620lb. of sugar, at barter price, will pay for the 200yd. of linen, at the bartering price. Value of the 200yd. of linen at cash price $50.00 Do. of the 620lb. of sugar at Ans. B gets the best bargain, by 40 cents. LOSS AND GAIN, Is a method of computing the profit or loss on the purchase and sale of goods. The rules for making calculations of this kind, are only particular applications of the Rule of Three. CASE I. When the buying and selling prices are given, to find what is gained or lost by selling. RULE. First, find the value of the commodity at the price it cost; then find its value at the price sold at; and the difference between these will be the gain or loss. Or, as 1 yard, or 1lb. &c. : is to the given quantity :: so is the gain or loss on lyd. or llb. &c. to the whole gain or loss. EXAMPLES. 1. A merchant sold 100 yards of cloth at ID. 50c. a yard, which cost him ID. 25c. a yard: how much did he gain by the sale? $1.50×100 $150 Selling price. Ans. $25 Whole gain. Or, by the second method thus: $1.50-1.25-$.25, the gain per yard. Then, as lyd. : 100yd. :: $.25 : $25, Ans. 2. Bought 25 yards of broadcloth at 5 D. a yard, and sold the same at 5 D. 75 cts. a yard: how much did I gain by the bargain? Ans. $18.75 3. Bought a piece of baize containing 42 yards, for 11D. Slc., and sold it at 31 cents a yard: what was the gain or loss on the whole piece? Ans. $1.21 gain. 4. Bought 11cwt. of sugar at 37. 8d. per cwt., but could not sell the same for more than 27. 16s. per cwt.: how much did I lose on the whole? Ans. 27. 11s. 4d. 5. Bought a pipe of wine at $1.75 per gallon; paid the freight $3.46; paid for carting the same $2.52; and by accident 46 gallons leaked out: at what rate must I sell the remainder per gallon to gain on the whole $6 ? Ans. $2.906. Note. When goods are bought or sold on credit, you must calculate, (by Discount,) the present worth of their price, in order to find the truc gain or loss. 6. Bought 204 yards of broadcloth, at $2.25 a yard, and sold the whole for $510, on 4 months credit: what did I gain or lose, allowing discount at 6 per cent. a year? $ $ $ $ As 102 510 :: 100: 500 Present worth. $ 41 Gain, Ans. 7. Bought 412 bushels of rye for $206, and sold the same at 60 cents a bushel, on 6 months credit: what did I gain, allowing discount at 6 per cent. per annum? Ans. $34. CASE II. To find what is gained or lost per cent. RULE. As the prime cost is to $100 or L100 :: so is the gain or loss on the cost to the gain or loss per cent. EXAMPLES. 1. If I buy cloth at 88 cents per yard, and sell it at 1D. 10c. per yard: what do I gain per cent., or in laying out $100? Then, as $.88 : $100 :: $.22 : $25 Ans. R 2. If tea be bought for 874 cents per lb. and sold at ID. 12c. per lb., what is the gain per cent.? Ans. $28.571+ 3. Bought a pipe of wine for $150, and sold the same at $1.25 per gallon: did I gain or lose by the sale, and how much per cent.? Ans. Gained 5 per cent. 4. If I buy cloth at 6s. 8d. per yard, and sell the same at 7s. 4d. per yard, what do I gain per cent.? Ans. L 10. 5. Bought Wheewell's Mechanics and Dynamics for $7.25, Laplace's System of the World for $5.75, Bonnycastle's Algebra for $6.375, and Simpson's Fluxions for $5.75: sold all those books for $30; how much is the gain per cent? Ans. $19.402+ 6. If I buy cloth at $4.16 per yard, on 8 months credit, and sell it at $3.90 per yard, ready money, what do I lose per cent., allowing 6 per cent. discount on the purchase price? Ans. $2.50 CASE III. To know how a commodity must be sold to gain or lose a certain rate per cent. RULE. As $100 is to $100 with the gain per cent. added, or loss per cent. subtracted :: so is the purchase price : to the selling price. EXAMPLES. 