20. What is the difference between the true and bank discount of

$2500, payable in 90 days at 7 per cent.? 22/

21. Which is the more advantageous, to buy flour at $5 a bbl. on 6 mo., or $4.87% cash, money being worth 7 %? Ans. At $5 on 6 mo. 22. Sold of a lot of lumber for what of it cost; what % was gained on the part sold? Ans. 25 %.m

23. If $500 gain $50 in 1 yr., in what time will $960 gain $60? 7 24. Received an invoice of crockery, 12 per cent. of which was broken; at what per cent. above cost must the remainder be sold, to clear 25 per cent. on the invoice? Ans. 42

25. The sum of two numbers is 365, and their difference is .0675;

what are the numbers? 2.46625-4182.533>

26. If the interest of $445623 be $128.99 for 7 yr., what will be the interest of $650 for 3 yr. 10 mo. 15 da.?/04/5-3

27. Received from Savannah 150 bales of cotton, each weighing 540 lb., and invoiced at 7d. a pound Georgia currency. Sold it at an advance of 26 %, commission 1 %, and remitted the proceeds by draft What was the face of the draft, exchange being % discount? Ans. $12629.28+.

28. A man in Chicago has 5000 francs due him on account in Paris. He can draw on Paris for this amount, and negotiate the bill at 193 cents per franc; or he can advise his correspondent in Paris to remit a draft on the United States, purchased with the sum due him, exchange on U. S. being at the rate of 5 francs 20 centimes per $1. What sum will the man receive by each method?

Ans. By draft on Paris, $970; by remittance from Paris, $961.53. 29. What sum must be invested in stocks bearing 6%, at 105, to produce an income of $1000?153.64

30. A person exchanges 250 shares of 6 per cent. stock, at 70 %, for stock bearing 8 per cent., at 120 %; what is the difference in his income? Ans. $333.33. 31. If of A's money equals of B's, and of B's equals of C's, and the interest of all their money for 4 yr. 8 mo. at 6% is $15190, how much money has each ?

4

Ans. A has $18859.41+; B, $16763.94+; C, $18626.60.

32. A boy 14 years old is left an annuity of $250, which is deposited in a savings bank at 6 %, interest payable semi-annually how much will he be worth when of age? Ans. $2482.375.

33. If a boy buys peaches at the rate of 5 for 2 cents, and sells them at the rate of 4 for 3 cents, how many must he buy and sell to make a profit of $4.20 ?

126

34. What % in advance of the cost must a merchant mark his goods, so that, after allowing 5 % of his sales for bad debts, an average credit of 6 months, and 7 % of the cost of the goods for his expenses, he may make a clear gain of 12% on the first cost of the goods, money being worth 6 %? Ans. 27%.

25256+

420

MISCELLANEOUS EXAMPLES.

35. Four men contracted to do a certain job of work for $8600; the first employed 28 laborers 20 da., 10 h. a day; the second, 25 laborers 15 da., 12 h. a day; the third, 18 laborers 25 da., 11 h. a day; and the fourth, 15 laborers 24 da., 8 h. a day. How much should each contractor receive?

4

37

Ans. 1st, $2686; 2d, $2158.39; 3d, $2374.23; 4th, $1381.42. 36. If I exchange 75 railroad bonds of $500 each, at 36 % below par, for bank stock at 5 % premium, how many shares of $100 each will I receive? 238

37. A trader has bought merchandise as follows: July 3, $35.26; July 4, $48.65, on 30 da.; Aug. 17, $6.48; Sept. 12, $50. What is due on the account Oct. 12, interest at 9 % 72,60 Ans. $192.04.

38. A farmer sold 34 bu. of corn, and 56 bu. of barley for $63.10, receiving 35 cents a bushel more for the barley than for the corn; what was the price of each per bushel? 8 = 4 8 3 5

39. A speculator purchased a quantity of flour, Sept. 1; Oct. 1 its value had increased 25 %; Nov. 1 its value was 30 % more than Oct. 1; Dec. 1 he sold it for 15% less than its value Nov. 1, receiving in payment a 6 months' note, which he got discounted at a bank, at 7 %, receiving $12950 on it. How much was his profit on the flour? Ans. $3704.10.

322857

40. A flour merchant bought 120 bbl. of flour for $660, paying $5.75 for first quality and $5 for second quality; how many barrels were first quality? Ans. 80.

41. Two mechanics work together; for 15 days' work of the first and 8 days' work of the second they receive $61, and for 6 days' work of the first and 10 days' work of the second they receive $38; how much does each man. earn? Ans. 1st, $63; 2d, $36.

