Analysis. Since at 104% the market value of one share is 104 of $100, or $104, and the market value of 5 shares is 5 times $104, or $520; and since at $% the brokerage is ado of $520, or $.65, the entire cost is, etc. Hence, etc. Find the market value or entire cost of 1. 8 shares of R. R. stock at par, brokerage $% ; at 90. 2. 10 shares Penna, 6's, quoted at 104, brokerage 3%. 3. Four $1000 U. S. 5-20's at 120, brokerage 3% ; at 1183. 4. A broker bought 20 shares of bank stock at 21% discount, and sold them at 1011. What did he gain ? 5. An insurance company declared a dividend of 41%. How much did a stockholder owning 10 shares receive ? 6. When gold is quoted at 123% premium, what is the currency value of $500 in gold? When quoted at 1131 ? 378. If 4 shares of stock cost $381, including brokerage at 1%, at what rate does it sell ? Analysis. Since the par value of 4 shares is 4 times $100, or $400, at 1% the brokerage is ado of $400, or $1. $381 less $1 is $380, the market value of 4 shares; and I of $380 is $95, which is .95, or 95%, of the par value. Find the market value and rate of premium or discount 7. If 8 shares of R. R. stock cost $801, brokerage 3%. 8. If 10 shares $50 stock cost $451 , brokerage 1%. 9. If a $1000 bond U.S. 5-20's sells for $1185; for $1177.50. 10. If 20 shares bank stock sell for $105 above par, including brokerage 5%; for $205 discount; for $50 premium. 11. A company with a capital of $50000 receives $2500 more than it expends. Find the dividend on ten $50 shares. 379. When stock is at 5% premium, how many shares, each $50, can be bought for $421, brokerage 4 %? Analysis. — Since the market value is 5% above par, each share with brokerage costs 1051 % of $50, or $52.62; and for $421 there can be bought as many shares, etc. Find the par value, or number of shares 12. Of bank stock bought for $975, at 974, brokerage 1%. 13. Of a U.S. bond that cost $1172.50, at 1173, bro. %. 14. Of Lehigh R. R. bought for $824, at 102, bro. %. 15. When gold is at a premium of 127, how much can be bought for $451 ? For $902? For $676.50 ? 16. A broker bought mining stock at 23% discount, and sold it at 1013, and cleared $60. Find the number of shares. 380. What must I invest in 6% stock, at 95, to yield $300 ? Analysis. — Since the interest of 1 share of 6% stock is $6, to yield $300 there must be invested as many dollars, etc. And 50 shares at $95 a share cost $4750, the amount of investment. What sum must be invested 17. In 5% stock, at 1023, to yield an income of $500? 18. In U. S. 5's of '81, at 115}, brokerage 3%, to give $600 ? 19. In R. R. 7's, at 90, brokerage 1 %, to give $350 ? 20. U.S. 10-40's are quoted at 1183, brokerage 5%. What must be invested to give a yearly income of $1000 ? 21. What sum must I invest in stock at 110, paying 10% annual dividends, to realize $500 a year? 381. What % do 8% bonds yield when bought at 120 ? Analysis. Since each share at $120 yields $8 interest, the rate of income is Tio, or 1's, of 100%, or 63%. Hence, etc. Find the rate of income realized from 22. 6% bonds bought at 90; at 102; at 96. 23. Stock paying 10% annual dividend, bought at 120. 24. U. S. 5-20's bought at 1163, brokerage %. 25. What % of income is realized from an investment paying 10%, bought at 1123, brokerage 5%? 26. If I buy for $100 State 6's, at 97%, what interest do I receive? What rate on the investment, brokerage £%? 382. At what price must 6% stock be bought to yield an income of 8% on the investment? Analysis. Since $6 is the interest on each share, $6 must be 8%, or 187, of the price; and if $6 is 8% of the price, etc. At what price must 30. What premium must be paid on stock paying 10% dividend, to realize 73% ? 8% ? 31. Which is the better investment and how much %, U. S. 5-40's at 112, or U. S. 5-20's at 120 ? Miscellaneous Problems. 1. What is the relative value of 8 yards compared with 24 yards? What is the relation of 8 to 24? The ratio of 8 to 24? 