MISCELLANEOUS PROBLEMS. Note.—The following problems are selected mainly from sets of examination questions supplied to the author for this purpose by one hundred school principals and superintendents. 1. Each edge of a cube is diminished by 10 of its length. (a) By what fraction of itself is the volume diminished ? (b) By what fraction of itself is the surface diminished ? 2. How many cubical blocks, each edge of which is į ft., are equivalent to a block 8 ft. long, 4 ft. wide, and 2 ft. thick ? 3. A ladder 78 ft. long stands perpendicularly against a building. How far must it be pulled out at the foot that the top may be lowered 6 ft. ? 4. A merchant sold of a quantity of cloth at a gain of 20% and the remainder at cost. (a) His gain was what per cent of the cost ? (b) If he gained $7.29 what was the cost of the goods ? 5. What must I pay for 4% stock to get 5% on the investment? 6. The cubical content of one cube is eight times that of another: (a) How does an edge of the first compare with an edge of the second ? (b) How does the surface of the first compare with the surface of the second ? 7. A creditor receives $1.50 for every $4.00 that is due him and thereby loses $301.05. (a) What was the sum due him? (b) What per cent of the debt did he lose ? 8. At $20 per M., board measure, what is the cost of the following: A stick of timber 30 feet long and 14 inches square, and a plank 18 feet long, 8 inches wide, and 21 inches thick ? 9. A and B hire a pasture for $85; A puts in 8 cows and B puts in 12 cows. How much should each pay? 10. Simplify the following: į of of 1). 11. Seven times John's property plus $32200 equals 21 times his property. How much is he worth? 12. Two men engage in business with a joint capital of $5000. The first year's gain was $1760, of which one received $1056. How much capital did each furnish? 13. Thirty-five per cent of the men in a regiment being sick, only 637 men were able to enter battle. How many men were there in the regiment ? 14. A lawyer collected 80% of a debt of $2360 and charged 5% commission on the sum collected. How much did the creditor receive ? 15. Write a negotiable note for $500, making yourself the payee and James J. Rogers the maker. Interest at the legal rate. 16. A speculator bought stock at 25% below par and sold it at 20% above par. He gained $1035. How much did he invest? 17. What is the rate per cent per annum if $712 gains $142.40 in 3 yr. 4 mo.? 18. A person asked for a lot of land, 40% more than it cost him, but finally reduced his price 15% of his asking price and sold it, making $9.50. (a) What per cent did he make? (b) How much did the land cost him ? (c) How much did he receive for it? 19. Purchased stock at a premium of 8 per cent. What rate of interest do I receive on the investment if it pays an annual dividend of 6% ? 20. Find the volume of a cube the area of whose surface is 100.86 square inches. 21. How many apples must a boy buy and sell to make a profit of $9.30, if he buys at the rate of 5 for 3¢ and sells at the rate of 4 for 3¢ ? 22. Find the cost of 1875 lb. hay at $6.50 per ton. 23. What is the interest on $1200 from Sept. 21, 1898, to May 5, 1899, at 7% per annum? 24. The area of a square field is 10 acres. What is the distance diagonally across the field ? 25. A “drummer” earns $2500 a year. One thousand dollars of this sum is a guaranteed salary. The remainder is his commission of 5% on his sales. What is the amount of his annual sales ? 26. The area of a triangle is 325 square inches. Its base is 25 inches. What is its altitude ? 27. Gave 6 lb. butter, worth 364 a pound, for 3} gal. oil. What was the cost of the oil per gallon ? 28. A can build a certain wall in 10 days; B can build it in 12 days, and C in 15 days. In how many days can they build the wall working together ? 29. A horse and a carriage together cost $550. The horse cost as much as the carriage. Find the cost of each ? 30. A man willed of his property to his wife, į of the remainder to his daughter, and the rest to his son. The difference between the wife's portion and the son's portion was $12480.33] How much was the man worth ? 31. (a) How many loads, each containing a cubic yard, will be required to fill a street 150 feet long, 50 feet wide, and 24 feet deep? (b) How much will it cost at 18¢ per cubic yard ? 32. A right triangle has two equal sides. Its hypothenuse is 100 rods long. (a) Find one of its two equal sides. (b) Find its area. 33. What is the ratio of the area of a circle to the area of its circumscribed square ? 34. What is the ratio of the square of the radius to the square of the diameter of the same circle ? 35. A man's tax is $37.50. The rate of tax is 15%. Property is assessed at 30% of its value. What is the man's property worth? 36. A field containing 160 acres is 40 rods wide. At 45° a rod, how much less would it cost to fence a square field containing the same number of acres ? 37. My agent in Baltimore having sold a consignment of grain, after taking out his commission at 3% and paying a freight bill of $1,125.00, sent me a draft for the amount due me—$19,536.00. For how much was the grain sold ? 38. How many pickets 4 inches wide, placed 3 inches apart, are required to fence a garden 21 rods long and 14 rods wide ? 39. At $6.30 a cord, what is the value of wood that can be piled under a shed 50 ft. long, 25 ft. wide, and 12 ft. high? 40. Find the curved surface of a cylinder 6 ft. in diameter and 12 ft. long. 41. (a) What is the bank discount and (b) what are the proceeds on a note for $125 payable in 90 days, the rate of discount being 8%? 42. If sugar that cost 54 a pound is sold at 18 lb. for a dollar, what is the gain per cent ? 43. What is the area of a circle 30 inches in diameter ? 44. What is the volume of a 12-inch globe ? 45. What is the circumference of a circle that is 40 rods in diameter ? 46. The “number belonging" in a certain school was 74. Five were absent in the forenoon and seven in the afternoon. What was the per cent of attendance for the day? 47. A rectangular piece of land 41 rods by 24 rods is how many acres ? 48. Find the value of x in the following proportion: 17.5 : 25 :: 3 : 40. 49. A circular 3-mile race track encloses how many acres ? 50. If the same number be added to the numerator and to the denominator of a proper fraction, will it make the fraction greater or less ? 51. A certain roof is 40 feet long and, measured horizontally, 24 feet in width. A 2-inch rain-fall should give how many inches in depth in a cistern that receives the water from this roof, the cistern being 6 feet long and 4 feet wide ? 52. A can do a piece of work in ý of a day. B can do the same amount of work in ] of a day. In what part of a day can both working together do the piece of work ? 53. C can do a certain piece of work in 3 days. D can do the same amount of work in 4 days. In how long a time can both working together do the piece of work ? 54. If the 6-foot drive wheel of a locomotive makes 840 revolutions in moving a certain distance, how many revolutions will a 7-foot wheel make in moving the same distance? |