MISCELLANEOUS EXAMPLES. 1. What number increased by of itself gives 20? 3. The sum of two numbers is 54 and one of the numbers is B times the other; what are the numbers? 4. Three roods and ten rods are what part of an acre? 5. The difference between two numbers is 37 and the smaller number is 12; what is the larger? 6. What number multiplied by 331 gives 1000 ? 7. What number divided by 37 gives 64? 8. What is the greatest common divisor of 84 and 144? 9. What is the least common multiple of 72 and 364? 10. What is the interest of $756.64 for 8m. 17d.? 11. The difference between two numbers is 25, and the smaller number is 10; what is the larger? What the sum of the two numbers? 12. The difference of two numbers is 563492, and the larger number is 3642538; what is the smaller? What the sum of the two numbers? 1st Ans. 3079046. 13. How many bricks 8 inches long, 4 inches wide, and 2 inches thick, will be required to build a wall 20 feet long, 16 feet high, and 2 feet thick? 14. How many bricks whose dimensions are 8', 4′, and 2′, will it take to build the walls of a house 40ft. long, 28ft. wide, and 22ft. high, the walls to be 1ft. 6′ thick, and no allowance made for doors and windows? 15. The salary of the President of the United States is $25000 per annum; what sum may he expend daily, and yet save $41560 in one term of office, viz. 4 years? Ans. $40. 16. What number, multiplied by of itself, will produce 121⁄2? 17. What number, multiplied by of itself, will produce 27? 18. How many square feet of boards will it take to lay a floor 20ft. long and 16ft. wide? 19. How large a square floor can be laid with 676 square feet of boards? 20. The fore wheel of a carriage is 9 feet, and the hind wheel 10 feet in circumference; how many times will each turn round in running from Boston to Andover, 20 miles? 21. A rectangular piece of land, containing 60 acres, has its length to its breadth as 3 to 2, what are its length and breadth? 22. Bought a cask of molasses, containing 84 gallons, for $28; but 9 gallons having leaked out, at what price per gallon must I sell the remainder to gain $4.25 ? Ans. 43 cents. 23. If a pipe 6 inches in diameter will discharge a certain quantity of water in 4 hours, in what time will a 4-inch pipe discharge the same quantity? Ans. 9 hours. 24. In 12gal. 3qt. 1pt. 2gi., how many gills? Ans. 2, 2, 3, 3, 5, 11, 13. 27. Reduce, 1, 1, and to equivalent fractions having the least common denominator. 28. Reduce 3s. 4d. 2qr. to the fraction of a pound. 29. Reduce of a pound to shillings and pence. 30. Add lb. oz. dwt. gr. together. 31. From lb take 13. 32. A colonel, arranging his men in a square battalion, found that he had 31 men remaining; but, increasing the rank and file by 1 soldier, he wanted 20 men to make up the square. Of how many men did his regiment consist? Ans. 656. 33. How shall I mark gloves that cost me 80c. per pair so that I may discount 333 per cent. from the marked price and yet gain 25 per cent. on the cost? Ans. $1.50. 34. Suppose that in a shower the water falls to the depth of 2 inches, how many gallons will fall upon a township that is 6 miles square, each gallon containing 231 cubic inches? 35. How many bricks 8′ long, 4' wide, and 2′ thick, will be required to build a house 32ft. long, 24 ft. wide, and 20ft. high, the walls being 1ft. 4′ thick, the house having 2 doors, each 4ft. wide and 8ft. high, and 21 windows, each 3ft. wide and 6ft. high, no allowance being made for the space occupied by the mortar? 36. What is the square root of the square root of 16 times 81? 37. If a horse travels 64 miles per hour, how many hours will it take him to travel as far as a rail car will run in 6 hours, the car running 22 miles per hour? 38. Light moves about 192000 miles per second and sound about 1142 feet per second; what is the ratio of the velocity of light to that of sound? Ans. 887705144. 39. What is the square root of 4 times the square of 8? 40. What is the cube of the square root of 25? 41. What is the cube root of the square of 8? 42. What is the square of the cube root of 8? 43. Two ships sail from the same port, one due north and the other due west, one at the rate of 6 miles and the other 8 miles per hour. Suppose the surface of the ocean to be plane, how far apart are the ships in 10 hours? 44. An army consists of 59049 men; how many shall be placed in rank and file to form them into a square? 