CASE 5. To find how a thing must be sold to gain or lose a given rate per cent. RULE. As 100 dollars is to the given price, so is 100 dollars, with the gain added or loss subtracted, to the gaining or losing price. The operation may be performed more concisely by taking parts of the given price, and adding or subtracting them, as the case requires. EXAMPLES. 1. A tobacconist bought a quantity of tobacco at 15cts. per lb.; at what rate per lb. must he sell it to gain $33.334cts. per ct.? $100.00 33.33 cts. 100: 15 :: 133.33 2. A merchant bought a piece of cloth at $2.50cts. a yd., which not proving so good as he expected, he is willing to lose $17 per cent. by the sale of it; how must he sell it by the yard? $cts. $100.00 2.50: 82.50 2.50 412500 16500 3. If I buy a piece of linen at 75cts. a yard, at what price must I sell it by the yard to gain $50 per cent.? Ans. $1.12 cts. 4. If I buy a yard of silk velvet for $4.623cts. and sell it at $100 per cent. advance, what is the amount? Ans. $9.25cts. 5. I have a quantity of cork, which is worth $4 a barrel, but I am willing to lose $10 per cent. in the sale of it; what is the selling price? Ans. $3.60cts. by the barrel. CASE 6. How to find the prime cost of any commodity, when there is a certain sum gained or lost per cent. RULE. As $100, with the gain per cent. added, or the loss per cent. subtracted, is to the selling price, so is $100 to the prime cost. 4,00)60,00.00 Ans. 15cts. per lb. 3. If I sell a piece of linen at $1.12дcts. a yard, and thereby gain $50 per cent., what was the prime cost? Ans. 75cts. 4. If I sell a yard of silk velvet for $9.25cts., and thereby gain $100 per cent., how much did it cost me? Ans. $4.623cts. 5. I have sold a parcel of corn at $3.60cts. per barrel, and thereby have lost $10 per cent.; what did it cost by the barrel? Ans. $4. CASE 7. Having the whole quantity and its prime cost given, to find the retailing price, when a certain sum is gained or lost thereon. RULE. As the whole quantity is to its prime cost, with the gain added or the loss subtracted, so is any part of the given quantity to the price for which it must be sold. 3. An ordinary keeper bought a pipe of French brandy at $1.371 cents a gallon; he paid $2.25cts. for the pipe, $3.50cts. for cartage, and 11 gallons leaked out on the way home; how must he sell it by the gallon to gain $22.25cts. on the whole quantity? Ans. $1.75 per gallon. 4. A grocer bought 40 gallons of molasses at 50 cents a gallon, and by some accident 6 gallons leaked out on the way home; what must the retailing price be, by the gallon, to gain $7.20cts. on the whole quantity? Ans. 80cts. per gallon. CASE 8. Having the whole quantity and its prime cost given-to find the retailing price of any part of it, when a certain rate per cent. is to be gained or lost thereon. RULE. 1. Say-As $100 is to the prime cost of the commodity, so is $100, with the gain per cent. added, or the loss per cent. subtracted, to the gaining or losing price of the whole quantity. The operation may be abbreviated by taking parts of the prime cost, and adding or subtracting them, as may be required. 2. Say-As the whole quantity is to its gaining or losing price, found as above directed, so is any part of the given quantity to the retailing price for which it must be sold. EXAMPLES. 1. A wholesale merchant bought 48 pieces of fine Irish linen, at $18 a piece, and sold 18 of the best pieces at $24 a piece, and 12 more of them at $21.75cts. a piece; at what rate by the piece must he sell the rest to gain $25 per cent. on the whole quantity? Pieces. p. c. $18 $25=1)864 the prime cost. 216 the interest at 25 p. c. 1080 the whole amount. 18 at $24,00cts.=432-price of 18 pieces) Subtract 30 and As 18. 693 from 48 and $1080. added. 3871 piece.. $21.50ct. Ans. yds. 115 yd. 3. If I buy 1200lbs. of sugar at $12 per cent., how must I sell it by the pound to gain $50 p. c. on the whole? Ans. 18c. per lb. 4. Bought 12 pieces of white cloth at $21.663cts. a piece, and paid $3.33 cts. per piece for dying it; how much must each piece be sold for to gain $20 p. c. on the whole ? Ans. $30. 5. If a bag of cotton, weigh 100:218.50:: 1.. $2.18 c. Ans. ing 8cwt. Oqrs. 20lbs. cost $45.55cts., how must it be sold by the lb. to lose $3 per cent. ? CASE 9. Ans. 4cts. 5m.+ If, when a thing is sold at a given price, there is so much gained or lost per cent.-to find how much would be gained or lost per cent. if it were sold at another given price. RULE. 1. Say-As the first given price is to $100, with the gain per cent. added, or the loss per cent. subtracted, so is the other given price to its gain or loss per cent. N. B. If the answer exceeds $100, the excess will be the gain per cent., but if it be less than $100, the deficiency will be the loss per ct. EXAMPLES. 4. If by selling cassimer at $2.25cts. a yd. I gain $12 per cent. what shall I gain or lose by selling 8 yds. of the same for $24? Ans. I shall gain $50 p. c. CASE 10. To find the gain per cent. per annum, when the commodity is bought for ready money and sold on credit. RULE. The operation in questions belonging to this case is performed by the Double Rule of Three Direct, as in the following example; or by two single statings. EXAMPLES. 1. A merchant bought a parcel of goods for $60 ready money, and sold them immediately on 4 months credit for $83.33 cts.; how much did he gain per cent. per annum ? mo. $ cts. 83.33 the credit price. 2. A tobacconist bought a quantity of tobacco for $120 in cash, which he sold immediately for $150 on a credit of 6 months; what did he gain per cent. per annum ? Ans. $50 p. c. p. a. CASE 11. When a given rate per cent. is lost by the sale of a single thing, or by any quantity of merchandise, and the seller ought to have gained another given rate per cent., to find how much the said thing, or quantity of merchandise, was sold under its just value. RULE. 1. As 100, with the loss per cent. subtracted from it, is to 100, with the gain per cent. added to it; so is the selling price of the thing, &c. to the sum for which it ought to have been sold. 2. Subtract the selling price of the thing from the sum for which it ought to have been sold, and the remainder will be the answer required. |