32. A cannon-ball 15 inches in diameter weighs 460 pounds; what is the weight of a similar ball 5 inches in diameter, the weight being as 53: 153?

33. A board with tapering sides measures 30 ft. in length; its width at one end is 18 inches, and at the other end 24 inches, the thickness being 14 inches; how many board feet does it contain?

34. I am to receive $5000 out of an estate which will require 18 months for settlement; what is the present value of my legacy, money being worth 6%?

35. A farmer buys a team of horses and a wagon at auction, on 9 months' credit; the amount of his bill is $420; how much would be required to pay it at the end of 3 months, money at 7%?

36. A mechanic finds that he can save $12 a month; if he wishes to build a house, how large a sum can he borrow so as to pay the interest with his savings?

37. Two steamers sail westward from the same port, one at the rate of 195.25 miles a day, and the other at the rate of 164.5 miles; in how many days will they be 2618 miles apart?

38. A railroad employee has had his wages twice reduced 10%; he now receives $2.02 per day; what did he get before the reduction?

39. A machinist now earning $2.42 per day has had his wages twice increased 10%; what did he get before the increase?

40. How many square feet of tin will cover a roof 16 feet wide and 30 feet long, allowing 5% for joints and waste?

41. What is the value of £1100 19 s. 6 d., at $4.8665 per pound sterling?

42. A merchant's stock of goods cost him $78965.34. His sales amount to $60543.25, and the goods on hand cost $32575.69. What is his per cent. of profit on the goods sold?

43. Lent a man $5000 for 3 years; at the end of that time he paid me $6350; what was the rate of interest? 44. A merchant buys goods as follows:

June 1, 1876, $1500 on 9 months.

October 27, he gives a note for the whole amount. What should be the time of the note?

45. If a mechanic invests his money in a building society that earns annually 8 per cent. compound interest, how much will he save in 9 years, his deposits being $120 a year?

46. A railroad company wishes to build a tank that will contain 4000 gallons of water; what must be the depth, if the length is 16 feet and the width 8 feet?

47. A merchant sold goods for $1000, after allowing 5 per cent. for prompt payment; what did the goods cost him, he having gained 20 per cent.?

48. What weight can be sustained by a balloon that weighs 500 lb., the shape being that of a sphere, whose diameter is 60 feet; the balloon being filled with a gas which weighs of an ounce to the cubic foot, air weighing 1 ounces to the cubic foot?

49. A vessel sails 8 miles an hour in still water; going up stream it requires 72 minutes to sail 8 miles; how long will it require, going down stream?

50. A bankrupt offers to pay a creditor, to whom he owes $10000, 40% in cash, or guaranteed notes at 3, 6, and 9 months for $1500 each; which is the better offer, and by how much, money being worth 10%?

51. My house rents for $420 a year; the taxes and repairs amount to $75 a year; allowing 6 per cent. per annum for interest, what is the value of the house?

52. How many bricks, 8 inches long, 4 inches wide, and 24 inches thick, will be required in building a house 40 feet long, 20 feet wide, and 30 feet high, the walls being 131 inches thick, and the courses of mortar of an inch thick; the house having 4 doors, each 7 feet high and 46 inches wide, and 18 windows, each 38 inches wide and 70 inches in height?

53. How many feet of boards will it require to lay two floors in the above house, each floor being of the full size of the inside dimensions of the building; the allowance for waste being one-sixth?

54. How many bricks 81 × 43 × 23 in. will it require for a pavement 20 feet long and 8 feet wide?

55. How many cubic quarter inches are there in one cubic inch?

56. A man working on a railroad earns $1 a day more than his board, paying 50 cents a day for the latter; at the end of 60 days he has saved $25; how many days was he idle?

57. Which is the better investment, a 6% stock bought at 108, or a 5% stock at 90, the par value being 100?

58. How many yards of carpet 27 inches wide will it require to cover the floors of a room 26 ft. long, and 11 ft. 3 in. wide; and what will be the cost, at $2.25 a yard?

59. A house that cost $3800 is rented for $35 a month. The owner pays $65 a year for taxes and $38 for repairs; what per cent. does the house pay on its cost?

60. What sum must be invested in a 10 per cent, stock that costs $134, the par value being $100, to derive an income of $1000 per annum?

61. How many tons of clover hay can be packed in the upper part of a barn, level with the eaves, the rectangular dimensions being 27 feet by 40 feet, and the height 11 feet?

62. How much farther does a man walk in going round two sides of a square field containing 5 acres, than in walking diagonally across the field from opposite corners?

63. What is the equated time of the following account, and the cash balance May 25, 1877, allowing 6% interest?

64. William Thompson, John Henry, and Joseph Wilkins formed a partnership with a capital of $20000; Thompson's share of the capital is $3000, Henry's share is $15000, and Wilkins contributes $2000. At the end of 3 months Wilkins contributes $5000 to supply the place of an equal amount withdrawn by Henry. Thompson closes his connection with the firm and receives his $3000 at the end of 10 months. At the end of a year they divide $6000. What is the amount received by each, allowing Thompson his fair share of the gains?

ALLIGATION.

Alligation treats of the mixture of articles of different values to form a compound of a certain value.

CASE I.

To find the average price of a mixture, the quantity and cost of each article being given.

1. A grocer mixes 5 pounds of sugar worth 10 ct. a pound, with 16 pounds worth 12 ct. a pound, and 25 pounds worth 16 ct. a pound; what is the value of one pound of the mixture?

Find the total value of all the articles, and divide by the number which denotes the sum of the articles.

2. A miller mixes 20 bushels of wheat worth $1.00 per bushel with 25 bushels worth $1.10 and 30 bushels worth $1.25; what is the value of a bushel of the mixture?

3. If I mix 26 gallons of oil worth 75 ct. a gallon, 32 gallons worth 80 ct. a gallon, 50 gallons worth 40 ct. a gallon, and 150 gallons worth 90 ct. a gallon, what is the value of a single gallon of the mixture?

4. By accident some cigars were mixed, worth 8, 10, and 12 dollars per hundred respectively, there being 200 of the first, 100 of the second, and 200 of the third; how should they be sold apiece to gain 20 per cent. on the cost?