50. If 120 gallons of water, in one hour, fall into a cistern containing 600 gallons, and, by one pipe in the cistern, 35 gallons run out, and, by another pipe, 65 gallons run out, in what time will the cistern be filled? A. 30 hours.

51. A certain clerk, in a country store, purchased the whole stock in trade, the quantity and price being as follows:

Amount of stuck, $1671+.

By agreement, 15 per cent. was to be deducted from the amount of stock. For the above goods, the clerk has paia as

follows: his services for the two last years, at $26 per month; turned in a note on James Spencer, of 500 dollars, with 5 years' compound interest due on it-669112; and, for the balance, he was to give his note, payable in 6 years from the date of the transaction, without interest: now the question is, what sum of ready money will discharge said note? A. $93,557.

After the clerk had purchased the above stock, and settled for the same, he commenced business for himself. The rent of his store costs him $29 a year; his clerk-hire $27,814 precisely, in addition to which is the interest of his capital, $1420,35, (that is, the interest of the amount of stock, after the 15 per cent. is deducted, $85221). He next considered what price he must put on each article, to make a certain per cent He recollected that the goods were already rated in the inven tory at 15 per cent. more than their actual cost. Now, said he, if I can make 5 per cent. in advance on their present valua tion, clear of all expenses, I shall be satisfied. The question, then, is, at what price he must mark each article, commencing with the first on the inventory, so as to clear the 5 per cent.

The pupil will find, by calculation, that the expenses amount to 10 per cent. on the actual cost of all the articles; this, added to the 5 per cent., makes 15 per cent. advance; that is, each article must be marked 15 per cent. higher than its present valuation in the inventory. The answer to each follows in the same order as the articles stand in the above inventory, commencing with the 3 bbls. of sugar, and finding the selling price of each per ib., &c.

Note.-In marking goods, it is customary to neglect the mills, if under 5; if exactly 5, add of a cent, and if over 5, add 1 cent to the cents.

hds..... 129...

52. Bought 42 gallons of rum, for $37,80; how much water must be mixed with it, that it may be afforded for $,80 per gallon?

$,80: $37,80:: 1 gal. : 471 galls.; then, 47) — 42+5} galls., Ans. 53. A thief, having 30 miles the start of an officer, makes off at the rate of 8 miles an hour; the officer presses on after him at the rate of 10 mi es 'n hour: how much does he gain on the

thief in one hour? how long before he will overtake the thief? A. 2 miles; 15 hours.

54. A person, looking at his watch, was asked what o'clock it was; he replied it was between 4 and 5; but, a more particular answer being requested, he said the hour and minute hands were then exactly together. What was the time? See the Key. 55. At 12 o'clock the hour and minute hands of a clock are exactly together; when will they be together again?

Ans. 1 h. 5 m. 27 sec.

56. If 10 men can perform a piece of work in 25 days, how many men will accomplish another piece of work, four times as large, in a fifth part of the time? A. 200.

57. A can do a piece of work in 8 days, and B in 12; in what time would both finish it by working together?

Days. Day. Work. Work.

8: 1 :: 1 :

§ +- 12 = 24. Then, 2:1::1: 4, A.

12 : 1 :: 1 : 12 58. What number is that, from which if you take, the remainder will be į? } + 1 = 12, Ans.

59. What number is that, from which if you take 3, the remainder will be ? Ans. §.

60. What number is that, from which if you take of 3 of 24, the remainder will be? Ans. 2 = 116.

61. What number is that, which, being divided quotient will be ? 4. 19.

by 3,

the

the

62. What number is that, which, being multiplied by, product will be 31? A. 332.

63. What number is that, from which if you take of itself, the remainder will be 12?

1, or 4,-,, remainder. Then, the remainder 12, being 4 × 12 = 48 imes greater than the remainder, the number itself will be 48 times greater

than 1. A. 48.

64. What number is that, to which if you add of of itself, the sum will be 39?

of, and the number itself 18; then,

+18=18; if to the

whole number of of it be added, the sum will be ; consequently 39 is of the number. Ans. 30.

