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Multiply the amount of one dollar for one year at the given rate per cent., involved to the time of reversion, by the ratio, for a divisor; by which divide the yearly payments; the quotient will be the answer.
1. Suppose a freehold estate of 140 dollars per annum, to commence three years hence, is to be sold, what is it worth, allowing the purchaser 7 per cent. ? Ans. $1632.59,5.
2. What is an estate of 290 dollars per annum, to continue for ever, but not to commence till the expiration of 4 years, worth in ready money, allowing the purchaser four
per cent. ?
PROMISCUOUS EXAMPLES. 1. Let the product of two numbers be 576, and one of them 16-I demand the other
Ans. 36. 2. Required the gain per cent. on buying a bushel of potatoes for 50, and selling them for 56 cents ? Ans. 12. 3. A person was 17 years of age 29 years since, and
suppose he will be drowned 23 years hence ; pray, in what year of his age will this happen?
Ans. in his 69th year. 4. What is the length of a road 33 feet broad, to contain just one acre ?
Ans. 1320ft.=80 poles. 5. If 12 boarders drink in 7 days half a barrel of beer, how long would the same quantity last, if 2 boarders more came among them?
Ans. 6 days. 6. Required the cubic feet in a grindstone 40 inches diaméter, and 5 inches thick; likewise its value, at $1.50 per cubic foot.
Ans. 3.63 cubic feet; value $5.44,5. 7. If A has ; of of the half of a trading schooner and cargo, worth $16131.70, and sells his brother B of of his interest therein, at prime cost; what did it cost the brother, and what did his cousin P pay at the same rate and time, for 8 of the remainder ? 8. What is the interest of 456 dollars for one year, at six
Ans. $27.36. 9. Required the square root of 729.
Ans. 27. 10. A owes B 136, to be paid in 10 months, $96 in 7
per cent. ?
months, and $260, to be paid in 4 months—what is the equated time for the payment of the whole ?
Ans. 6 months and 7 days+ 11. Two ships, A and B, sailed from a certain port at the same time; A sailed north 8 miles an hour, and B east 6 miles an hour-what was their distance apart at the end of 12 hours ?
Ans. 120 miles. 12. If I buy coffee at 20 cents per lb., how must I sell it to gain 10 per cent. ?
Ans. 22cts. 13. If a family of 9 persons spend 450 dollars in 5 months, how much would be sufficient to maintain them 8 months, if 5 persons more were added to the family? Ans. $1120.
14. Reduce lqr. and 7lbs. of wheat flour to the decimal of a cwt., and find its value at $4 per cwt.
Ans. .3125 of a cwt.; $1.25 value. 15. A has sçantling that is 3 inches by 6 inches, and B wishes to purchase 75 feet; admitting it is in one stick, what is its length ?
Ans. 50 feet. 16. Required the greatest common measure of 1224 and 1080.
Ans. 72. 17. What is the cube root of 1728?
Ans. 12. 18. A has ļ share of a ship, of which he sells to B 4, and B sells out of his share to C, half of his interest--the question is, what part had each man in said ship?
Ans. A }, B jo, and C p. 19. What will 500 dollars amount to in 4 years, at six per cent. per annum, compound interest?
Ans. $631.23,848+ 20. Required the value of a load of Spanish oak bark, that measures 14.5 feet in length, 3.8 feet in width, and 2.5 feet in height, at 10 dollars
Ans. $10.76+ 21. What is the interest of 75 dollars for 25 days?
Ans. $.30,8. 22. What is the measurement of a stick of seantling 30 feet in length, 8 inches in breadth, and 6 inches in depth ?
Ans. 120 feet. 23. What will an annuity or annual rent of 75 dollars amount to in 3 years, at 6 per cent. compound interest ?
Ans. $238.77. 24. A owns & of £ of a ship, and sells of his share to B, for 100 dollars--what was the whole ship worth at that rate?
per cord ?
PROMISCUOUS EXAMPLES. 25. Multiply 4628 by 41 at one operation, (or one line) and tell the product with 6 figures exclusive of the factors.
Ans. 189748. 26. A trader having increased his estate annually 10 per cent., for 7 years, at compound interest, finds himself worth $19487.171—what was his capital at the commencement of the term ?
Ans. $10000. 27. A hare has 50 of its own leaps the start of a greyhound, and takes 4 leaps while the hound takes 3; but the hound goes as far at 2 leaps as the hare does at 3-how many leaps will the hound take to catch the hare?
Ans. 300. 28. Two persons comparing their ages, find them, at present, in the ratio of 7 to 5, but that 30 years ago they were as 2 to 1-what is the age of each? Ans. 70 and 50.
29. What is the 4th power of ?
30. A and B commence trade in company; A advanced at first $500, and B $750;, at the end of 4 months A adds $600 to his stock = what sum must B advance at the same time, to entitle him at the end of the year to equal profits with A?
Ans. $225. 31. Required the admeasurement of a pile of stone 22.5 feet in length, 8.3 feet in width, and 4 feet in height.
