for 3 months; B, 9 horses for 5 months; and C, 4 horses for 6 months: what part of the rent should each pay? 3. A commenced business with a capital of $10000. Four months afterwards B entered into partnership with him, and put in 1500 barrels of flour. At the close of the year their profits were $5100, of which B was entitled to $2100: what was the value of the flour per barrel? 4. On the 1st of January, 1864, A commenced business with a capital of $23000; two months afterwards he drew out $1800; on the 1st of April, B entered into partnership with him, and put in $13500; four months afterwards he drew out $10000; at the end of the year their profits were $8400 : how much should each receive? 5. Three persons divided their profits to the amount of $798. A put out $4000 for 12 months; B, $3000 for 15 months; and C, $5000 for 8 months to what part of the profits was each entitled? 6. Three persons, C, D, and E, form a copartnership; C's stock is in trade 3 months, and he claims of the gain; D's stock is in 9 months; and E put in $756 for 4 months, and claims of the profits: how much did C and D put in? 7. Two persons form a partnership for one year and six months. A, at first, put in $3000 for 9 months, and then $1000 more. B, at first, put in $4000, and at the end of the first year, $500 more; but at the end of 15 months, he drew out $2000. At the end of 12 months, C was admitted as a partner with $73333. The gain was $7400: how much should each man receive? 8. Three men take an interest in a mining company. A put in $480 for 6 months; B, a sum not named for 12 months ; and C, $320 for a time not named: when the accounts were settled, A received $600 for his stock and profits; B, $1200 for his; and C, $520 for his what was B's stock, and C's time? 254. What is the rule when the capital is employed for unequal times? PERCENTAGE. 255. PER CENT. means by the hundred. Thus, 1 per cent. of a number is one-hundredth of it; 2 per cent. is two-hundredths of it; 3 per cent. three-hundredths, &c. 256. The RATE PER CENT. is the number of hundredths taken. Thus, if 1 hundredth is taken, the rate is 1 per cent.; if 2 hundredths are taken, the rate is 2 per cent.; if 3 hundredths, the rate is 3 per cent., &c. 257. The BASE is the number whose part is taken. 258. The PERCENTAGE is the result of the operation, and is the part of the base taken. The rate per cent. is generally expressed decimally; thus, NOTE.-Per cent. is often expressed by the character %. Thus 5 per cent. is written 5%; 8 per cent., 8%. Write, decimally, 5%; 8%; 15%; 100%; 204%; 327%; 672.3%; 49%; and 507.5%. 255. What is the meaning of per cent.? What is 5 hundredths of a number?--256. What is the rate per cent.? If four hundredths of a number is taken, what is the rate?-257. What is the base?-258. What is the percentage? How is the rate per cent. generally ex pressed? 259. To find the percentage, when the base and rate are known. 1. What is the percentage of $450, the rate being 6 per cent.? ANALYSIS.-The rate, expressed decimally, is .06. The percentage is, therefore, six hundredths of the base, or the product of the base and rate. Hence, to find the percentage of any number: OPERATION 450 .06 $27.00 Ans. Rule.-Multiply the base by the rate, and the product will be the percentage. Examples. Find the percentage of the following numbers : 1. 4 per cent. of $1256. 2. 12% of $956.50. 3.1 per cent. of 475 yards. 12. 12% of 126 cows. 13. 50 per cent. of 320 bales. 14. 37 per cent. of 1275 yds. 15. 95% of $4573. 16. 105 per cent. of 2500 bar. 18. 250 per cent. of $5000. 11. 8 per cent. of $3465.75. | 22. What is 44% of 960 bush.? 23. What is the difference between 43% of $1000 and 7 per cent. of $1500? 24. If I buy 895 gallons of molasses, and lose 17 per cent. by leakage, how much have I left? 25. A grocer purchased 250 boxes of oranges, and found that he had lost in bad ones 18 per cent.: how many full boxes of good ones had he left? 259. How do you find the percentage from the base and rate? 260. Parts of percentage. There are three parts in percentage: 1st. The Base; 2d. The Rate; and 3d. The Percentage. 261. To find the rate, when the base and percentage are known. 1. What per cent. of $64 is $16? or, $16 is what part of $64? OPERATION. 1.25, ANALYSIS.-In this example, 16 is the percentage, and 64 the base, and the rate is required. Since the percentage is equal to the base multiplied by the rate, the rate is equal to the quotient of the percentage divided by the base. 25 per cent. Rule.-Divide the percentage by the base, and the first two decimal places will express the rate. Examples. 1. What per cent. of 10 dollars is 2 dollars? 2. What per cent. of 32 dollars is 4 dollars? 3. What per cent. of 40 pounds is 3 pounds? 4. Seventeen bushels is what per cent. of 125 bushels? 5. Thirty-six tons is what per cent. of 144 tons? 6. What per cent. is $84 of $96 ? 7. What per cent. is of ? 8. What per cent. is 3 miles of 400 miles? 9. Four and one-third is what per cent. of 9? 10. One hundred and four sheep is what per cent. of a drove of 312 sheep? 11. A grocer has $325, and purchases sugar to the amount of $121.87: what per cent. of his money does he expend? 12. Out of a bin containing 450 bushels of oats, 56 bushels were sold what per cent. is this of the whole? NOTE. If the base be regarded as a single thing, and denoted by 1, a fractional percentage expressed decimally will denote the rate. 260. How many parts are there in percentage? What are they? 261. How do you find the rate, from the base and percentage? 13. of a number is what per cent. of the number? 17. 13 times a number is what per cent. of the number? 262. To find the base, when the rate and percentage are known. 1. Of what number is $960, 16 per cent.? ANALYSIS.-By Art. 259, the percentage is equal to the base multiplied by the rate; hence, to find the base, OPERATION. 960.16 = 6000 Rule.-Divide the percentage by the rate, expressed deci mally. Examples. 2. The number 475 is 25% of what number? 3. The number 87 is 12% of what number? 4. Five hundred and sixty dollars is 140% of what number? 5. The number 75 is % of what number? 6. One dollar and twenty-five cents is 7% of what number? 7. The fraction is 45% of what number? 8. The fraction is 5% of what number? 9 If a person receives $5850, and that sum is 75% of what is due him, what is the debt? 10. A bankrupt can pay only 37 per cent. of his debts: what did he owe to that merchant to whom he paid $1647? 11. In an army, 15600 men are mustered after a battle, in which 25% were killed and wounded: what was the original number of men? 263. AMOUNT is the percentage plus the base. 264. DIFFERENCE is the percentage minus the base. 262. How do you find the base, when the rate and percentage are known?-263. What is the amount?-264. What is the difference? |