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Analysis.

Since at 104% the market value of one share is 184 of $100, or $104, and the market value of 5 shares is 5 times $104, or and since at % the brokerage is

$520;
entire cost is, etc. Hence, etc.

Find the market value or entire cost of

of $520, or $.65, the

1. 8 shares of R. R. stock at par, brokerage %; at 90. 2. 10 shares Penna, 6's, quoted at 104, brokerage %. 3. Four $1000 U. S. 5-20's at 120, brokerage %; at 1182. 4. A broker bought 20 shares of bank stock at 21% discount, and sold them at 1013. 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 121% 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 ʊ of $400, or $1. $381 less $1 is $380, the market value of 4 shares; and 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 %. 8. If 10 shares $50 stock cost $4511, brokerage %. 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 %; 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 %?

Analysis. Since the market value is 5% above par, each share with brokerage costs 105% 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 117, bro. %. 14. Of Lehigh R. R. bought for $824, at 1023, bro. %. 15. When gold is at a premium of 123, how much can be bought for $451? For $902? For $676.50?

16. A broker bought mining stock at 21% discount, and sold it at 1011⁄2, 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 102, to yield an income of $500? 18. In U. S. 5's of '81, at 1153, brokerage 1%, 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 %. 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 ʊ, or 15, 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 1167, brokerage %.

25. What % of income is realized from an investment paying 10%, bought at 1123, brokerage %?

26. If I buy for $100 State 6's, at 973, 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 18, of the price; and if $6 is 8% of the price, etc. At what price must

27. 6% stock be bought to yield an income of 9% ? 28. 8% stock be bought to yield 6% interest? 7% ? 29. U. S. 6's of 1881 to yield 5% in gold? 6%?

30. What premium must be paid on stock paying 10% dividend, to realize 7%? 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 12 to 75? Of 121 ft. to 61 ft.? $1 to $4? The ratio of 5 to 10? Of 21 ft. to 7 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 $11. 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 6 divided by 14?

the same ratio to 3
That 1 has to 9?

that 12 has to

9 to 11⁄2?

5. What number has 4? That 4 has to 12? 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 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 25 cents, how much are 2 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 2 cords can be bought for $17?

cords of wood, how many 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 bushels of potatoes cost $3, what will be the cost of 5 bushels at the same rate? Of of 63 bu.? 914

15. How many tons of hay will 4 horses eat in 33 months, if 3 horses eat 1 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 153 tons of coal in 6 days, how long will 201 tons supply 5 furnaces?

18. If $80 gain $4 in 12 months, in how many months will $50 gain $21 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

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

can saw it in 11⁄2 da.

cord of wood in of a day, and his son In what time can both saw it?

26. If A can do of a piece of work in one hour, B 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 of it, what part does A mow? In what time could A alone mow all of it?

20

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?

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