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QUEST. 8. A can do a piece of work alone in 12 days, and B alone in 14; in what time will they both together perform a like quantity of work ?
Ans. 6 days. QUEST. 9. A person who was possessed of a share of a copper mine, sold of his interest in it for 18001; what was the reputed value of the whole at the same rate? Ans. 40001.
QUEST. 10. A person after spending 201 more than of his yearly income, had then renaining 301 more than the half of it; what was his income?
Ans. 2001. Quest. 11. The hour and minute hand of a clock are exactly together at 12 o'clock; when are they next together?
Ans. at 111 hr, or 1 hr, 51 min. Quest. 12. If a gentleman whose annual income is 15001, spend 20 guineas a week; whether will save or run in debt, and how much in the year?
Ans, save 408l. QUEST. 13. A person bought 180 oranges at 2 a penny, and 180 more at 3 a penny; after which, selling them out again at 5 for 2 pence, whether did he gain or lose by the bargain?
Ans. he lost 6 pence., Quest. 14. If a quantity of provisions serves 1500 men 12 weeks, at the rate of 20 ounces a day for each man; how many men will the same provisions maintain for 20 weeks, at the rate of 8 ounces a day for each man? Ans. 2250 men.
Quest. 15. In the latitude of London, the distance round the earth, measured on the parallel of latitude, is about 15550 miles; now as the earth turns round in 23 hours 56 minutes, at what rate per hour is the city of London carried by this motion from west to east ? Ans: 6493 | miles an hour.
Quest. 16. A father left his son å fortune, of which he ran through in 8 months : } of the remainder lasted him 12 months longer; after which he had bare 8201 left. What sunt did the father bequeath his son? Ans. 1913/ 6s 8d.
Quest. 17. If 1000 men, besieged in a town, with provisions for 5 weeks, allowing each man 16 ounces a day, be reinforced with 500 men more; and supposing that they cannot be relieved till the end of 8 weeks, how many ounces a day must each man have, that the provision may last that time?
Ans. 6 ounces. Quest. 18. A younger brother received 81001, which was just of his elder brother's fortune : What was the father worth at his death?
QUEST. 19. A person, looking on his watch, was asked what was the time of the day, who answered, It is between 5 and 6; but a more particular answer being required, he said that the hour and minuté hands were then exactly together : What was the time?
Ans. 277. min. past 5. QUEST. 20. If 20 men can perform a piece of work in 19 days, how many men will accomplish another thrice as large in one-fifth of the time?
Ans. 300. QUEST. 21. A father devised is of his estate to one of his sons, and is of the residue to another, and the surplus to his relict for life. The children's legacies were found to be 5141 6s 8d different: Then what money did he leave the widow the use of ?
Ans. 1270715 91d. Quest. 22. A person, making his will, gave to one child i of his estate, and the rest to another. When these legacies came to be paid the one turned out 12001 more than the other : What did the testator die worth? Ans. 40001.
QUEST. 23. Two persons, A and B, travel between London and Lincoln, distant 100 miles, A from London, and B from Lincoln, at the same instant. After 7 hours they meet on the road, when it appeared that A had rode 1 miles an hour more than B. At what rate per hour then did each of the travellers ride? Ans. A 73 şi and B 675 miles.
QUEST. 24. Two persons, A and B, travel between London and Exeter. A leaves Exeter at 8 o'clock in the morn. ing, and walks at the rate of 3 miles an hour, without intermission; and B sets out from London at 4 o'clock the same evening, and walks for Exeter at the rate of 4 miles an hour constantly. Now, .supposing the distance between the two cities to be 130 miles, whereabouts on the road will they meet?
Ans. 69 miles from Exeter. QUEST 25. One hundred eggs being placed on the ground, in a straight line, at the distance of a yard from each other: How far will a person travel who shall bring them one by one to a basket, which is placed at one yard from the first egg?
Ans. 10100 yards, or 5 miles and 1300 yds. Quest. 26. The 'clocks of Italy go on to 24 hours: Then how many strokes do they strike in one complete revolution of the index?
Ans. 300. QUEST. 27. One Sessa, an Indian, having invented the game of chess, shewed it to his prince, who was so delighted
A 120 more,
with it, that he promised him any reward he should ask; on which Sessa requested that he might be allowed one grain of wheat for the first square on the chess board, 2 for the second, 4 for the third, and so on, doubling continually, to 64, the whole number of squares. Now, supposing a pint to contain 7680 of these grains, and one quarter or 8 bushels to be worth 27s 6d, it is required to compute the value of all the corn?
Ans. 64504682162851 17s 3d 327679* QUE'st. 28. A person increased his estate annually by 1001 more than the part of it; and at the end of 4 years found that his estate amounted to 103421 35 9d. What had he at first?
