40. A and B found a watch worth $45, and agreed to divide the value of it in the ratio of to §. was each one's share? How much Ans. A's, $20. B's, $25. 41. A man received $33.25 interest on a sum of money, loaned 5 yr. previous, at 7%. What was the sum loaned? 42. The diameter of a ball weighing 32 What is the diam. of a ball weighing 4 lb. ? Ans. $95. lb. is 6 in. Ans. 3 in. 43. Divide $360 in the proportion of 2, 3, and 4. 44. If by working 63 h. a day a man can accomplish a job in 12 da., how many days will be works 8 h. per day? required if he Ans. 9 da. 45. An open court contains 40 sq. yd. stones, 9 in. sq., will be required to pave it? How many Ans. 640. 46. A drover paid $76 for calves and sheep, paying $3 for calves and $2 for sheep; he sold 3 of his calves and of his sheep for $23, and by so doing lost 8% on their cost. How many of each did he purchase? 47. If a cistern, 171⁄2 ft. long, 101 ft. broad, and 13 ft. deep, holds 546 bbl., how many barrels will a cistern hold which is 16 ft. long, 7 ft. broad, and 15 ft. deep? 48. If 12 men, working 9 h. a day for 155 da., were able to execute of a job, how many men may be withdrawn, and the rest be finished in 15 da. laborers are employed only 7 h. a day? more, if the Ans. 4 men. 49. A general formed his men into a square, that is, an equal number in rank and file, and found that he had 59 men over; and increasing the number in both rank and file by 1 man, he wanted 84 men to complete the square. How many men had he? Ans. 5100. 50. Divide $630 among 3 persons, so that the second shall have as much as the first, and the third as much What is the share of each? as the other two. Ans. 1st, $240. 2d, $180. 3d, $210. 51. I bought wheat at $1.50 per bushel, corn at $.75 per bushel, and barley at $.60 per bushel; the wheat cost twice as much as the corn, and the corn twice as much as the barley; of the sum paid, $ 243 and of the whole was for the wheat, and $153 and 11⁄2 of the whole was for the corn. How many bushels of grain did I purchase? Ans. 756. 52. I bought a hogshead of molasses for $28, and 7 gal. leaked out. At what rate per gallon must the remainder be sold to gain 20%? 53. 20% of of a number is how many per cent of 2 times of 14 times the number? Ans. 7. 54. B and C, trading together, find their stock to be worth $3500, of which C owns $2100; they have gained 40% on their first capital. What did each put in? Ans. B, $1000. C, $1500. 55. If the ridge of a building is 8 ft. above the beams, and the building is 32 ft. wide, what must be the length of the rafters ? 56. I paid $375, at the rate of 21%, for insurance on a cotton factory and the machinery. For what amount was the policy given? 57. If 12 workmen, in 12 da., working 12 h. a day, can make up 75 yd. of cloth, of a yard wide, into articles & of clothing, how many yards, 1 yd. wide, can be made up into like articles, by 10 men, working 9 da., 8 h. each day? Ans. 23 yd. 58. In 1 yr. 4 mo. $311.50 amounted to $336.42, at simple interest. What was the rate per cent? Ans. 6%. 59. Three persons engage to do a piece of work for $20; A and B estimate that they do of it, A and C that they do of it, and B and C that they do of it. According to this estimate, what part of the $20 should each man receive? Ans. A, $63; B, $ 10; C, $ 3}. 60. A grocer sells a farmer 100 lb. of sugar, at $.12 a pound, and makes a profit of 9%; the farmer sells him 100 lb. of beef, at $.06 a pound, and makes a profit of 10%. Who gains more by the trade, and how much more? Ans. The grocer gains $.445+ more. 61. A merchant bought goods in Boston to the amount of $1000, and gave his note, dated Jan. 1, 1890, on interest after 3 mo.; six months after the note was given he paid $560, and 5 months after the first payment he paid $406. What was due Aug. 23, 1892 ? 62. If of A's money is equal to B's is equal to of C's, and and D has $45 more than C, Ans. $66.63+. of B's, and of of C's is equal to of D's, how much has each? Ans. A, $378; B, $336; C, $360; D, $405. 