5. What number, diminished by 14 % of itself, is equal to 129 ? SOLUTION. 100% 14% =86%; of 129 129.86 = 150. Ans. Ans. 563 yards. 6. 534.85 yards are 5% less than what number? 7. 1738 is 13% % less than what number? Ans. 2000. 9. What fraction, diminished by 10% of itself is equal to ? Ans. 271. It is sometimes most convenient to use the given rate per cent. expressed as a common fraction. 10. What number increased by 25 % of itself is equal to 750? = SOLUTION. 25%%%; 4, or the number, +={; if { = 750, =} of 750, or 150, and 150 × 4600, Ans. = = 11. $620 are 334 % less than what number? 12. is 16% more than what number? Ans. APPLICATIONS. 1. A candidate for re-election received 3640 votes, which was 12% more than he received at his first election; how many had he at the first? Ans. 3250 votes. 2. A regiment, which lost in a severe engagement 31 per cent of its men, had 440 men left; how many had it at first? Ans. 640 men. REVIEW QUESTIONS. How may rate per cent. be expressed? (264 What is used, in business, to stand for the word per cent.? (264) 3. A man spent 66% of his income, and saved $533.333; what was his income? SOLUTION. If he spent 664% of his income, he saved the whole or 100%-663 %, which is 33%, or 1; if $533.33 is,, or his whole income, must be $533.33 × 3 = = $1600, Ans. 4. The population of a certain village is 4059, which is 12% more than it was five years ago; what was it then? Ans. 3608. 5. A gentleman completed a journey by steamer in 26 d. 10.4 h. which was 30 % longer than would have been required to have performed it by railroad; how long would it have required by railroad? Ans. 20 d. 8 h. COMMISSION AND BROKERAGE. 272. A Commission Merchant, or Factor, is a person who buys or sells goods for others, for a percentage. 273. A Broker is a person who buys or sells stocks, bills of credit, etc., for a fee, or a percentage. 274. Commission is the percentage paid a commission merchant, or factor, for the transaction of business. 275. Brokerage is the percentage paid a broker for the transaction of business. The BASE is the amount of property sold or purchased, of money invested or collected, etc. 276. To find the commission or brokerage. 1. An agent sold property to the amount of $5650; what is his commission, at 3 per cent.? OPERATION. $5650.03 $169.50, Ans. = Since the commission is 3%, or .03, on $5650, it must be 3 hundredths of $5650, or $5650 .03, which is $169.50. Therefore, etc. RULE. Multiply the given amount by the rate per cent. expressed decimally. What is a Commission Merchant, or Factor? A Broker? What is Commission? Brokerage? The Base? Explain the operation. The Rule. Examples. 2. An agent collects debts to the amount of $965; what is his commission at 2% ? Ans. $19.30. 3. What is the brokerage for purchasing $10000 of gold, at %? 4. A commission merchant disposes of 718 barrels of flour at $7.13 per barrel; what is his commission at 4 per cent? Ans. $217.57+ 5. If a broker charges % for exchanging $5670 of currency, how much is the brokerage? Ans. $28.35. 6. If my agent charged 5 % for collecting a debt of $564.40, how much will he have to pay over to me, after deducting his fee? SOLUTION. $564.40 × .05 = $28.22; $564.40-$28.22 = $536.18, Ans. 7. What is the fee of a tax collector for collecting $19500, at 14%, and how much will he have to pay over? Ans. Fee, $292.50; pay over, $19207.50. 277. When the given amount includes the commission or brokerage. The given amount divided by $1, increased by the commission or brokerage on $1, will denote the sum to be invested. The sum to be invested subtracted from the given amount, will give the commission or brokerage. 8. A broker receives $6045, with instructions to deduct his brokerage, %, and invest the balance in bank stock; what sum had he to invest, and what was his brokerage? $6045 OPERATION. $1.00$6000, to be invested. $6045 $6000 $45, brokerage. = $1.00 for each dollar to be invested, and will have for investing as many dollars as $1.003 is contained times in $6045, or $6000; and the difference between the sum he receives and the sum to be invested, or $45, must be his brokerage. 9. An agent receives $3838.80 to lay out in purchase of goods, deducting his commission at 5 %; what value of goods shall the owner receive? Ans. $3656. 10. An agent receives $581.85 to lay out in coal, deducting his commission at 2 %; what value of coal can he purchase? 11. I remit a commission merchant in Chicago $2050, for the purchase of flour; the flour costs $10 a barrel, and his commission is 2%; after deducting his commission, how many barrels will the money enable him to send me ? Ans. 200 barrels. 12. A broker has $11000 to invest, after deducting his fees at the rate of %; what sum is there to be invested? 13. Sent an agent in New Orleans $64890 to purchase a quantity of cotton; if he deduct his commission at 3 %, and with the balance purchases 700 bales, how much is the cost per bale? Ans. $90. INSURANCE. 278. Insurance is an obligation by which one party is bound o indemnify another for a loss which he may sustain. PROPERTY INSURANCE has reference to houses, mills, ships, goods, etc. HEALTH and LIFE INSURANCE have reference to risks on health and life. The party taking the risk is the Insurer or Underwriter, and the party protected the Insured. 279. The Policy is the written contract made by the parties. 280. The Base is the amount insured; and 281. The Premium is the percentage charged for the insurance. What is Insurance? Property insurance? Health or Life insurance? The Policy? The Base? The Premium? 282. To find the premium of insurance. 1. What is the premium on a policy of $3840, at 4 per eent.? OPERATION. $3840 X .04 $172.80, Ans. = Since the premium is 43%, or .04, on $3840, it must be .04 of $3840, or $172.80. RULE. Multiply the amount insured by the rate per cent. of premium expressed decimally. Examples. 2. What is the premium for insurance of $3560 on a dwelling house, at 2 %? Ans. $71.20. 3. What is the cost of insuring a cargo of corn, worth $5000, at 3 %, and $1 for the policy? 4. If a person 36 years old takes out a life policy for $5000, payable at death, or when he is 45 years old, how much will he have paid, if he shall live to the latter age, the annual premium being $541.30? Ans. $4871.70. 5. What is the cost of insuring $7500 on a store and goods, at 2% ? 6. A ship and cargo are insured for $98000, at 31 %; if they should be destroyed by fire or storm, what would be the actual loss of the insurers? Ans. $94815. PROFIT AND LOSS. 283. Profit and Loss are commercial terms denoting gain and loss in business transactions. 284. The Base is the cost price, or the quantity on the which the gain or loss accrues. The Examples are like those of the four cases in Percentage, and may be solved by the application of rules already given, or by analysis. Explain the operation. Repeat the Rule. What do the terms Profit and Loss denote? What is the Base? How may the examples be solved? |