Ans. 40001. QUEST. 29. Paid 101210s for a principal of 7501, taken in 7 years before : at what rate per cent. per annum did I páy interest?
Ans. 5 per cent. QUEST. 30. Divide 1000l among A, B, C; so as to give and B 95 less than c.
Ans. A 415, B 230, c 325. QUEST. 31. A person being asked the hour of the day, said, the time past noon is equal to ths of the time till midnight. What was the time? Ans. 20 min. past 5.
Quest. 32. Suppose that I have 15 of a ship worth 12001; what part of her have I left after selling of of my share, and what is it worth? Ans. 1o, worth 1851.
QUEST. 33. Part 1200 acres of land among A, B, C; só that B may have 100 more than A, and c 64 more than B.
Ans. A 312, B 412, C 476. QUEST. 34. What number is that, from which if there be taken of }, and to the remainder be added is of 1 the sum will be 10?
Ans. 934 QUEST: 35. There is a number which, if multiplied by of of 11, will produce 1: what is the square of that number?
Ans. 116 QUEST. 36. What length must be cut off a board, s, inches broad, to contain a square foot, cr as much as 12 inches in length and 12 in breadth ? Ans. 1616 inches. ! QUEST. 37. What sum of money will amount to 133/ 2s 6d, in 15 months, at 5 per cent. per annum simple interest ? :
Ans. 1301. QUEST. 38. A father divided his fortune among his three sons, A, B, C, giving A 4 as often as B 3, and c 5 as often as
B 6; what was the whole legacy, supposing A's share was 40001.
Ans. 95001. QUEST. 39. A young hare starts 40 yards before a greyhound, and is not perceived by him till she has been up 40 seconds; she scuds away at the rate of 10 miles an hour, and the dog, on view, makes after her at the rate of 18: how long will the course hold, and what ground will be run over, counting from the outsetting of the dog ?
Ans. 6024 sec. and 530 yards run. QUEŠT. 40. Two
young gentlemen, without private fortune, obtain commissions at the same time, and at the age
of 18. One thoughtlessly spends 101 a year more than his pay; buts shocked at the idea of not paying his debts, gives his creditor a bond for the money, at the end of
every year, and also insures his life for the amount; each bond costs him 30 shillings, besides the lawful interest of 5 per cent. and to insure his life costs him 6 per cent.
The other, having a proper pride, is determined never to run in debt; and, that he may assist a friend in need, perseveres. in saving 101 every year, for which he obtains an interest of 5 per cent. which interest is every year added to his savings, and laid out, so as to answer the effect of compound interest.
Suppose these two officers to meet at the age of 50, when each receives from Government 4002 per annum ; that the onc, seeing his past errors, is resolved in future to spend no more than he actually has, after paying the interest for what he owes, and the insurance on his life.
The other, having now something before hand, means in future, to spend his full income, without increasing his stock.
It is desirable to know how much each has to spend per annum, and what money the latter has by him to assist the distressed, or leave tū those who deserve it? Ans. The reformed officer has to spend 661 19s 14.5389d
per annum. The prudent officer has to spend 4371 125 112:4379d
per annum. And the latter has saved, to dispose of,7521 19s 9•1896d.
END OF THE ARITHMETIC.
ARITHMS are made to facilitate troublesome calcuá lations in numbers. This they do, because they perform multiplication by only addition, and division by only subtraction, and raising of powers by multiplying the logarithm by the index of the power, and extracting of roots by dividing the logarithm of the number by the index of the root. For, lagarithms are numbers so contrived, and adapted to other numbers, that the sums and differences of the former shall correspond to, and show, the products and quotients of the latter, &c.
Or, more generally, logarithms are the numerical exponents of ratios; or they are series of numbers in arith
* The invention of Logarithms is due to Lord Napier, Baron of Merchiston, in Scotland, and is properly considered as one of the most useful inventions of modern times. A table of these numbers was first published by the inventor at Edinburgh, in the year 1614, in a treatise entitled Canon Mirificum Logarithmorum; which was eagerly received by all the learned throughout Europe. Mr. Henry Briggs, then professor of geonietry at Gresham College, soon after the discovery, went to visit the noble inventor ; after which, they jointly undertook the arduous task of computing new tables on this subject, and reducing them to a more convenient form than that which was at first thought of. But Lord Napier dying soon after, the whole burden fell upon Mr. Briggs, who, with prodigious labour and great skill, made an entire Canon, according to the new forın, for all numbers from 1 to 20000, and from g 0.0 to 10100, to 14 places of figures, and published it at London in the year 1624, in a treatise entitled Arithmetica Logarithmica, with directions for supplying the intermediate parts. Vol. I.