63. A owed B $900, to be paid in 3 years; but at the expiration of 9 mo. A agreed to pay $300 if B would. wait long enough for the balance to compensate for the advance. How long should B wait after the expiration of the 3 years? Ans. 13 mo. 64. A certain clerk receives $800 a year; his expenses equal of what he saves. How much of his salary does he save yearly? 65. A merchant sold cloth at $1 per yard, and made 10% profit. What would have been his gain or loss had he sold it at $.87 per yard? Ans. Loss, 33%. Ans. 24. Ans. 3. 68. On a certain day the mercury in the thermometer stood as follows: from 6 till 10 A.M., at 63°; from 10 A.M. till 1 P.M., 70°; from 1 till 3 P.M., 75°; from 3 till 7 P.M., 73°; from 7 P.M. till 6 A.M. of the next day, 55°. What was the mean temperature of the day, from sunrise to sunrise? Ans. 627°. 69. A man owes $6480 to his creditors; his debts are in arithmetical progression, the least being $40, and the greatest $500. What is the number of his creditors, and what the common difference between the debts? Ans. 24 creditors, $20 difference. 70. Two ships sail from the same port; one goes due north 128 miles, and the other due east 72 miles. How far are the ships from each other? Ans. 146.86+ miles. 71. If 10 lb. cheese are equal in value to 7 lb. of butter, and 11 lb. of butter to 2 bu. of corn, and 14 bu. of corn to 8 bu. of rye, and 4 bu. of rye to 1 cd. of wood, how many pounds of cheese are equal in value to 10 cd. of wood? Ans. 550. 72. A and B traded until they gained 6% on their stock; then of A's gain was $18. If A's stock was to B's as to, how much did each gain, and what was the original stock of each? Ans. A's gain, $45; {B's 73. If 20 men, in 21 da., by working 10 h. a day, can dig a trench 30 ft. long, 15 ft. wide, and 12 ft. deep, when the ground is estimated at 3 degrees of hardness, how many men, in 25 da., by working 8 h. a day, can dig another trench 45 ft. long, 16 ft. wide, and 18 ft. deep, when the ground is estimated at 5 degrees of hardness? Ans. 84. 74. Wishing to know the height of a certain steeple, I measured the shadow of the same on a horizontal plane, 27 ft.; I then erected a 10-ft. pole on the same plane, and it cast a shadow of 2 ft. What was the height of the steeple? Ans. 1031 ft. 75. A can do a piece of work in 3 da., B can do 3 times as much in 8 da., and C 5 times as much in 12 da. In what time can they all do the first piece of work? Ans. & da. 76. A person sold two farms for $1890 each; for one he received 25% more than its true value, and for the other 25% less than its true value. Did he gain or lose by the sale, and how much? Ans. Lost $252. 77. Three men paid $100 for a pasture; A put in 9 horses, B 12 cows for twice the time, and C some sheep for 2 times as long as B's cows; C paid one half the cost. How many sheep had he, and how much did A and B each pay, provided 6 cows eat as much as 4 horses, and 10 sheep as much as 3 cows? Ans. C had 25 sheep; A paid $18; B paid $32. 78. A man purchased goods for $10500, to be paid in three equal installments, without interest; the first in 3 months, the second in 4 months, the third in 8 months. How much ready money will pay the debt, money being worth 7% ? Ans. $10203.94+. 79. A fountain has 4 receiving pipes, A, B, C, and D; A, B, and C will fill it in 6 hours, B, C, and D in 8 hours, C, D, and A in 10 hours, and D, A, and B in 12 hours; it has also 4 discharging pipes, W, X, Y, and Z; W, X, and Y will empty it in 6 hours, X, Y, and Z in 5 hours, Y, Z, and W in 4 hours, and Z, W, and X in 3 hours. Suppose the pipes are all open, and the fountain full, in what time would it be emptied? Ans. 6 h. 80. A farmer sold 50 fowls, consisting of geese and turkeys; for the geese he received $.75 apiece, and for the turkeys $1.25 apiece, and for the whole he received $52.50. How many were there of each? Ans. 20 geese, 30 turkeys. 81. There is an island 73 miles in circumference, and 3 footmen start together and travel around it in the same |