PROOF. Some of the debts are due before the equated time, and some after. The sum of the interests on the former, from their several maturities to the equated time, will be equal to the sum of the interests on the latter from the equated time to their severul maturities. When the account has both debit and credit items, equate each side of the account, and the interest on the two sides for the time between the respective average dates, and the equated time will be the same, or nearly the same (Art. 299, Note 2). 303. PROFIT AND LOSS. "PROFIT AND Loss," as a commercial term, signifies the gain or loss in business transactions. The rule may refer to the absolute gain or loss, or to the percentage of gain or loss, on the purchase price of the property considered. 304. PROBLEM 1. To find the absolute gain or loss. on a quantity of goods sold at retail, the purchase price of the whole quantity being given: RULE. Find the whole sum received for the goods, and the difference between this and the purchase price will be the gain or loss. bbl.; Ex. 1. Bought 16 bbl. of flour for $100 and sold it at $7 per did I gain or lose? How much, total and per bbl.? 2. Bought 24 bbl. of flour for $168 and sold of it at $6.75 and the remainder at $7.50 per bbl.; did I gain or loss? much? 3. Bought 3cwt. 2qr. 18 lb. of 83c. per lb.; did I gain or lose? How Ans. Gained $6. sugar for $36.80 and sold it al How much, total and per lb. 1 4. Bought 164yd. of broadcloth and 287yd. of cassimere for $1107; sold the broadcloth at $3 and the cassimere at $2.27 per yd.; did I gain or lose? How much? 305. PROBLEM 2. To find the per cent. of gain or loss when the cost and selling price are given : 302. Proof of rule for equation of payments? 303. What is Profit and Loss? To what may it refer? 304. Rule for finding absolute gain or loss? Ex. 1. Bought 4 bbl. of flour for $32 and sold it at $9.50 per How much per cent.? bbl.; did I gain or lose? $38.00, whole sum rec'd. $32. RULE. Having found the total gain or loss by Problem 1, make a common fraction by writing the gain or loss for the numerator and the cost of the article for the denominator, and then reduce this fraction to a decimal. 2. Bought 50lb. of wool for $20 and sold it at 34c. per lb.; did I gain or lose? How much per cent.? Ans. Lost 15 per cent. 3. Bought a case of boots at $4 per pair and sold them at $5; what per cent. was gained? 4. Bought boots at $5 per pair and sold them at $4; what per cent. was lost? 5. Bought goods for $2000, and, in one year, sold the same for $2155, out of which paid $95 for storage, etc.; how much per cent. on the first cost was lost? 306. PROBLEM 3. To find the selling price, the cost and gain or loss per cent. being given. Ex. 1. Bought goods for $400; how must the same be sold so as to gain 25 per cent. 305. Rule for finding the per cent. of gain or loss? 2. Bought a horse for $150, but it being injured, I am willing to lose 6 per cent.; for what shall I sell him? RULE. Multiply the purchase price by the per cent. to be gained or lost, written decimally, and add the product to, or subtract it from, the purchase price. 3. Bought a farm for $4848; for what shall I sell the same to gain 5 per cent.? Ans. $5090.40. 4. Bought 3cwt. of sugar at 12c.; how shall the same be sold per lb. so as to gain 10 per cent.? 5. Bought a house for $3500, expended $750 in repairing it, and then sold it so as to lose 15 per cent. on the whole cost; what did I receive for it? 307. PROBLEM 4. To find the first cost of an article, the selling price and gain or loss per cent. being given. Ex. 1. Sold wheat at $1.50 per bushel, and thereby gained 25 per cent. on the cost; what was the purchase price? 2. Sold apples at $1.80 per barrel, and thereby lost 10 per cent. on the cost; what was the cost? 100- of $1.80 $2, Ans. The cost was 10: = of the selling price, .. the cost was of $1.80 $2. Hence, RULE. Make a fraction by writing 100 for a numerator, and 100+ the gain per cent., or 100— the loss per cent., for a denominator; then multiply the selling price by this fraction. 306. Rule for finding the selling price, the cost and gain or loss per cent. being given? 307. Rule for finding the first cost, the selling price and gain or loss per cent. being given? 3. Sold 6 yards of cloth for $26.88, and gained 12 per cent on the cost; what was the purchase price per yard? Ans. $4. 4. Sold 10 shares of the Fitchburg R. R. Stock for $1090. gaining 9 per cent. on the cost; what did I pay per share? 5. By selling 25 lb. of sugar for $2, I lose 20 per cent. on the cost; what was the cost per lb. ? 308. PROBLEM 5. The selling price of goods, and the gain or loss per cent. being given, to find what would be gained or lost per cent. if sold at some other price. Ex. 1. Sold a pair of oxen for $175 and gained 5 per cent. ; what per cent. should I have gained if I had sold them for $200? The proposed price is 49% of the actual selling price, but the actual selling price is 105 per cent. of of 105 per cent. 120 per cent.. 100 per cent. = 20 the cost,.. the proposed price is cent. of the cost; hence 120 per per cent. would be the gain per cent. if the oxen were sold for $200. 2. Sold a farm for $5000, and thereby made 25 per cent.: should I have gained or lost, and how much per cent., if I had sold it for $3500? 500 3688=38=1o; fo of 12587; 100-87}=12}= loss per cent., Ans. The proposed price is found to be 87 per cent. of the cost, ..there would be a loss of 123 per cent. if the farm were sold for $3500. RULE. Make a fraction by writing the proposed price for the numerator, and the actual price for the denominator, then multiply the per cent. at which the article is sold by this fraction, and the product will be the per cent. at the proposed price. The difference between the product and 100 is the gain or loss per cent. at the proposed price. 308. Rule for finding loss or gain per cent. when goods are sold at a proposeo price? 3. Sold flour at $7 per bbl. and thereby gained 12 per cent. ; what per cent. should I have gained if I had sold it at $7.25? Ans. 16 per cent. 4. Sold beef at $6 per cwt., and thereby lost 4 per cent.; should I have gained or lost, and how much per cent., had I sold it at $6.50? 5. Sold a watch for $21, and gained 5 per cent. on the cost; had I sold it for $18 should I have gained or lost, and how nuch per cent. ? 309. PROBLEM 6. To mark goods so that the merchant may fall a certain per cent. on the marked price and yet sell the goods at cost, or at a certain per cent. above or below cost. (a) To sell at cost. Ex. 1. How shall I mark a coat that cost me $18 so that I may fall 10 per cent. from the marked price and yet sell the coat at cost? 100 = 10; 10 of $18 $20, Ans. = Since I am to fall 10 per cent., it follows that the cost, $18, is only of the marked price, and if $18 is then will be of $18 $2, and 18 will be 10 times $2= $20 ; i. e. the marked price will be 0 of $18 = $20, Ans. PROOF. 10 per cent. of $20 = $2, which taken from $20 leaves $18, the cost. Hence, RULE. Make a fraction by writing 100 for the numerator, and 100 diminished by the per cent. to be abated for the denominator; multiply the cost by this fraction, and the product will be the marked price. 2. Bought a case of watches at $23.50; at what price shall I mark them to enable me to abate 6 per cent., and yet sell them at cost? Ans. $25. (b) To sell at a certain per cent. above or below cost: 309. Rule for marking goods so as to fall a certain per cent. and yet sell at Cost? To sell at a given per cent. above or below cost? |