42. The duty, at 15 %, on Rio coffee, in bags weighing 180 lbs. gross, and invoiced at $.121 per pound, was $961.871, tare having been allowed at 5%; how many bags were imported?

Ans. 300.

43. A dairyman took some butter to market, for which he received $49, receiving as many cents a pound as there were pounds; how many pounds were there? Ans. 70 lb.

44. A mechanic received $2 a day for his labor, and paid $4 a week for his board; at the expiration of 10 weeks he had saved $72; how many days did he work, and how many was he idle? 4 56 45. To what would $250, deposited in a savings bank, amount in 10 yr., interest being allowed semi-annually at 6 % per annum ?/>/ 46. How much water must be put with 100 gal. of wine that cost $120, so that 1 gal. of the mixture may be sold for $1, without loss? 47. If a pipe 3 in. in diameter will discharge a certain quantity of water in 2 h., in what time will 3 two-inch pipes discharge 3 times the quantity.?

Ans. 4 h. 30 min.

48. Wm. Jones & Co. become insolvent and owe $8100. Their assets amount to $4981.50. What per cent. of their indebtedness can

20

they pay, allowing the assignees 2% on the amount distributed for their services? Ans. 60 per cent.

49. Shipped a car load of fat cattle to Boston, and offered them for sale at 25 per cent. advance on the cost; but the market being dull I sold for 14 per cent. less than my asking price, and gained thereby $170. How much did the cattle cost; for how much did they sell and what was my asking price? Ans. Cost $2266.66; sold for $2436.66; asking price, $2833.35. 3

33

50. What must be the dimensions of a cubical cistern to hold 2000 gallons?

76.1+

51. A man died leaving $5000 to be divided between his three sons, aged 13, 15, and 16 yr. 6 mo., respectively, in such a proportion that the share of each being put at simple interest at 6 %, should amount to the same sum when they should arrive at the age of 21. much was each one's share?/536.76+ 1672.36+

Ans. Youngest, $1537; second, $1672; oldest, $1791. 52. A vessel having sailed due south and due east on alternate days, was found, after a certain time, to be 118.793 miles south-east of the place of starting; what distance had she sailed? Ans. 168 miles.

53. Imported 4 pipes of Madeira wine, at $2.15 a gallon, and paid $57.60 freight, and a duty of 24 per cent. I sold the whole for $1980; what was my gain %?

605

54. If 343 bu. of corn are equal in value to 17 bu. wheat, 9 bu. of wheat to 59 bu. of oats, 6 bu. of oats to 42 lb. of flour, and 56 lb. of flour to $1.96, how many bushels of corn will purchase 5 bbl. of flour?

42282

644

Ans. 432737.

55. If stock bought at 8% discount will pay 7% on the investment, at what rate should it be bought to pay 10 %?

56. A merchant in New York gave $2000 for a bill of exchange of £400 to remit to Liverpool; what was the rate in favor of England? 57. A, B, and C start from the same point, to travel around a lake 84 miles in circumference. A travels 7 miles, and B 21 miles a day in the same direction, and C 14 miles in an opposite direction. In how many days will they all meet? Ans. 12.

43200

58. The exact solar year is greater than 365 days by 1968 of a day; find approximately how often leap year should come, or one day be added to the common year, in order to keep the calendar right? Ans. Once in every 4 yr.; 7 times in every 28 yr.; 8 times in every 33 yr.; 31 times in every 128 yr.; or 163 times in every 673 yr.

59. A gentleman purchases a farm for $10000, which he sells after a certain number of years for $14071, making on the investment 5 % compound interest. He now invests his money in a perpetuity, which is in reversion 11 years from the date of purchasing the farm. Allowing 6 % compound interest for the use of money, find the annuity and the length of time he owns the farm.

Ans. Annuity, $1065.85 owned the farm 7 yr.

60. What will I gain % by purchasing goods on 6 mo., and selling them immediately for cash at cost, money being worth 7 % ?

61. What sum must a man save annually, commencing at 21 years of age, to be worth $30000 when he is 50 years old, his savings being invested at 5 % compound interest? Ans. $481.37. 62. Three sons are to share $10000 in the ratio of 3, 4, and 5, but the youngest dying it is required to divide the whole sum equitably between the other two. What are the shares of the other two? Ans. $44444, and $55555.

63. If 50 bbl. of flour in Chicago are worth 125 yd. of cloth in New York, and 80 yd. of cloth in New York are worth 6 bales of cotton in Charleston, and 13 bales of cotton in Charleston are worth 34 hhd. of sugar in New Orleans, how many hhd. of sugar in New Orleans are worth 1500 bbl. of flour in Chicago? Ans. 75.

