must I sell the remainder per gallon, to gain $25 on the whole ? Ans. $0, 91c. 0m.+ 2. To know how a commodity must be sold, to gain or lose so much per cent. RULE. Multiply the given sum by the rate per cent, written as a decimal fraction, and to the product add the given sum for the gain per cent, but subtract for the loss per cent. EXAMPLES. 1. If I buy wine at $1,50 per gallon, how must I sell it› per gallon, to gain 25 per cent ? $1,50 ,25 750 300 ,3750 + 1,50 Answer $1,8750=$1,874. 2. Bought broadcloth at $3,75 per yard, but being damaged I am willing to sell it so as to lose 12 per cent; what must I sell it at per yard? Ans. $3,30. 3. Bought tea at 54 cents per pound; how must I sell it per pound so as to gain 12 per cent ? Ans. $0,60,7 m. 4. Bought a hogshead of sugar weighing 8cwt. at $7 50cts. per cwt.; how much must I sell the whole for, to gain 30 per cent? Ans. $82, 87c. 5m. 5. If 350bbls. of flour cost $2275, what must it be sold per barrel to gain 15 per cent? Ans. $7,473. 6. Bought 120 gallons of wine at $1,08 per gallon, but by accident 10 gallons leaked out; at what rate must I sell the remainder per gallon, to gain upon the whole prime cost at the rate of 9 per cent? Ans. $1, 28c. 42m.+ 3. The prices at which goods are bought and sold being given, to find the rate per cent of gain or loss. RULE. First see what the gain or loss is by subtraction; then as the price it cost is to the gain or loss, so is $100 to the gain or loss per cent. 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. 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 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 each man's share of the stock, to his share of the gain or loss. EXAMPLES. 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? B's stock $400= of the whole; then $116, B's part, and In this example, the whole stock being $1200, A's stock $200 of the whole, thus 2000; of the whole, and C's stock $600 of $348=$58, A's part: of $348 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 ×,29 =$58, A's gain; B's stock $400 ×,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 or 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; 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 threw overboard 325 barrels; what number of barrels did each lose ? Ans. A lost 4218, B 5624, C 14114, D 8438. 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 $94,124, C $87,50, 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, $616,663. 8. Two partners, C and D, trade with a capital of $3500; C put in $1950 and D the rest. 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 $450, 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. RULE. 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. EXAMPLES. 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 Six cows for 4 months are the same as 24 cows for one month, for 6×4=24; and 12 cows for 3 months are the same as 36 cows for 1 month, for 12×3=36. Hence the question is the same as if A had put in 24 cows for 1 month, and B 36 cows for 1 month. 6×4=24 12 X3=36 Sum of the products 60 60: 24: 24: 9,60 A's. 60: 24: 36: 14,40 B's. 2. Three merchants enter into a partnership; B puts in $300 for 4 months, C $150 for 5 months, and D $200 for 8 months. They gain $400; what is each man's share? B's. Ans. C's. D's. 3. Three persons hire a pasture in company for which they pay $96. C put in 100 sheep for 2 months, D put in 300 sheep for 5 months, and E 450 sheep for 4 months; what must each pay? C. Ans. D. E. 4. Two men, B and C, gained by trading $250. B's stock was $350 for 8 months, C's $640 for 5 months; required each man's share of the gain? Ans. SB's share { 5. Three persons received $665 interest. B's principal was $4000 for 12 months, C's $3000 for 15 months, and D's $5000 for 8 months; what is each man's share? Ans. B's $240. C's $225. D's $200. Bat 6. B and C enter into partnership for 16 months. first put in $500 and at the end of 12 months he took out $300; C at first put in $300, and at the end of eight months he put in $500 more. They gained $525; required each man's particular share of the gain? Ans. B's $228,841. {C's $296,15 7. A commenced trade on the first of January with $850, and on the first of March he took in B with $560, and on the first of May he took in C with $650; at the end of the |