11. When Baltimore & Ohio pf. is selling at 96, how many shares can be bought for $5767.50, brokerage at the usual rate? 12. How many shares of Northern Pacific R. R. stock at 971 can be bought through a broker for $4862.50 ? 13. If Southern R.R. pf. stock can be bought at 100, how many shares of it can I buy through a broker for $ 8010? 14. How many shares of Pressed Steel Car stock pf. at 923 can be bought through a broker for $40,865 ? 15. I purchased 24 shares of Pennsylvania R.R. stock at 138 and, after receiving one quarterly dividend of 11%, sold the stock at 141. How much did I gain, allowing brokerage for both buying and selling? 16. Mr. Brown bought 125 shares of N. Y. C. R.R. stock at 1491, and after receiving one quarterly dividend of 14%, sold them at 1521. Allowing brokerage in each case, how much did he gain? 17. My money in the savings bank was paying me 31% interest. I drew out $2002 and invested it in railroad stock at 125, paying the usual brokerage. This stock yielded a semiannual dividend of 21%. Was my semiannual income increased or diminished, and how much? 18. A man bought 300 shares of a certain stock at 871. Later he received 15 shares of the stock as a dividend on his 300 shares. Becoming alarmed because the dividend was not in cash, he sold his shares at 817. Find his loss, including brokerage for both buying and selling. 19. How much must be invested in Galveston Street Railway 5% bonds (denomination $100) at 112, usual brokerage, to secure to the purchaser an annual income of $1000? SOLUTION Since the income from each bond is $5, it will take as many bonds to give an income of $1000 as $5 is contained times in $1000, or 200 bonds. At 112, each bond, including brokerage, will cost $112, and 200 bonds will cost 200 times $112, or $22,425. Therefore $22,425 must be invested to secure an annual income of $1000. 20. What sum must be invested in Imperial Japanese 6s, at 995, to give an annual income of $2400, allowing the usual brokerage? 21. What amount invested in Republic of Cuba 5s at 105g, brokerage as usual, will secure an annual income of $500? 22. What sum must I invest in American Hide & Leather 6s at 997, allowing brokerage, to secure an income of $1200? 23. What per cent shall I make on my money, if I buy 4% bonds at 80? SUGGESTION. $4 is what per cent of $80? 24. Find the per cent realized on an investment in 6% preferred stock at 75. 25. How much must I pay for 4% stock in order to realize 5% on my investment? the SUGGESTION. $4 is 5% of what must be paid for a share. 26. How much must be paid for 6% stock to realize 5% on money invested? 27. Find the cost of 3% stock when the money invested in it yields 8%. 28. A man receives a quarterly dividend of $50 on 25 shares of stock. Find the rate of dividend each quarter. 29. A company with a capital of $300,000 pays its stockholders $6000 quarterly. Find the quarterly dividend of a man who holds 40 shares of the stock. 30. During one year the net earnings of a company whose capital is $360,000 were $65,835. If it retained a surplus of $5835 and distributed the rest in dividends, how much was received by a man owning 60 shares? 31. What annual income will a man receive who invests $4835.25 in a 6% stock purchased at 115, brokerage at the usual rate? 32. A man bought at private sale 50 shares of a bank stock at 193, and afterward sold them through a broker at 1911. How much did he lose? 33. How much must be paid, including brokerage, for a sufficient number of U. S. 4s at 1331⁄2 to obtain an annual income of $1000? 34. At one time during the war between Japan and Russia, Japan borrowed a large sum of money by means of an issue of 7-year 6% bonds. They sold at 931. What rate of interest, to the nearest .01%, did Japan pay on a par basis? 35. Several years before the war Japan had sold an issue of 5% bonds at 103g. Find the true rate of interest paid. 36. A stock company declared a dividend of $375,000 for one quarter. The stock consisted of $12,500,000 preferred and $12,500,000 common, the preferred stock being allowed 7% annually before the common stock could participate in the profits. Find the dividend of a stockholder who owned 50 shares of preferred and 10 shares of common. RATIO AND PROPORTION RATIO 495. 1. Compare 15, 20, 25, and 30 with 5 in such a way as to tell how many times each contains 5. What number expresses the relation, or ratio, of 15 to 5? of 20 to 5? of 12 to 3? of $50 to $10? of 32 qt. to 8 qt. ? 3. What number expresses the ratio of 3 to 6? of 2 to 6? of 3 to 12? of $10 to $40? of 7 days to 28 days? 496. The relation of one number to another of the same kind, expressed by the quotient of the first divided by the second, is called the ratio of the first number to the second. All ratios are abstract numbers. Thus, the ratio of 15 to 3 is 15 ÷ 3, or 15, or 5. 497. The ratio sign is a colon (:). Thus, the ratio of 15 to 3 may be written 15: 3. 498. The first number in a ratio is called the antecedent, and the second number, the consequent. The antecedent and consequent of a ratio are called its terms. 499. Since a ratio may be written in the form of a fraction, and since multiplying or dividing both terms of a fraction by the same number does not change the value of the fraction, Multiplying or dividing both terms of a ratio by the same number does not change its value. Thus, 48 reduced to lowest terms is 1:2; also 4:8 = 12:24. EXERCISES 500. What is the ratio of 7 1. 14 to 7? 7 to 14? 18 to 6? 6 to 18? 5. 12 to 100? 371 to 100? 112 to 100? 125 to 100? 17 to 3? 25 to 8? 120 to 100? 621 to 100? 331 to 100? 6. 20% to 1? 50% to 1? 40% to 1? 87% to 1? 110% to 1? Reduce to lowest terms the ratios expressed by: 19. What is the ratio of $70 to $100? of $600 to $1000? 20. What is the ratio of 15 days to 30 days? of 21 days to 1 week? 21. What is the ratio of 1 rod to 1 mile? of 1 ounce to 1 pound? 22. What is the ratio of a long ton to a short ton? 25 12 1 4. .7: .8 1 5. .4: 10 8. 7. 10: 4.5 10. 4 ft. 16 in. 3. 1 : 11. 2 yd.: 18 in. 12. 1 Km. : 62.5 m. 13. The capital stock of a street railway company was $7,500,000, the gross earnings for a year $1,500,000, and the net earnings $600,000. Find the ratio of gross earnings to capital stock; of net earnings to gross earnings; of net earnings to capital stock. Then express each ratio in per cent. |