17. What must be the market value of 3 p. c. stock in order that, after deducting income tax of 7d. in the £, it may yield 3 per cent. interest?

18. What is the yearly interest on £76,978 bought into the 3p. c. at 77? What sum would be gained by selling out at 77?

19. How much must a 3 p. c. stock fall below par in order that a broker, charging p. c. fees, may get 4 p. c. interest for my money?

20. If a man receives 4 p. c. interest on his capital by investing in the 3 p. c., what is the price of stock, and how much stock can be bought for £1200?

21. If I transfer £2000 stock from the 3 p. c. at 99 to the 3p. c. at 86ğ, what is the difference in my income?

22. What sum muşt a person have invested in the 3 p. c. at 90 if a transfer of of his capital to the 4 p. c. at 115 would increase his income £7?

23. What percentage and what amount of interest will an investor receive, who puts his capital (£19,500) into the 3 p. c. standing at 89%, commission being per cent.?

24. How much money will be required to purchase £8621, 10s. 5d stock in the 3 p. c. standing 871, and what income will the purchaser receive?

25. A man invests £9600 in the 4 p. c. at 80, and at the end of each year invests the dividend which becomes due in the same stock. Find his dividend at the end of the third year, the funds remaining all the time at 80.

26. Find the simple interest for 7 years on £10,416, 135. 4d of stock sold out when standing at 96, and the resulting sum invested in 51 p. c. debentures at par.

27. The value of money increases from 4 p. c. to 5 p. c.; supposing this to have a corresponding influence on the funds, how much ought the 3 p. c. consols to fall?

28. A capitalist invests £5187, 10s. in the 3 p. c. at 83; he transfers of this sum to the 4 p. c. at 96. Find the alteration in his income.

29. Two persons buy respectively with the same sums of money into the 3 and into the 3 per cents., and get the same amount of interest, the 3 per cents. standing at 75; what do the 3 per cents. stand at?

30. If the 3 per cents. are at 92, and the 4 p. c. at 1234, what sum is one investing when the difference of income is one shilling?

31. What price are the 3 per cents. at when a man buys stock producing £17, 10s. a year for £401, 13s. 4d.?

32. The 3 per cents. standing at 981, what sum must be invested in them to produce an annual income equal to the whole interest on £500 for 14 years at 2 per cent. ?

33. B has a fortune which yields £288 a year in the 3 p. c. at 92; A has £6633 ready money. How much per cent. must A's money be increased that it may equal the selling price of B's?

34. If I purchase £1000 3 p. c. consols standing at 967, and selling out again when they have fallen to 82, invest in 34 p. c. stock at par, what do I lose by the transaction in capital, and what do I gain in income?

35. What income would be derived from laying out £10,587 10s. in 5p. c. stock standing at 105, broker's commission being per cent. ?

36. If a broker sells 1066, 13s. 4d. out of the 3 p. c. at 934, how much will he require to add to the sum thus realized in order to purchase £1150 in the 3 p. c. at 92? What will be the increase of income when the transaction is completed?

37. By investing a certain sum in the 3 per cents. at 911, a man obtains an income of £464; what would he obtain by investing an equal sum in the 4 per cents. at 96?

38. If I sell out my property in the 3 p. c. standing at 961, and invest the proceeds in 100 railway stock standing at 55, and paying a dividend of 13 p. c.; if be allowed for brokerage in each case, will this transaction increase or diminish my income?

39. A's fortune, if increased 6 p. c., would be equal to of the selling value of B's, which yields £576 a year in the 3 p. c. standing at 92; what is A's fortune?

40. If I withdraw my fortune (£3000) from 4p. c. stock standing at par, and re-invest in 4 p. c. stock standing at 96,

the transfer expenses paid out of my capital being £9, 4s. 7 d., what is the effect on my income?

41. What sum will be left out of the amount realized by selling 1000 stock standing at £91, if enough be set aside to clear £43, 125. in 13 years at 3 p. c. per ann. ?

18

42. I have £26,080 to invest, and the 3 p. c. are at So; I wait 11 days for a fall, but the funds rise steadily p. c. per day, and on the 11th day I invest, and am now compelled to pay a brokerp. c.: what loss of capital do I sustain by my delay, and what will be the amount of my annual income from the investment?

43. Explain the following extract from the Times:-'Consols, which left off last evening at 943 to 1, opened at 94 to, and remained without variation till the close of business;' and find the alteration in the income of a capitalist who has 200 shares in a railway bought at £100 a share, by his selling them all at £46 per share when they are paying 2 p. c., and investing in the 3 p. c. at 92.

