classes; those not involving time and those involving time The following are the most important of these applications 1ST CLASS. 1. Profit and Loss. 2. Commission. 3. Stocks, Dividends, etc. 4 Premium and Discount. 5. Brokerage. 6. Stock Investments. 7. Taxes. 8. Duties or Customs. 2D CLASS. 1. Simple Interest. 2. Partial Payments. 3. True Discount. 4. Discounting and Banking. 5. Exchange. 6. Compound Interest. 7. Annuities. 8. Insurance. NOTES.-1. In the different cases of the application of percentage, care should be taken to see clearly the base upon which the percentage is reck oned. 2. A percentage deducted from the price of goods is called a Discount, and is treated under Profit and Loss. Successive Discounts called "Trade Discounts" are often taken off, as "10 and 5 per cent. off," meaning 10 per cent. off and 5 per cent. off of the remainder. PROFIT AND LOSS. 391. Profit and Loss are terms which denote the gain or loss in business transactions. 392. The Quantities considered are as follows: 1. The Cost, which is the base. 2. The Rate of profit or loss. 3. The Profit or Loss, which is the percentage. 4. The Selling Price, which is the amount or difference. NOTE. In marking goods it is customary to take one or more words or a phrase or sentence, consisting of ten different letters, and let each letter in succession represent one of the Arabic figures. The prices marked thus can only be read by those who have the key. CASE I. 393. Given, the cost and rate of profit or loss, to find the profit or loss, or the selling price. MENTAL EXERCISES. 1. A lady paid $10 for a shawl, and sold it at a loss of 20%・ re quired the loss. SOLUTION.-At a loss of 20 per cent., %, or of the cost equals the loss. of $10 is $2. Therefore, etc. 2. A grocer bought tea at 80 cents a pound, and sold it so as to gain 25%; what was the gain? 3. Mr. Wilson paid $150 for a horse, and sold it at 163% advance ; what was his gain? 4. A dry goods merchant bought calico at 8 cents a yard, and sold it at a gain of 12%; what was the selling price? 5. A farmer paid $48 for a cow; for what must he sell her to lose 6% by the transaction? 6. A furniture dealer bought a second hand sofa for $40, and hav ing spent 10% on repairs, sold it at a gain of 25% on its whole cost; for what did he sell it? WRITTEN EXERCISES. 1. A man bought a horse for $250, and sold it so as to gain 20%; what did he gain? SOLUTION.-If the horse was bought for $250 and sold at a gain of 20%, the gain was .20 times $250, which is $50. OPERATION. $250 .20 $50.00 Rule I.-Multiply the cost by the rate, to find the profit or loss. Rule II. Multiply the cost by 1 plus the rate of profit, or by 1 minus the rate of loss, to find the selling price. 2. I bought $640 worth of English prints and sold them at a gain of 12%; what was the gain? Ans. $76.80. $3680, at a loss 3. Mr. Morgan sold his house, which cost of 5%; what did he receive for it? Ans. $3496. 4. A man weighing 162 lb., loses 33% of his weight in a month; how much did he then weigh? 5. A dealer bought coal at $3.75 a ton, 20% advance; what was his price? 6. I sold a lot of envelopes marked $7.50 10% off; what was the price received? Ans. 108 lb. which he sells at Ans. $4.50. 7. Some valentines marked $15 were sold at 25, 20, and 10% off; what was the selling price? Ans. $8.10. 8. I retail flour which cost $6.50 a barrel, at 15% advance; Ans. $.04-. at what price per pound do I sell it? 9. An agent gets pianos at 40% off, and sells at a gain of 25%; what does he get for a $650 piano? Ans. $487.50. 10. Mr. Bowman is obliged to mark down old-fashioned goods 20%; what does he deduct from those marked 61, 124, 18, 25%, and 40g? 11. What deduction from price is 10 and 15% off? what deduction is 5, 10, and 15% off? Ans. 231%, 2718%. 12. What is the difference between 10% on and 5 and 5% on? between 20 and 10% on and 20 and 10% off? Ans. %; 60%. 13. A merchant bought 84 yd. of French chintz, at 20 per yard, and sold it a gain of 33%; what did he gain in the transaction? Ans. $5.60. 14. Henry bought a boat for $850, and sold it at a gain of 25%, and the buyer sold it at a loss of 20%; what did the latter receive for it? Ans. $850. 15. Mr. Warner's key for marking goods is, "now be quick;" if he buy a lot of calicoes at 10 a yard, how must he mark them to gain 35% ? Ans. nw. CASE II. 394. Given, the rate and the profit or loss, or the selling price, to find the cost. MENTAL EXERCISES. 1. A boy sold a knife for 5 cents less than cost, and thereby lost 20%; what did it cost him? SOLUTION.-If he lost 20 per cent, then, or of the cost equals the loss, which equals 5 cents; if of the cost equals 5 cents, §, or the whole cost, equals 5 times 5 cents, or 25 cents. 