64. Seven men all start together to travel the same way round an island 120 miles in circumference, and continue to travel until they all come together again. They travel 5, 6, 71, 81, 91, 101 and 11 miles a day respectively. In how many days will they all be together again? Ans. 1440 da.

65. There are two clocks which keep perfect time when their pendulums beat seconds. The first loses 20 seconds a day, and the second gains 15 seconds a day. If the two pendulums beat together when both dials indicate precisely 12 o'clock, what time does each clock show when the pendulums next beat in concert?

Ans. The first shows 41 min. 8 sec. past 12; and the second 41 min. 9 sec. past 12.

66. If a body put in motion move of an inch the first second of time, 1 in. the second sec., 3 in. the third, and so continue to increase would it move in 30 seconds? Ans. 1624772191,080

in geometrical ratio, how far 5 4/5 7 0 7 36 2 2 2 2 0

16693 mi.

67. If stock bought a 5% premium will pay 6 % on the investment, what % will it pay if bought at 15 % discount?

68. If 6 apples and 7 peaches cost 33 cts., and 10 apples and 8 peaches cost 44 cts., what is the price of one of each?

Ans. Apples, 2 cts. ; peaches, 3 cts. 69. A gentleman in dividing his estate among his sons gave A $9 as often as B $5, and C $3 as often as B $7. C's share was $3862.50 what was the value of the whole estate? Ans. $28817.50.

70. A farmer sold 16 bu. of corn and 20 bu. of rye for $30, and 24 bu. of corn and 10 bu. of rye for $27. How much per bushel did he receive for each? Ans. Corn, $.75; rye, $.90.

71. A drover sold some oxen at $28, cows at $17, and sheep at $7.50 per head, and received $749 for the lot. There were twice as many cows as oxen, and three times as many sheep as cows. How

many were there of each kind? 70/en.cctv, 42 sheep

72. For what sum must a vessel, valued at $25000, be insured, so

that in case of its loss, the owners may recover both the value of the

vessel and the premium of 24 %?

32894,72

73. A boy hired to a mechanic for 20 weeks, on condition that he should receive $20 and a coat. At the end of 12 weeks the boy quit work, when it was found that he was entitled to $9 and the coat; what was the value of the coat?

Ans. $7.50.

74. An irregular piece of land, containing 540 A. 36 P., is exchanged for a square piece containing the same area; what is the length of one of its sides? If divided into 42 equal squares, what will be the length of the side of each? 45.36+

75. What will be the difference in the expense of fencing two fields of 25 acres each, one in the form of a circle, and the other in the form of a square, the fence costing $.62 a rod? Ans. $17.98 +.

76. At what time between 5 and 6 o'clock are the hour and minute hands of a watch exactly together?

77. A general, forming his army into a square, had 284 men remaining; but increasing each side by one man, he wanted 25 men to complete the square. How many men had he? Ans. 2400. 200 78. Divide $3648 among 3 persons, so that the share of the first to that of the second shall be as 7 to 9, and of the first to the third as 3 to 4. Ans. $1008, $1296, $1344.

79 If a lot of land, in the form of an oblong or rectangle, contains BAR. P., and its length is to its width as 21 to 13. What are its dimensions; and how many rods of fence will be required to inclose it? Ans. to last, 136 rd. of fence. 80. Five persons are employed to build a house. A, B, C, and D can build it in 13 days; A, B, C, and E in 15 days; A, B, D, and E in 12 days; A, C, D, and E in 19 days; and B, C, D, and E in 14 days. In how many days can all together build it; and which one could do the work alone in the shortest time?

12137

Ans. 11483 da. ; B in shortest time. 81. Divide $500 among 3 persons, in such a manner that the share of the second may be greater than that of the first, and the share of the third greater than that of the second.

Ans. 1st, $105; 2d, $15717; 3d, $23615.

82. A and B engage in trade; A puts in $5000, and at the end of 4 mo. takes out a certain sum. B puts in $2500, and at the end of 5 mo. puts in $3000 more. At the end of the year A's gain is $10663, and B's is $1333. What sum did A take out at the end of 4 mo.? Ans. $2400.

83. What sum of money, with its semi-annual dividends of 5% invested with it, will amount to $12750 in 2 yr.? /of you 454

81. If a speculator invests $1500 in flour, and pays 5 % for freights, 2% for commission, and the flour sells at 20 % advance on cost price, on a credit of 90 days, and he gets this paper discounted at bank at 7 %, and repeats the operation every 15 days, investing all the proceeds each time, how much will be his whole gain in two months?