44. Required an annual income of £460. I have my choice of investing in three per cent. stock at 87, or in shares costing £233 each, on each of which a dividend of £7, 13s. 4d. is paid annually; what sum must I invest in the former, and what in the latter, to produce the required income?

45. I bought into the 3 p. c. standing at 921, and sold out again when they had risen to 962, improving my income by investing the proceeds in 5 p. c. stock at par to the extent of £183, 15s. per ann.; what amount of stock did I purchase in the 3 p. c., and what had I to pay for it?

46. To what fraction of 10s. will 18 of a farthing in the £, on the income derivable from investing £7927, 10s. in the 3 p. c. at 94, amount?

47. If I possess £1000 stock in the 3 p. c. consols, purchased at 96, and sell out when they have fallen to 82, how much do I lose on my purchase money, and what interest shall I receive for the sum realized by the sale, if I invest it in 5 railway stock at par?

48. Wanted an income of £61, 53. million of money must be invested in the 3 at 933, to produce it?

E

What fraction of a

per cents., standing

49. Explain the nature of 'Stock'-(1) If the three per cents. are at 89, what should be the price of the three and a-half per cents.? If the latter are at 104, which is the better investment? What dividend will a man receive who invests £3107 in each?

PERCENTAGES.

1. How much p. c. is 7 of 16, 69 of 300, 187.98 of 56.394?

2. In standard gold, 11 parts out of 12 are pure gold; what percentage is there of alloy?

3. The former population of a parish was 1775, now it is 1917; what has been the increase per cent.?

4. The population of a town in 1857 was 15,786, and in 1877 it was 19,670; what was the increase per cent.?

5. How much per cent. is (a) 2d. in the shilling, and (₹) 2s. 9d. in the £?

6. What is the percentage on 378 at 5, at 175, at 20·625, and at ·3?

7. A cask of rum containing 78 galls. leaked 29 p. c. ; what quantity remained in the cask?

8. What number does 7.875 p. c. on a million and threequarters amount to?

9. A clock goes '04 p. c. too fast; how much will it gain in a day?

10. How often will a tumbler containing 1 of a gill be filled out of a cask which originally contained 20 galls., but had leaked 10 p. c.?

11. If 113 galls. of spirits be diluted with 37 galls. of water, what are the percentages of spirit and water?

12. If a tradesman takes off 91 p. c. for ready money payment, what should he be willing to accept down for a bill of £81, 5s.?

13. Find the percentage of each ingredient, and the quantity of each ingredient, in 11 cwts. of adulterated coffee, each pound of which contains 3 ozs. of chicory.

14. A gardener sows a drill 44 yards in length with a quart of peas; the plant fails partly, and on transplanting he finds that he has a row of only 108 feet long: what does he lose per cent. ?

15. If in a school of 360 children, 27 play truant, and 63 are sick, what percentage of non-attendance is due to truancy and to sickness respectively?

16. If the duty on an article be in 5 consecutive years 193, 20, 17.5, 231, and 18.6 p. c., what is the average yearly duty per cent. ?

17. If 1185 parts of copper be added to 715 parts of tin and 100 parts of zinc, what is the percentage of each metal in the compound?

18. The population of a country amounts to 26,584,000, and increases at the rate of 10 p. c. in every 10 years; what will it amount to in 30 years?

19. If the population of the globe be eleven hundred millions of souls, and 3,300,000 of these be Jews, 172,700,000 Mahometans, 337,700,000 Christians, what is the percentage of each?

20. Between 1821 and 1831 the population of a certain town increased by 24 p. c., and in the last-named year amounted to 62,093; what was the population in 1821?

21. A grocer uses for a lb. weight one which weighs only 1575 ozs.; to what extent per cent. are his customers defrauded?

22. Find the percentage of alloy in sterling gold, if 10 dwt. contain 21 grains of alloy.

23. What percentage of 89 is 056, and what percentage of the square root of '04 is the square of ∙19?

24. An army consists of a number of men equal to the quotient of 72 by 0045; what percentage of men may be killed so as still to leave a number equal to the square root of 225 millions?

25. The annual consumption of meat in the United Kingdom being 33,697,785 cwt., what amount of saving would be effected to the community by a reduction of 21d. per lb., and what percentage would be saved by such reduction if we take the present average price of meat 91d.?

26. A certain officer has a salary of £1250 per ann.; what is the salary of his chief clerk, which is 44 p. c. of his own? The junior clerk's salary is 78 p. c. of the senior's; what is the junior's salary per week?