45. What is the diameter of a circular pond which shall contain 36 times as much area as one 20 rods in diameter? 46. What is the mean proportional between 16 and 64? 47. What is the third proportional to 3 and 30? 48. A ladder 41 feet long, will reach a window 40 feet high on one side of a street, and, without moving the foot, it will reach a window 9 feet high on the other side; how wide is the street? Ans. 49ft. 49. What is the difference in the expense of fencing a circular 40-acre lot and one of the same area in a square form, the fence costing 50c. per rod? 50. Sold to J. P. F. goods as follows: When shall he pay me the balance of the debt? 51. What is the side of a square equivalent in area to a rectangular field, which is 81 rods long and 49 rods wide? 52. Sent an invoice of goods to my agent in Liverpool which he sold for $25000; what sum can he invest for me, his commission for selling being 2 per cent. and for investing 1 per cent.? 53. A house worth $8000 is insured for its value; what is the premium at 3 of 1 per cent.? 54. What is the amount of $325, at 6 per cent., compound interest, for 3yr. 8m. 12d.? 55. $1200. Boston, May 12, 1860. For value received of A. B. I promise to pay him, or his order, one thousand two hundred dollars, on demand, with interest. CHARLES Dane. INDORSEMENTS: Aug. 18, 1860, $300; Dec. 18, 1860, $10; May 6, 1861, $16.50; June 24, 1861, $400; Dec. 24, 1861, $100; what was due Apr. 12, 1862? 56. A bushel measure is 18 inches in diameter and 8 inches deep; what are the dimensions of a similar measure that holds half a peck? Ans. 9țin. diameter; 4in. deep. 57. Sold a lot of goods for $100 and thereby gained 25 per cent.; what per cent. should I have gained, had I sold them for $120 ? 58. A garden whose breadth is 5 rods, and whose length is 13 times its breadth, has a wall 3 feet thick and 4 feet high, around it, outside of the line; what was the cost of this wall at 34c. per cubic foot? 59. What will be the cost of digging a ditch around the abovementioned garden, within and adjacent to the wall 3 feet wide and 23 feet deep, at § of a cent per cubic foot? 60. What would be the cost of walling the above-mentioned garden, the central line of the wall to be on the bounding line, the wall to be 3 feet thick and 33 feet high and to cost 61c. per cubic foot? 61. A hare has 45 rods the start of a hound, but the hound runs 12 rods while the hare runs 9; how many rods will the hare run before the hound overtakes him? 62. A hare has 32 rods the start of a hound, but the hare runs only 16 rods while the hound runs 20; how far will the hound run before he overtakes the hare? 63. What is the interest of $72.50 from Aug. 8, 1861, to July 20, 1862? 64. A, B, and C engage to do a piece of work; A can do it in 20 days, B in 24, and C in 30. In what time can the three' together do the work? 65. A gentleman left his son an estate, of which he spent in 1 year and of the remainder in 6 months more, when he had only $1400 remaining; what was the value of the estate? 66. The commander of a besieged fortress has 2 lb. of bread per day for each soldier for 45 days, but wishes to prolong the seige to 60 days; what must be the allowance per day? 67. A man sold a watch for $60, which was of its cost; what was lost by the transaction? 68. If a bar of silver 1ft. 6in. long, 4in. wide, and 2in. thick, is worth $1240, what is the value of a bar of gold 1ft. 3in. long, 8in. wide, and lin. thick, the weight of a cubic inch of silver being to the weight of a cubic inch of gold as 10 to 19, and the value per ounce of silver being to that of gold as 2 to 33? 69. Jan. 1, 1861, A, B, and C form a partnership for 1 year, and each furnishes $2000. May 1, A furnishes $1000 more; June 1, B furnishes $1500 and C withdraws $500; Oct. 1, A withdraws $500, and B and C furnish $1000 each. Having gained $3000, at the close of the year the partnership is dissolved. What is each partner's share of the gain? . 70. How many gallons of wine at 6, 10, 15, and 20s. per gal. may be taken to form a mixture of 95 gallons worth 12s. per gallon? 71. Find the difference in time due to a difference of 17° 20′ 40" in longitude. 72. The difference in the time of two places is 3h. 18m. 15sec.; what is the difference in longitude? 73. A merchant bought a number of bales of velvet, each containing 12917yd., at the rate of $7 for 5yd., and sold them out at the rate of $11 for 7yd., and gained $200 by the bargains; how many bales were there? Ans. 9. |