2. What is the relation of 121 to 75? Of 12 ft. to 63 ft. ? $. to $4? The ratio of 5 to 10? Of 21 ft. to 74 ft. ? Of $9 to $24? Of 16.5 yd. to 5.5 yd. ? 3. Name two numbers having a relation or ratio to each other equal to the ratio of $6 to $13. Of 3 yd. to 7 yd. 4. What number divided by 7 gives the same quotient as 8 divided by 2? The same quotient as 6divided by 1; ? 5. What number has the same ratio to 3} that 12 has to 4? That 4 has to 12? That 1.1 has to 9? 9 to 1, ? 6. The relation of 5 ft. to 15 ft. is the same as the relation of $4 to how many dollars ? The ratio of 4. mi. to 9 mi. equals the ratio of 5.4 days to how many days? 7. If 2 oranges cost 10 cents, what will 8 oranges cost at the same rate? The ratio of 2 oranges to 8 oranges equals the ratio of 10 cents to how many cents ? 8. If 6 men do a piece of work in 8 days, how many men would be required to do it in 1 day? In 4 days? 9. If 2 yards of muslin are worth 254 cents, how much are 24 yards worth ? How much are 3} yards worth ? 10. If of a barrel of flour cost $63, what must be paid for of a barrel ? For 2, barrels ? 11. If $114 will pay for 21 cords of wood, how many cords can be bought for $17.1? For $213? 12. If 4 men do a piece of work in 6. days, working 10 hours a day, in how many days can they do the same amount of work, if they work 12 hours a day? 13. When $23 will pay for of a barrel of flour, how much money is required to pay for 2 barrels ? 14. If 3.1 bushels of potatoes cost $31, what will be the cost of 51 bushels at the same rate? Of i of 63 bu.? 15. How many tons of hay will 4 horses eat in 3 months, if 3 horses eat 11 T. in 1 month ? 16. How many days will it take 7 men to earn $49, if 5 men earn $7 in } of a day? 17. Suppose 3 furnaces consume 15% tons of coal in 6 days, how long will 204 tons supply 5 furnaces ? 18. If $80 gain $44 in 12 months, in how many months will $50 gain $24 at the same rate ? 19. If a man can cut a field of grass in 21 days, what part of the field can he cut in one day? 20. If B can plow of a field in one day, in how many days can he plow the whole field ? 21. If B can do a piece of work in 4 days, and C in 6 days, what part can each do in one day? Both ? M 22. If B and C together can do is of a piece of work in one day, in what time can they do all of it? 23. A shoemaker can fill a certain order in 3 days, and his apprentice in 3 days. In what time can both fill it? 24. If a cistern can be filled by one pipe in half an hour, and by another in 20 minutes, in what time can it be filled by both pipes running together ? 25. A man saws a cord of wood in of a day, and his son can saw it in 1.1 da. In what time can both saw it? 26. If A can do } of a piece of work in one hour, B 1 of it, and C of it, what part can they all do in one hour? 27. If A can do a piece of work in 2 days, B in 3 days, and C in 4 days, what part can each do in 1 day? What part can all do? In what time can all do it together? 28. A can do a piece of work in 3 days, B in 4 days, and C in 6 days. In what time can all do it together? 29. If A and B together can mow § of a field in a day, and B alone mows zo of it, what part does A mow? In what time could A alone mow all of it? 30. A man and his son make a fence in 4 days. The son alone can do it in 12 days. In what time can the father do it? 31. Three men can reap a field of wheat in 4 da. A can do it alone in 8 days, and B in 12 days. In what time could C alone reap the field ? 32. A, B, and C could dig a ditch in 4 days, A and B in 6 days, and B and C in 9 days. In what time can each alone finish the work? In what time can A and C do it? 33. A and B can build a wall in 16 days, but with the aid of C they can build it in 10 days. In what time can C alone do it? 34. A, B, and C can dig a ditch in 6 days, A and B in 8 days, and B in 12 days. In what time could each dig it? |