ONE GIVEN NUMBER A PERCENTAGE ON ANOTHER. RULE L. § 253. To find what PERCENTUM one given number is of another. Divide the number which is made the percentage by that which is made the basis of percentage. The quotient will be the ratio of percentage; and this quotient multiplied by 100, will produce the required rate per cent. EXAMPLE. To find what percentum $9 is of $150. 9 150.06, the ratio of percentage; and .06X100=6, the required rate per cent. (§ 247). This Rule follows from the preceding one. (§ 249). Proportion. $150: $100 :: $9: the required rate per cent. TAXES. § 254. TAXES are contributions in money, imposed by Government on property, and frequently on persons, for public purposes. A poll or capitation tax is a tax on the person, without regard to property. A tax on property is sometimes specific, that is, a specified sum on certain articles; but it is most commonly ad valorem, or a specified percentum on the value. EXERCISES. 21. A person paid a tax of $52.88 on $3525.50 worth of property; at what rate per cent. was the tax assessed? Ans. 1 per cent. 22. The property of a town amounts to $50000, and the citizens resolve to tax it to the amount of $1125, for public improvements. At what percentum must the tax be laid? Ans. 2 per cent. 23. Allowing a gentleman to pay a tax of $1379.16, on property amounting to $82750, at what rate per cent. is the tax assessed? Ans. 1 per cent. 24. A citizen pays taxes as follows, viz: for three polls at $1.25; on a carriage $10; on silver plate valued at $500, 3 per cent.; on $15000 of other property, & per cent. What amount of tax does he pay? Ans. $141.25. 25. The taxable polls in a State amount to 325830, and are assessed at $1.12. The landed property in the State is valued at $38400000; at what percentum must the land be taxed, that the revenue from both sources may amount to $462558.75 ? Ans. per cent. A Required Number, increased by a Percentum of itself, equal to a Given Number. RULE LI. $255. To find a number which, increased by a specified PER CENTUM OF ITSELF, shall be equal to a given number. Divide the given number by 1 plus the ratio of percentage: the quotient will be the number required. EXAMPLE. What number, increased by 5 per cent. of itself, is equal to 210? The ratio of percentage is .05; and 1+.05 is 1.05. Proportion. 100+5 100 210: the number required. The reason of the Rule is evident from considering that, as the required number multiplied by 1+ the r tio of percentage, would be increased by the specified percentum of itself, and thus be equal to the given number; so the given number divided by 1+ the ratio of percentage, will give the required number. In the example, 200×1.05=210, which is 200 increased by .05 of 200; then 210-1.05 gives 200, the required number. COMMISSION. § 256. COMMISSION is a compensation to an Agent, Factor, or Commission Merchant, for buying or selling for another; and is usually reckoned at a certain percentum on the amount of purchase or sale. BROKERAGE is a commission charged by Brokers, or dealers in money, stocks, &c., on the amount of exchange, purchase or sale, which they effect for another. EXERCISES. 26. An agent receives $500 to purchase goods-himself to retain a commission of 2 per cent. on the amount of purchase. What is the amount of purchase to be made? Ans. $490.196'. 27. A factor receives a remittance of $1200 to purchase cloth, at a commission of 14 per cent. on the purchase. What will be the amount of purchase? Ans. $1185.185'.. 28. A commission merchant sold goods amounting to $1785.81; at a commission of 11⁄2 per cent. What sum must the merchant pay to the owner of the goods? Ans. $1759.025'. 29. An agent is intrusted with $450 to purchase iron. His commission being per cent. on the purchase, how many tons of iron can he buy at $30 per ton? Ans. 14.888' T. 30. A, as factor for B, sells 50 bales of cotton, averaging 450 pounds, at 71⁄2cts. per lb.—commission 13 per cent. With the proceeds A purchases for B, a supply of provisions,-commission per cent. on the purchase. What sum is expended for provisions? Ans. $1649.71'. A Required Number, diminished by a Percentum of itself, equal to a Given Number. $257. To find a number which, diminished by a specified percentum of itself, shall be equal to a given number. Divide the given number by 1 minus the ratio of percentage; the quotient will be the number required. EXAMPLE. What number diminished by 5 per cent. of itself, is equal to 190? The ratio of percentage is .05; and 1—.05 is .95. Proportion. 