49. A son asked his father's age, the father replied, “Your age is 12 years, to which if g of both our ages be added, the sum will be equal to mine ;" what was the father's age? Ans. 52 years. 50. Three men, A, B, and C, undertake to.dig a ditch for $57.50. Now A and B together are supposed to do of the work, A and C, and B and C 18, they are to divide the money according to the proportion of the work done by each? how must it be divided? Ans. { A $25.00. C $20.00. 51. Thomas sold 150 pineapples at 33 cents a piece, and took no more money than Harry did for melons at 25 cents a piece; how many melons had Harry? Ans. 200 melons. 52. A person having spent in one year all his income and as much more, found that by saving of his income afterwards, he could in 4 years make good the deficiency, and have $20 left; what was his income? Ans. $1200. 53. A gatekeeper is to receive 6 cents for every wagon, 4 cents for every gig, 2 cents for every horseman, and I cent for every footman that passed the gate; at the end of the year he found that 3150 gigs had passed, and that 7 gigs passed when 5 wagons did, and 4 horsemen passed when 6 footmen did, and 5 footmen passed when three gigs did; what number of wagons, horsemen, and footmen passed, and how much did the gatekeeper receive? 3150 gigs, Ans. 2250 wagons, 5250 footmen, 3500 horsemen. Amount of toll $383.50. 54. A trader having increased his estate annually 10 per cent, for 7 years, finds himself worth. $19487.171; what was his capital at the commencement of the term? Ans. $1000. 55. A market-woman having bought a quantity of apples, at the rate of 250 for a dollar, and sold one half of them at 2 for a cent, and the remaining half at 3 for a cent, finds she has gained 14 cents by the transaction; how many apples did she buy? Ans. 840. 56. A man who was but slightly versed in numbers, bequeathed his estate, valued at $6500, to his wife and two children, as follows: to his wife, to his eldest son, and to the other; how much must they severally receive to fulfil the design of the testator? Ans. Wife $3000, eldest son $2000, youngest son $1500. 57. A man and his wife usually consumed a barrel of flour in 36 days, but when the man was from home it lasted the woman 90 days; how long would the man be alone in consuming it? Ans. 60 days. NOTE. The smallest common multiple of 36 and 90 is 180; then, since they both together consume 1 barrel in 36 days, in 180 days they will consume 5 barrels, and in the same time the woman will consume 2 barrels, leaving 3 barrels for the man to consume in 180 days; hence he will consume 1 barrel in 60 days. 58. A, B, and C can complete a piece of work in 15 days; A can do it in 30 days, and B in 40 days, in what time can C perform it? Ans. 120 days. 59. Joseph and Samuel together can do a piece of work in 18 days; Joseph alone can do it in 30 days; in what time can Samuel do it alone? Ans. 45 days. 60. A man meeting a boy driving a flock of geese, said, Good morning, sir, with your hundred geese; I have not a hundred, said the boy; but if I had as many more, and half as many more as I now have, and 2 geese besides, I should have a hundred; how many had he? Ans. 39 geese. 61. Suppose a man contracts to dig 80 rods of canal, 30 feet wide at the bottom, 40 at the surface, and 41⁄2 feet deep; what would it amount to, at 20 cents per cubic yard? Ans. $1540. (0.) 62. What will the digging of a cellar 40 feet long, 30 feet wide, and 6 feet 6 inches deep amount to at 22 cents per cubic yard? Ans. $63.555. 63. A sheepfold was robbed three nights successively; the first night, half the sheep were stolen and half a sheep more; the second night, half the remainder and half a sheep more; and the last night, they took half the remainder and half a sheep more, which reduced the number to 42; how many were there before any were stolen? Ans. 343 sheep. 64. Bought 1000 barrels of flour at $4.25 a barrel, and 68. A grocer gains 25 per cent. by selling tea at 87 cents Ans. 171 per cent. (6.) 70. A man exchanged 760 gallons of molasses, at 37 71. Sold 342 pounds of beef, at 6 cents per pound, and 72. A gentleman left his son a fortune, of which he 73. At what time between 5 and 6 o'clock are the hour Ans. 273 minutes past 5. 12 11 5 60 5-273 minutes. The minute hand must pass over 12 spaces to gain 11, but less to gain 5. 74. A man dying left a son and a daughter travelling in a foreign country; and making his will, ordered that if the son alone should return, of the estate should belong to him, and the remainder to his mother; but if the daughter alone should return, the mother was to have, and the daughter the remainder; now it so happened that the son and daughter both returned, by which the widow lost in equity $2400 more than if the daughter only had returned; what would have been her dowry had the son only returned? Ans. $1200. 75. A Greek epitaph designed for the tomb of Diophantus, is said to have stated that he passed of his life in childhood, in adolescence; that after and 5 years more had been passed in a married state, he had a son who lived to his own age, and whom he survived 4 years; what was then the age of Diophantus ? Ans. 84 years. 76. A person being asked the time of day, said that the time past noon was equal to of the time till midnight; what was the time? Ans. 36 min. past 5. 77. A person being asked the time of day, replied, the day is now 16 hours long, and the sun rises at 4 o'clock; now if you add of the hours that have passed since the sun rose to of those which must elapse before he sets, you will have the exact time of day; what was the time? In order to solve this question we reason thus, as the whole time that has passed since the sun rose, added to the whole time that must elapse before he sets is 16 hours, it follows that half the time that has passed since the sun rose, added to half the time that must elapse before he sets must be 8 hours, and therefore the time that has passed since the sun rose, added to the time that must elapse before he sets, will be more than 8 hours; hence the time passed is evidently greater than the time yet to elapse. Again, since of the time passed added to of the time yet to elapse, will give the time of day, or the whole number of hours that have passed since the sun rose, it is readily inferred that of the time passed must be equal to of the time yet to elapse, because of the time passed added to of the time passed must also give the time of day or number of hours that have elapsed since the sun rose. ! Wherefore 2 parts of the time passed are equal to 3 parts of the time yet to elapse, and the time yet to elapse is consequently equal to but of the time passed, it is therefore evident that the whole time passed added to of the time passed, (that is, of the time passed,) must be equal to 16 hours. And of course the time passed is 16 53 48 9 hours 36 minutes, That is, the time of day was 36 minutes past 1 o'clock. 78. A gentleman has 2 horses, and a saddle worth $60; now if the saddle be put on the first, it will make his value double that of the second horse; but if it be put on the second, it will make his value triple that of the first; what was the value of each horse? First was worth $36. Ans. Second worth $48. 79. A and B invested equal sums in trade; A gained a sum equal to of his stock, and B lost $378; then A's money was double of B's; what sum did each invest? Ans. $945. 80. Three towns are so situated that A lies 90 miles south of B, and C 120 miles west of A; what is the distance from A to C ? Ans. 150 miles. 81. A lady purchased silk for a dress at $1.50 per yard, and lining for the same at 80 cents a yard; the whole number of yards of both silk and lining was 16, and the whole cost 20; how many yards were there of each? Ans. {10, yards of silk, 5 yards of lining. 82. A farmer having driven his cattle to market, received for them all $576, being paid at the rate $24 per ox, $16 per cow, and $6 per calf; there were as many oxen as cows, and four times as many calves as cows: how many were there of each sort? Ans. 9 oxen, 9 cows, 36 calves. 83. There is a fish, whose head is 16 inches long, his tail is as long as his head and half the length of his body, and his body as long as the head and tail; what is the whole length of the fish? Ans. 128 inches. 84. Three men, A, B, and C, playing at cards, staked |