65. What number is that, to which if you add of itself, the sum will be 18? A. 12.

66. A wns of a vessel, B, C, and D the remainder; D's part is $100 can you tell me how many dollars is each man's part, and what part of the vessel D owns?

Ans. A's part, $100; B's, $200; C's, $400; and D's part is

67. There is a beam,

of which is in the ground, in the water, and the rest, being 2 feet, out of water; how long is the beam? A. 16 feet.

68. The third part of an army was killed, the fourth part taken prisoners, and 1000 fled; how many were in this army? how many killed? how many taken captives?

+, of the whole army; then, as

=

=

more makes 13, or the whole army, 1000; and if be 1000, how much is , or the whole? Ans. 2400, the whole army; 800 killed, 600 captives.

69. Suppose that there is a mast erected, so that of its length stands in the ground, 12 feet in the water, and of its length in the air, or above water; I demand the whole length Reducing the fractions to the least common denominator, gives

+18=1; therefore 12 feet. A. 216 feet. 70. In an orchard of fruit-trees, of them bear apples, pears, plums, 40 of them peaches, and 10 cherries; how many trees does the orchard contain? 50+10. Ans 600.

=

71. A man spent one third of his life in England, one fourth in Scotland, and the remainder, which was 20 years, in the United States; to what age did he live? A. 48 years.

72. The number of scholars in a certain school is as follows: of the pupils study geography, grammar, ) arithmetic, and 10 learn to read; what number is pursuing each branch of study? A. 30 in geography, 80 in grammar, 120 in arithme tic, and 10 learn to read.

73. The double and the half of a certain number, increased by 7 more, make 100; what is that number? A. 37.

74. A man, having purchased a drove of cattle, was driving them to market, when he was met by a gentleman, who inquired of him where he was going with his 100 head of cattle ? Sir, said he, I have not near 190, but if 1 had as many more as I now have, as many more, and 7 cattle and, I should have a hundred. How many had he? A. 37.

75. Five eighths of a certain number exceed of the same aumber by 36; what is that number?

-; hence 36 is of the number sought. A. 160. 76. What number is that, which, being increased by 1, §, and of itself, the sum will be 131? Ans. 737.

The eleven foregoing questions are usually performed by a mile called Position, but this method of solving them by frac vens is preferable

77. A hare starts up 12 rods before a hunter, and scuds away

at the rate of 10 miles an hour; now, if the hunter does not change his place, how far will the hare get from the hunter in 45 seconds? A. 52 rods.

78. If a dog, by running 16 miles in one hour, gain on a hare 8 miles every hour, how long will it take him to overtake her, provided she has 52 rods the start? A. 97 seconds.

79. A hare starts 12 rods before a greyhound, but is not perceived by him till she has been up 45 seconds; she scuds away at the rate of 10 miles an hour, and the dog after her at the rate of 16 miles an hour; what space will the dog run before he overtakes the hare? A. 138 rods, 3 yards, 2 feet.

80. A gentleman has an annuity of $2000 per annum; I wish to know how much he may spend daily, that, at the year's end, he may lay up 90 guineas, and give 20 cents per day to the poor of his own neighborhood? A. $4,128.

81. What is the interest of $600 for 120 days?-12. For 2 days?-20. For 10 years, 10 mo. and 10 days?-391. For 5 years, 5 mo. and 5 days?-19550. For 6 years, 6 mo. and 6 days?-23460. For 4 years, 4 mo. and 4 days ?-15640.

A. Total, $989,70. 82. What is the present worth of $3000, due 2 years hence, discounting at 6 per cent. per annum? A. $2608,695+

83. Suppose A owes B $1000, payable as follows; $200 in 4 mo., $400 in 8 mo., and the rest in 12 mo.; what is the equated time for paying the whole? A. 8 months.

84. How many bricks, 8 inches long, 4 inches wide, and 2 inches thick, will it take to build a house 84 feet long, 40 feet wide, 20 feet high, and the walls to be 1 foot thick?

The pupil will perceive that he must deduct the width of the wall, that is, 1 foot, from the length of each side, because the inner sides are 1 foot less in length than the outer sides.

21

A. 105408 bricks.