42. Eight oxen have, in seven weeks, eaten all the grass which grew on 400 square rods of land, in such a manner that they not only ate all the grass which at first was there, but also that which grew during the time they were grazing. In like manner, have 9 oxen, in eight weeks, eaten up all the grass upon 500 square rods of land. How many oxen can in this way, graze, for 12 weeks, upon 600 square rods of land?

Ans. 8.

43. A and B possess, together, only of the property of C; B and C have, together, 6 times as much as A; were B $680 richer than he actually is, then he would have as much as A and C together. How much has each ?

Ans. A has $200, B $360, and C $840. 44. How often can the 26 letters of the alphabet be trans. posed ? Ans. 403291461126605635584000000 times.

NOTE. All the inhabitants of the globe, taken together, could not, in a thousand millions of years, write out all these transpositions of the 26 letters, even supposing that each wrote 40 pages daily, each of which pages should contain 40 different transpositions of the letters.

45. A debt, due at this present time, amounting to $1200, is to be discharged in seven yearly and equal payments. What is the amount of one of these payments, if the interest be calculated at 4 per cent.? Ans. $199.931.

46. A usurer lent a person $600, and drew up for the amount a bond of $800, payable in 3 years, bearing no interest. What did he take per cent., if compound interest be taken into consideration? Ans. 10.06424 per cent.

47. A person being asked about his salary, answered, "At present I have $550; but when I first entered into office I had no more than $100; but, on account of my industry, I received, each year, an addition of $30 to my income. How long was he engaged? Ans. 16 years.

48. A debtor being unable to pay his debt, amounting to $12950, at once, agrees with his creditors to discharge it by monthly instalments, viz: $600 the first month, and each succeeding month $50 more than the preceding one. In how many months will he have discharged his whole debt? And how much does he pay the last month?

Ans. In 14 months, and $1250.

49. A person dying leaves half of his property to his wife, one-sixth to each of two daughters, one-twelfth to a servant, and the remaining $600 to the poor. What was the amount of his property? Ans. $7200.

50. We know, from natural philosophy, that any body, which falls in vacuo, passes, in the first second, through a space of 16 feet; and in each succeeding second, 324 feet more than in the one immediately preceding. Now, if a body has been falling 20 seconds, how many feet will it have fallen the last second? And how many in the whole time? Ans. 627 feet, and 6433 feet.

51. An estate of $7500 is to be divided between a widow, two sons, and three daughters, so that each son shall receive twice as much as each daughter, and the widow herself $500 more than all the children. the share of each child?

What was her share? And what

52. Three soldiers, in a battle, make $96 booty, which they wish to share equally. In order to do this, A, who made the most, gives B and C as much as they already had; in the same manner, B then divided with A and C, and after this, C with A and B. If, then, by these means, the intended equal division is effected, how much booty did each soldier make?

Ans. A $52, B $28, and C $16.

53. A purse of $2850 is to be divided among three persons, A, B, and C. A's share is to be to B's as 6 to 11, and C is to have $300 more than A and B together. What is each one's share?

Ans. A's $450, B's $825, C's $1575.

54. A father leaves a number of children, and a certain sum, which they are to divide amongst them as follows: The first is to receive $100, and then the 10th part of the remainder; after this, the second has $200, and the 10th part of the residue ; again, the third receives $300, and the 10th part of the remainder; and so on, each succeeding child is to receive $100 more than the one immediately preceding, and then the 10th part of that which still remains. At last it is found that all the children have received the same. What was the fortune left? And how many children were there?

55. Two carpenters, 24 journeymen, and 8 apprentices, received at the end of a certain time $144. The carpenters received $1 per day, each journeyman half a dollar, and each apprentice 25 cents. How many days were they employed? Ans. 9 days.

56. A man, to please his children, brings home a number of apples, and divides them as follows: To the first and eldest of his children he gives the half of the whole number, less 8; to the second, the half of the remainder, again diminished by 8; and he does the same with the third and fourth. After this he gives the 20 remaining apples to the fifth. How many apples did he bring home? Ans. 80.

57. A farmer being asked how many sheep he had, answered that he had them in five fields; in the first he had, in the 2d, in the 3d, and in the 4th, and in the 5th 450. How many had he?

Ans. 1200.

58. I once had an untold sum of money lying before me. From this I first took away the 3d part, and put in its stead $50. A short time after I took from the sum thus augmented, the 4th part, and put again in its stead $70. I then counted my money and found $120. What was the original sum?

Ans. $25.

59. After paying and of my money, I had 66 guineas left in my purse. How many guineas were in it at first?

Ans. 120.

60. A countryman brings his eggs to market, and first sells 4 more than the half of them, then he goes further, and sells half of the remainder, and 2 over. Now, 6 eggs more than half of the remainder are stolen from him, and dissatisfied about this loss, he returns to his village with the two eggs which remained in his basket. How many eggs did he take to town? Ans. 80.

61. A person goes to a tavern with a certain sum of money in his pocket, where he spends 2 shillings; he then borrows as much money as he had left, and going to another tavern, he there spends 2 shillings also; then borrowing again as much money as was left, he went to a third tavern, where likewise he spent 2 shillings and borrowed as much as he had left; and again spending 2 shillings at a fourth tavern, he then had nothing remaining. What had he at first?

Ans. 3s. 9d.

62. A cistern can be filled by three pipes; by the first in 11 hours, by the second in 3 hours, and by the third in 5 hours. In what time will this cistern be filled when all three pipes are open at once? Ans. In 48 minutes. 63. To divide the number 36 into 3 such parts that of the first,of the second, and of the third, may be all equal to each other. Ans. 8, 12, and 16.

64. A person possesses a wagon with a mechanical contrivance, by which the difference of the number of revolutions of the wheels on a journey may be determined. It is known that each of the fore-wheels is 51, and that each of the hind wheels is 7 feet in circumference. Now, when in a journey the fore-wheel has made 2000 revolutions more than the hindwheel, how great was the distance traveled?

Ans. 39900 feet. 65. A dog pursues a hare. Before the dog started, the hare had made 50 paces, and this is the distance between them at first. The hare takes 6 paces to the dog's 5; and 9 of the hare's paces are equal to 7 of the dog's. How many paces can the hare take before the dog overtakes her? Ans. 700.

66. A person wishes to dispose of his horse by lottery. If he sells the tickets at $2 each, he will lose $30 on his horse; but if he sells them at $3 each, he will receive $30 more than his horse cost him. What is the value of the horse, and the number of tickets? Horse worth $150, No. tickets, 60.

67. The four following numbers,

2080913082956455142636, 4937801347510680732948,

7262810476410016163052, 214972108693241589340948, when added together, by taking two at a time, produce six distinct sums; each of which is a perfect cube. What are the six roots of these cube numbers ?

Ans.

{

19146344, 21062342, 60097344, 23021160, 60359866, 60571840.

68. What is the square of 12890625 ?

Ans. 166168212890625.

NOTE.-In this question it will be observed that the square of the above number ends with the same set of figures as the number itself; and this must hold good for any power of the above number.