100-5: 100 :: 190: the number required. The reason of the Rule is evident from considering that, as the required number multiplied by 1 minus the ratio of percentage, would be diminished by the specified per centum of itself, and thus be equal to the given number; so the given number divided by 1 minus the ratio of percentage, will give the required number. In the example, 200×1-.05=190, which is 200 diminished by .05 of 200; then 190÷÷1-.05 or .95=200, the required number. STOCK. § 258. STOCK, or Capital, is money or other property employed in any way to produce a profit; as in manufactures, banking, &c. Bonds of the Government are also called Government Stock. The stock of a Company is divided into shares, usually of $100 each; and the owner of one or more shares is called a Stockholder. The nominal value, or par value of a share of stock, is its first cost, or the sum originally invested in it. Stock is said to be above par, at a premium, or an advan when it sells for more than its nominal value; and below par, or at a discount, when it sells for less than its nominal value. The rise or fall of stock is expressed by a percentum on its nominal or par value. EXERCISES. 31. When bank stock sells at 5 per cent. below par, what nominal amount of stock can be bought for $945 ? The nominal amount is such, that, when diminished by 5 percentum of itself, it will be equal to $945. Ans. $1000. 32. When rail road stock sells at a discount of 7 per cent., what nominal value of it can be bought for $2775 ? Ans. $3000. 33. What nominal amount of stock in an insurance office, at an advance of 5 per cent., can be purchased for $2100? and what amount in another, at a discount of 5 per cent., can be purchased for $1900 ? Ans. $2000 in each. 34. What amount of stock in the capital of a manufacturing company, at a discount of 3 per cent., can be purchased for $1930 and what amount in another, at an advance of 4 per cent., can be purchased for $3120. Ans. $2000; and $3000. 35. A merchant ships, from New York to Charleston, a stock of goods amounting to $5000. He wishes to insure for a sum which shall cover both the value of the goods, and the premium for insurance. For what amount must the policy be taken, at per cent.? The amount of the policy, diminished by per cent. of itself, will be $5000. Ans. $5025.125'. 36. A manufactory valued at $2500, is insured, at 14 per cent., in such a sum, that, in case of a total destruction of the establishment, the proprietors may claim, at the insurance office, the value of the property, together with the premium paid for insurance. What was the amount insured? Ans. $2531.645'. PERCENTAGE OF PROFIT AND LOSS. The preceding Rules of Percentage are applicable to various questions relating to profit and loss in trade. This application of the subject will be seen in the following Exercises. It must be carefully observed that, § 259. In calculating the Percentage of Profit, or Loss, in trade, the cost of the commodity is always regarded as the basis of percentage (§ 248). The amount of Profit or Loss found from the Cost, and the percentum of Profit or Loss. § 280. The amount of profit or loss is the amount of percentage on the cost, at the given rate per cent. of profit or loss. (§ 249). When the rate per cent. is an aliquot part of 100, the amount of percentage will often be found, most readily, by taking such part of the cost, or basis of percentage. EXERCISES. 1. A merchant bought a quantity of cloth for $330, and sold the same at a profit of 33 per cent. What amount of profit did he make. The amount of profit is $330×.33; or since the rate per cent. 33 is of 100, the answer will be found, more readily, by taking of $330. Ans. $110. 2. A grocer bought a hogshead of sugar for $55.75, and sold it at a profit of 12 per cent. What amount of profit did he make? 12 is of 100. Ans. $6.968'. 3. A merchant bought silk for $160, and, on account of its becoming damaged, sold it at a loss of 5 per cent. What amount of loss did he sustain ? Ans. $8.80. 4. A flour dealer bought 130 barrels of flour, at $4.12 per barrel, and sold it at a profit of 10 per cent. of profit did he make? What amount Ans. $53.625'. 5. A person purchased 25 barrels of dried apples, at $2.12 per barrel. On account of damage received, he must sell them at a loss of 15 per cent.; what amount of loss will he sustain ? Ans. $7.968'. 6. A grocer purchased 100 gal. 3 qt. of wine, at $.614 per gallon. He sold one half of the wine at a profit of 40 per |
