of molasses at $0,30 per gallon, and thereby gained 25 per cent; what did the hogshead cost me ?
then, 1hhd.=63 gals.
Ans. $15,12 cost of
2. Sold goods for $951,03, by which I gained 121, or $12,50, per cent; what did the goods cost me ?
Ans. $845,36. 3. A merchant sold indigo at $100,80 per cwt., and thereby lost 25 per cent; what did it cost him per lb.? As 75 : 100,80 :: 100 : $134,40 cost per cwt.
Then $134,40:-112=$1,20 Ans. 4. Sold 350bbls. of flour for $2616,25 by which I gained at the rate of 15 per cent; what did it cost per barrel ?
Ans. $6,-50 cents.
Questions. What is Barter ?
much per cent ? What is the Rule ?
III. Having the prices at which goods What is Loss and Gain !
are bought and sold, how do you find What does it instruct merchants and the rate per cent, of gain or loss? traders to do?
IV. Having the price sold for, and II. How do you find how a commodi- gain or loss per cent given, how do you ty must be sold so as to gain or lose so find the cost of any article ?
is a rule by which persons trading in partnership adjust their accounts so that each may have his share of the gain, or sustain his share of the loss, in proportion to his share of the stock. Also, by this rule a bankrupt's estate may be divided among his creditors.
SINGLE FELLOWSHIP İs when the several shares of stock are continued in trade an equal term of time.
As the whole stock, is to the whole gain or loss, so is each man's share of the stock, to his share of the gain or loss.
1. Three men, A, B and C, traded in company ; A put in $200, B $400, and C $600 ; they gained $348: what was each man's share of the gain ?
As gain B's gain. C's gain.
A's stock $200
1200 : 348 :: 200: 58 C's stock 600
1200 : 348 ::
: : 400 : 116
1200 : 348 :: 600 : 174 Whole stock 1200
In this example, the whole stock being $1200, A's stock $200=ă of the whole, thus 20%=; B's stock $400=} of the whole, and C's stock $600=1 of the whole ; then
of $348=$58, A's part : } of $348=$116, B’s part, and of $348=$174, C's part, as before. Or, we may first find the gain on $1
Thus, 1200 : 348::1:0,29; then A's stock 200 X,29 =$58, A's gain ; B's stock $400 x ,29=$116, B's gain ; and C's, stock $600 X,29=$174, C's gain.
Proof. It is evident that if the several shares of gain oi loss, added together, be equal to the whole gain or loss, the work is right. Thus, $58+$116+$174=$348, the whole gain.
2. Three merchants, E, F and G, gained by trading in company $300 ; E's stock was $300, F's $600, and G's $900; what was the gain on $1, and how much was each man's share of the gain ? Ans. The gain on $1 is $£; then, £ of $300=$50, E's part; d of $600=$100, F's part, and of $900=$150, G's part of the gain.
3. A and B trade in company; A puts in $1250, and B $850. They find they have gained $700; what is the gain on $1, and what is each one's share of the gain?
Ans. $}. and A's $416,666+ B's $283,333+ 4. Four men, A B C and D, shipped 1150 barrels of flour; A put on board 150 barrels, B 200 barrels, C 500 barrels, and D 300 barrels ; in a storm the seamen threwo overboard 325 barrels; what number of barrels did each lose ? Ans. A lost 4216, B 5628, C 14116, D 8426
5. Two men, C and D, join their stock and trade in company ; C put in $650 and D $550. They gained $300 what is each man's share of the gain ?
Ans. C's $162,50, D's $137,50. 6. A bankrupt is indebted to A $375, to B $125,50, to C $110, to D $695,50, and to E $294, and his whole es:
tate amounts to only $1200, which he gives up to his creditors ; what must each receive in proportion to his claim?
Ans. A $281,25, B $94,121, C $82,50, D $521,62}, and E $220,50.
7. Divide $1850 among 5 persons so that their shares shall be to each other as 1, 2, 3, 4, 5.
Ans. $123,33}, $246,66%, $370, $493,331, $616,66 8. Two partners, C and D, trade with a capital of $3500 ; C put in $1950 and
By misfortune they lose $700; what was D's stock, and how much is each one's share of the loss ?
Ans. D's stock $1550, and C's loss $390, D's $310. 9. Two merchants, E and F, traded in company and gained $875. E put in $1150, F put in so much that his share of the gain was $300; what was F's stock, and what was E's share of the gain ?
Ans. F's stock $600. E's gain $575. 10. Two men, B and C, traded in company with a joint capital of $1350. They gained $450, of which B took $300, and C the remainder; what was each one's stock ?
Ans. B's stock $900. C's $4504 11. C, D and E drew a prize of $2500, of which C is to have 5 shares, D 8 shares and E 7 shares; what is each man's part ?
Ans. C $625, D $1000, E $875:
COMPOUND FELLOWSHIP. When the several stocks, &c. of the partners are continued in trade an unequal term of time, it is called Compound, or Double Fellowship.
Multiply each man's stock, or share, by the time it was continued in trade.
Then, as the sum of the products, is to the whole gain or loss, so is each man's product, to his share of the gain or loss.
1. Two men hired a pasture for $24 ; A put in 6 cows for 4 months, and B 12 cows for 3 months ; what ought each to pay ?