Ans. 30.18.4 perches. 32. Bought a pipe of wine containing 126 gallons, at 10s. per gallon, but by accident 16 gallons leaked out-at what
rate must the remainder be sold per gallon, to gain on the whole prime cost, at the rate of 12 per cent. ?
Ans. 12s. 10 10. 33. What will 75 chests of souchong tea cost, weighing neat 4875lb. at 44 tales per picul; and likewise the amount of the bill in federal money ?
Ans. 1608.75 tales=1608 tales, 7 mace, 5 candareens,
which equal $2380.95. 34. The great stone wall of China (erected as a barrier against the northern Tartars) is 1500 miles in length, 20 feet in height, and 20 feet in width-I demand the number of perches of stone it contains ?
Ans. 128000000. 35. The great imperial canal of China is 620 miles in length, 50 feet wide, and 10 feet deep-required the cost of constructing one of the same dimensions, at 9 cents per cubic yard?
36. A and B would barter; A has 150 bushels of wheat at $1.25 per bushel, for which B gives 65 bushels of barley worth 62) cents per bushel, and the balance in oats at 375 mills per bushel-what quantity of oats must A receive from B?
Ans. 3913 bushels. 37. A man dying left his wife in expectation that a child would be afterwards added to the surviving family; and making his will, ordered, that if the child were a son, of his estate should belong to him, and the remainder to his mother ; but if a daughter, the mother was to have }, and the child the remainder. But it happened that the addition was both a son and a daughter, by which the widow lost in equity $2400 more than if there had been only a girl.What would have been her dowry had she had only a son ?
Ans. $2100. 38. What number is that, which, being increased by ,, and í of itself, the sum will be 216 ?
Ans. 90. 39. What number taken from the square of 54, will leave 19 times 46 ?
Ans. 2042. 40. Three towns are so situated, that Blies 80 miles south of A, and C 60°miles west of A-what is the distance betwen B and C?
Ans. 100 miles. 41. Extract the 8th root of 1785793904896. Ans. 34.
42. What is the difference in time, of the sun's coming to the meridian of two places, whose difference of longitude is 31° 27' 30', the sun passing through 15° in an hour ?
Ans. 2h. 5' 50". 43. What is a freehold estate of $600 per annum, to continue for ever, worth in ready money, allowing 6 per cent. to the purchaser ?
Ans. $10000. 44. Required the quantity of stone in a well 20 feet 3 inches deep, the wall 1 foot 3 inches, and 3 feet 6 inches in the clear.
Ans. 15.267 + perches. 45. Required the square of 999, and the work to contain but fifteen figures.
Ans. 998001. 46. Reduce £125 10s. Canada currency, to federal money.
Ans. $502. 47. Suppose 21 to be a divisor, and 76 the quotientrequired the dividend.
Ans. 1596. 48. A tree was broken off by the wind 48 feet from the ground, the part broken off was ļ as long as the part stand.
PROMISCUOUS EXAMPLES. ing-required to know the height of the tree before it was broken.
Ans. 80 feet. 49. Required the value of a bill of exchange, for $1200, at 6 per cent. above par.
Ans. $1272. 50. Reduce 75 piculs, or 7500 cattas of China, to pounds of the United States.
Ans. 10000lbs. 51. Sold 55 thousand feet of sap-pine boards, in Jamaica, at €15 per thousand required the value in federal money.
Ans. $2474. 52. If the } of 6 be 3, what will the of 20 be?
Ans. 7} or 7.5. 53. The smaller of two numbers is 127, and the differ. ence 198—required the larger number.
Ans. 325. 54. What is the difference between thrice five and thirty, and thrice thirty-five ?
Ans. 60. 55. What number is that, which, being multiplied by 15, the product will be for .75?
56. Required the quantity of stone in a pile 16.5 feet in length, 4.5 feet in width, and 4 feet in height, computed at 16.5 cubic feet per perch.
Ans. 18 perches. 57. Required the quantity of potatoes in a bin 10 feet in length, 8 feet in width, and 4.25 feet in height.
Ans. 230bu. 2qt. + 58. A master of a shop hires a journeyman on this condition, that he shall have 50 cents a day and his diet, for every day he works, but for every day he does noi work, he is to pay the master 25 cents for his diet; on the 30th day they account, but neither of them receives or pays any money-how many days did he work, and how many was he idle ? Ans. he worked 10 days, and was idle 20.
59. How much is the freight of a bale that is 7 feet 9 inches in length, 6 feet in breadth, and 3 feet 6 inches thick, at 20 cents per cubic foot?
Ans. $32.55. 60. How much is the insurance on $5000, from Philadel. phia to New-Orleans, at 1} per cent. ?
Ans. $75. 61. Required the cubic and square feet in a round log, whose diameter is 2 feet, and length 30 feet.
Ans. 94.4 +c.ft., and 1131.+ft. of square meas. 62. How many shingles will it require to roof 30 feet in length, and 20 feet in breadth, with shingles that are 5 inches in width, and of such a length as to admit them to be laid 8 inches to the weather?