2. A shoemaker charged 50 cents more for a pair of shoes than they cost him, and thereby gained 10%; what was the cost? 3. Edward sold his watch for $91, and thereby lost 35%; what did the watch cost him? 4. Mr. Pelton sold a set of maps for $15, and thereby lost 25%; for what should he have sold them to gain 30% ? 5. A horse-jockey bought a horse for 15% less than its value, and sold it for 40% more than its value; what % did he gain? 6. A picture-dealer sold two pictures for $120 each; on one he gained 25%, and on the other he lost 25%; what was his gain or loss? 7. A merchant sold a stove for $30, and thereby lost 25%; he then bought another stove for $30, and upon it gained 25%; what was the gain or loss? WRITTEN EXERCISES. 1. A man gained $28 on a watch by selling it at a gain of 95%; what did the watch cost? SOLUTION.-At a gain of 25%, .25 times the cost equals the gain, which is $28; if the cost multiplied by .25 equals $28, the cost equals $28 divided by .25, or $112. OPERATION. $28.25 $112 Rule I-Divide the profit or loss by the rate, to find the cost. Rule II.-Divide the selling price by 1 plus the rate of profit, or by 1 minus the rate of loss, to find the cost. 2. A merchant lost 15% by selling damaged delaines at 17 a yard; what did they cost him? Ans. 209. 3. Flour, sold at $7.54 a barrel, yields a profit of 16%; what did it cost per Ans. $6.50. 4. A furrier sold a set of sable furs at 12% less than cost, and lost $25; what did he get for them? Ans. $175. barrel? 5. What must I mark silks that cost $2.25 a yard so that I may fall 5% on my price and make 15%? Ans. $2.727. 6. A merchant's income is $5760 in a year, at a gain of 18% on his capital; how much would have been his income at a gain of 25% on his capital ? Ans. $7680. 7. By selling my interest in a lead mine for $16,872, I gain 14%; how much would I have received for it if I had lost 14% ? Ans. $12,728. 8. Prof. Winslow loses 16% by selling his library for $960 less than it cost; what must he have received for it if he had gained 16% ? Ans. $6960. 9. On opening a case of goods that cost me $1.20 a yard, 1 find them slightly damaged; how shall I mark them that I may abate 25% and lose only 5% ? Ans. $1.52. 10. A speculator sold two dwelling-houses for $6090 each; on one he gained 16%, and on the other he lost 16%; how much was gained or lost by the sale? Ans. Lost, $320. 11. A merchant bought a quantity of paper muslin @ 8¢, and marked it so that he could fall 9% on his marked price and gain 25% on cost; how must he mark it ? Ans. 119. 12. Mr. Smith's key for marking goods was "Republican · if he marked some grenadines e.bn and gained at that rate 111% on the cost; what was the cost per yard? Ans. $2.25. 18. Mr. Baker sold Mr. Albert a farm for $85 an acre and lost 15% on it; Mr. Albert sold the farm afterward to Mr. Hull, and made 15%; did Mr. Hull pay more or less an acre than Mr. Baker? Ans. $2.25 less. CASE III. 395. Given, the cost and the profit or loss or the selling price, to find the rate. MENTAL EXERCISES. 1. A man bought a watch for $50, and sold it at a gain of $15; what was his gain per cent.? SOLUTION.-If on $50 he gained $15, on $1 he gained of $15, which is $18, or $; and on $100 he would gain 100 times $, which are $300, or $30, hence the gain is 30 per cent. 2. If a coal dealer buys coal @ $5, and sells it at a gain of $2, what is his gain per cent.? 3. Sold a set of parlor furniture which cost $500 for $375; what was the loss per cent.? 4. What % is gained by selling goods at double their cost? What % is lost by selling them at one-half their cost? 5. A grocer buys a quantity of A No. 1 mackerel at $20 a barrel, and retails them at 15 a lb.; what is his gain %? 6. If a miller takes 3 quarts out of every bushel he grinds for toll, what % does he take for toll? 7. If goods are bought at 20% below market price and sold at 16% below that price, what is the gain %? 8. I bought a lot of goods at 5% below current prices, and sold them 5% above those prices; what was my gain %? 9. I imported a quantity of foreign goods, but some of them hav ing got wet on the voyage, I sold them at a loss of of their cost; what was my loss %? 10. A lady sold some silk for $12, and thereby cleared of this money; what would she have lost %, if she had sold it for $6? WRITTEN EXERCISES. 1. A man bought a horse for $200 and sold it at a loss of $20; what was the loss per cent.? SOLUTION. Since $200, the base, multiplied by the rate, equals $20, the rate must equal $20 divided by $200, which is .10, or 10%. OPERATION. $20-$200.10 Rule I. Divide the profit or loss by the cost, to find the rale. |