11. Mr. Green paid $258,750 for bonds at a premium of 31%. What was the face value of the bonds?

12. I bought 96 shares of mining stock, face value $50, for $4476. Find the rate of discount.

13. I paid my broker $125 brokerage for buying N. Y. Central. How many shares did he buy, brokerage being 1% ? 14. I bought some railway stock at 73, received $94.50 as a 21% dividend, then sold my stock at 861. How many shares had I, and what was my gain?

15. The earnings of a company, capitalized at $40,000, are $8650, and the expenses are $1250. If a surplus of $1200 is reserved, what dividend can be declared?

16. What is the annual income from $160,500 invested in B. & O. R. R. Co. 6's at 107?

17. What income can be secured by investing $684 in 6 % stock at 95?

18. What sum must be invested in 5% stock, at 105, to produce an income of $10,010?

19. I sold $8320 of 6's at 104 and invested the proceeds in 5's at 797, brokerage in each case. How much did I gain or lose annually?

20. How much must I invest in Milwaukee 4% Park bonds at 1027, brokerage, in order to have an annual income of $600?

SOLUTION

A 4% bond earns $4 per share.

$600 ÷ $4 = 150, number of shares required.

$1027 $1 = $103, cost of one bond.

150 × $103 = $15,450. Ans.

21. How much must be invested in St. Paul 7's at 1497, brokerage, to produce an annual income of $420?

22. What sum must I invest in 5-20's at 1123, brokerage , to insure an annual income of $500?

23. I wish to leave an annual income of $1200 to my daughter. Which is the better offer, 3% bonds at 87%, or 4% bonds at 1027, brokerage in each case being ?

24. A exchanges 250 shares of 6% stock at 70 for 8% stock at 125. What is the difference in his income?

25. What per cent of income is realized by buying a 7% bond at 95?

SOLUTION: A 7% bond nets $7 a year.

of 100% = 71%, rate of income.

26. What is the rate of income on U. S. 6's bought at 106? 27. On bank stock bought at 73, a dividend of 4% was declared. What was the rate of income?

28. Which is the better investment, to purchase 3's at 90, or 4's at 112?

29. Wishing to secure a permanent investment, I have the option of taking 5's at 75, or 7's at 90. Which is the better?

30. What is the rate of income on 4 %

31. How much must be paid for 4% income?

bonds bought at 85? stock to yield 5%

SOLUTION: 4% is of 5%, hence 4% stock yields of desired income. Since 4% stock yields only # of desired income, it must be bought for of its face value; of $100 $80, a share.

=

Ans.

32. How much may be paid for 3% stock to yield 4% income?

33. At what rate of discount must 5 % bonds be purchased so as to net an income of 61% on the investment?

34. At what price must 6% bonds be bought to yield 5% income?

COMPOUND PROPORTION

212. TO THE TEACHER. Several solutions are given in order to drill pupils in accuracy and readiness in the various forms of questions and statements required in different problems. The use of correct and concise forms of expression is of more importance here than the getting of the answer.

Study Recitation

1. If 10 men can build 50 rods of wall in a certain time, how many men can build 80 rods of wall in the same time? STATEMENT:

50 80 10: ?

2. If 10 men can build a wall in 12 days, how many men can build it in 16 days?

The above problems are problems in simple proportion. Each statement is the statement of a simple proportion. Combining the two problems into one, we have the following problem :

3. If 10 men can build 50 rods of wall in 12 days, how many men can build 80 rods of wall in 16 days?

This problem is a problem in compound proportion. It will be noticed that in each of the two statements given above, the third term is 10. The first ratio in the first statement differs from the first ratio in the second statement. Bringing these statements together as the statement of a compound proportion, we have the third term 10, and the first and second terms, a compound ratio.

Multiplying the two ratios together, term by term, we have: (50 × 16): (80 × 12) : : 10 : ?

have:

Multiplying the means together, and dividing by the extremes, we 80 × 12 × 10 50 × 16

It will thus be seen that problems in compound proportion result from combining two or more problems in simple proportion.

In solving such problems, it is best to use the fractional form of solution. This gives us the last expression above, without the preceding steps. Notice that in the above problem there are two numbers representing rods, two numbers representing days, and one number representing men, and that what is asked for is the number of men. In getting the statement for multiplication, proceed as in simple proportion, using the third term first with the two numbers representing rods.

Q. If 10 men can build 50 rods of wall, will it take a greater or a less number to build 80 rods of wall in the same time? Ans. A greater number, or 8 x 10 men.

80

× 10. 50

Write the expression 8 x 10 men at the right as follows:
Next deal with the men and days. Drop out everything else.
Q. If 10 men can build a wall in 12 days, will it take more or less
Ans. Less men, or 12 x 10 men.

men to build it in 16 days? Write this fraction, 1,

it now stands :

at the left of the expression above, so that

12 80

X × 10.

16 50

Canceling and performing the indicated operations, we secure the result, 12.

4. If 18 men build 75 rods of fence in 10 days of 9 hours each, how many hours a day must 24 men work to build 144 rods in 12 days?

In this problem, hours a day are called for. We have two numbers, 18 and 24, representing men; two numbers, 75 and 144, representing rods; two numbers, 10 and 12, representing days; and one number, 9, representing hours. Each set of two like numbers constitutes a ratio, and must be compared with the number representing hours.

Q. If 18 men build a fence working 9 hours a day, must 24 men work more or less hours a day to build it in the same number of days? Ans. Less, or as many hours.

18

× 9.

24

Q. If a number of men build 75 rods of fence working 9 hours a day, must they work a greater or less number of hours a day to build 144 rods in the same number of days? Ans. A greater number of hours a day, or as many hours. Write 14 at the left of the expression above.

144 18
X
75 24

X 9. Q. If it requires a number of men 10 days working 9 hours a day to build a fence, will it take a greater or a less number of hours a day if they work 12 days? Ans. A less number, or 12 as many hours. Prefix this fraction to the others with the multiplication sign. 10 144 18 X 12 75 24

X × 9.

5. If 37 horses in 5 days eat 75 worth of oats, how much will it cost to feed 60 horses on oats for 8 days?

Q. In this problem what is asked for? Ans. Cents.

In the solution of these problems begin the question with the statement given in the problem.

Q. If 37 horses eat 75 worth of oats in a certain time, will it cost more or less to feed 60 horses the same time? Ans. More, as much. Write this fraction at the left of 75, with the sign of multiplication between them.

60

× 75.

37

Q. If a number of horses eat 750 worth of oats in 5 days, will it cost more or less to feed the same number of horses 8 days? Ans. More, § as much. Write at the left of the other numbers.

60 X × 75. 37

6. If 30 masons in 15 days can build a wall 387.5 ft. long, what is the length of a wall that can be built by 48 masons in 20 days?

What is asked for in this problem? What is the number to be multiplied by the fractions to be found?

If 30 masons can build a wall 387.5 ft. long in a given time, will 48 masons build a greater or less length of wall in the same time? What is the resulting fraction?

If a number of masons can build a wall 387.5 ft. long in 15 days, can they build a greater or less length of wall in 20 days? What is the resulting fraction?