1. How must tea, which cost 92 cents per lb., be sold per lb. to gain 25 per cent.? $100 $125 (=100+25) :: $.92 $1.15 Ans. 2. How must pork, which cost 4 cents per lb., be sold to gain 20 per cent.? Ans. At 5c. 4m. per lb. 3. Bought cloth at 50 cents per yard, which not proving as good as I expected, I am willing to lose 10 per cent.: at what price per yard must I sell it? Ans. 45 cents. 4. Bought goods to the amount of $875, and by selling the same gained 25 per cent.: what did I get for the goods? Ans. $1093.75 CASE IV. When the gain or loss per cent. and the selling price are given, to find the first cost. As $100 increased by the loss per cent. to the prime cost. RULE. by the gain per cent. or diminished is to $100 so is the selling price : :: Note.-Cases III. and IV. prove each other. EXAMPLES. 1. If 25 per cent. be gained by selling tea at $1.15 per lb., what was the prime cost per lb.? As $125 $100 :: $1.15: $.92 Ans. 2. If 20 per cent. be gained by selling pork at 5c. 4m. per lb., what was the prime cost per lb.? Ans. 4 cents. 3. If 12 per cent. be lost by selling 120 yards of broadcloth for $422.40, what was the prime cost per yard? CASE V. Ans. $4. If by goods sold at a given rate there is so much gained or lost per cent., to find what would be gained or lost per cent. if sold at another rate. RULE. As the first price is to the second :: so is $100 increased by the gain per cent. or diminished by the loss per cent. to a fourth number. If this fourth number exceeds $100, the excess is the required gain per cent.; but if it be less than 100, that deficiency is the loss per cent. EXAMPLES. 1. Sold a quantity of wheat at $1.50 per bushel, and thereby gained 25 per cent.: what should I have gained or lost per cent. if I had sold the wheat at $1.08 per bushel? $1.50 $1.08 :: 125: 90. Then 100-90-10. Ans. I should have lost 10 per cent. 2. If I sell sugar at $8 per cwt., and thereby gain 12 per cent.; what should I gain per cent. by selling it at $9 per ewt.? Ans. 26 per cent. 3. If by selling coffee at 24 cents per lb. I gain 20 per cent., what should I gain or lose per cent. by selling it at 20 cents per lb.? Ans. Nothing. FELLOWSHIP, Is a rule, by which any sum or quantity may be divided into any number of parts, which shall be in any given proportion to one another. By this rule are adjusted the gains or loss or charges of partners in company; or the effects of bankrupts, or legacies in case of a deficiency of assets or effects, &c. Fellowship is either Single or Double. It isSingle, orSimple, when the shares or portions are to be proportional each to one single given number only; as when the stocks of partners are all employed for the same time, or when they are considered without regard to time: And Double, or Compound, when each portion is to be proportional to two or more numbers; as when the stocks of partners are employed for different times. SINGLE, OR SIMPLE FELLOWSHIP. GENERAL RULE. Add together the numbers which denote the proportion of the shares. Then say, As the sum of the said proportional numbers: is to each particular proportional number :: so is the whole sum to be parted or divided to the share or part corresponding to each respective proportional number. Or, As the sum of the stocks of all the partners is to each partner's particular stock :: so is the whole gain or loss to each partner's share of the said gain or loss. Or, if the given sums be federal money, you may divide the whole gain or loss by the whole stock, as in Division of Decimals, and the quotient will be the gain or loss on the dollar; which being multiplied into each partner's share of the stock, will give the required shares of the partners. To prove the work: Add all the shares or parts together, and the sum will be equal to the whole stock, or number to be shared, if the work be right. EXAMPLES. 1. To divide the number 240 into three such parts, as shall be in proportion to each other as the three numbers 1, 2 and 3. |