SECTION V.

MISCELLANEOUS QUESTIONS.

1. What number taken from the square of 48 will leave 16 times 54? Ans. 1440. 2. What number added to the 31st part of 3813 will make the sum 200? Ans. 77.

3. What will 14 cwt. of beef cost, at 5 cents per pound?

Ans. $78.40. 4. How much in length that is 83 inches wide, will make a square foot? Ans. 171 inches.

5. What number is that to which if 2 of § be added, the sum will be 1?

Ans.

6. A father dividing his fortune among his sons, gave A 4 as often as B 3, and C 5 as often as B 6; what was the whole legacy, supposing A's share $5000 ? Ans. $11875.

7. A tradesman increased his estate annually by £100 more than 4 part of it, and at the end of 4 years found that his estate amounted to £10342 3s. 9d.; what had he at first? Ans. £4000.

8. A person being asked the time of day, said the time past noon is equal to of the time till midnight; what was the time? Ans. 20 minutes past 5. 9. The hour and minute hand of a clock are together at 12 o'clock, when are they next together? Ans. 1h. 55m.

10. A young hare starts 40 yards before a grey hound, 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 it at the rate of 18. In what time and distance will the dog overtake the hare? Ans. 60s. time. 530yds. distance. 11. What part of 3d. is part of 2d.? Ans. . 12. A hare is 50 leaps before a grey-hound, and takes 4 leaps to the grey-hound's 3; but 2 of the grey-hound's leaps are as much as 3 of the hare's; how many leaps must the hound take to catch the hare? If 3:1:1: the hare's gain.

2:1:1: the hound's gain.

Then and ::: 50: 300-300 Ans.

15. A post is in the sand, in the water, and 10 feet above the water; what is its length ?

Ans. 24 feet.

14. A man being asked how many sheep he had, said, if he had as many more, half as many more, and 7 sheep, he should have 20; how many had he?

15 In an orchardthe trees bear apples, 4 pears, 50 of them cherries; how many trees are there in all ?

Ans 5.

plums, and Ans. 600.

16. A can do a piece of work alone in 10 days, B can do it in 15, in what time will both together do it? Ans. 5 days. 17. What is the difference between the interest of £350 at 4 per cent. for 8 years, and the discount of the same sum at the same rate, and for the same time? Ans. £27 5.

18. Sound moves at the rate of 1142 feet in a second; if the time between the lightning and thunder be 20 seconds, what is the distance of the explosion? Ans. 4.32+miles.

19. If the earth's diameter be 7911 miles, and that of the moon be 2180; how many moons will be required to make one earth? Ans. 47.788+ 20. If a cubic foot of iron were drawn into a bar of an inch square, what would be its length, supposing no waste of metal ?

21. A lent B a solid stack of hay measuring 20 feet every way; some time after, B returned a quantity measuring every way 10 feet; what proportion of the hay is yet due ? Ans.

22. A general disposing his army into a square, finds he has 284 soldiers over and above, but increasing each side by one soldier, he wants 25 to fill up the square; how many soldiers had he?

Ans. 24000. 23. Supposing a pole 75 feet high to stand on a horizontal plane, at what height must it be cut off, so as that the top of it may fall on a point 55 feet from the bottom, and the end where it was cut off, rest on the stump or upright part?

75x75-55-55-173 feet, Ans.

75×2

RULE. From the square of the length of the pole, (i. e. the sum of the hypothenuse and perpendicular) take the square of the base; then divide the remainder by twice the length of the pole, and the quotient will be the height at which it must be cut off.

24. Suppose a ship sail from lat. 43° N. between N. and E. till her departure from the meridian be 45 leagues, and the sum of her distance and difference of latitude be 155 leagues; what is the distance sailed, and the latitude come to?

135 x 135-45x45 lea.

135 × 2

m.

135-60-751. dis. s'd. 60-180=3° of lat. 43°+3°46° come to. S

Ans.

25. Four men bought a grindstone 60 inches in diameter; how much of its diameter must each grind off to have an equal share of the stone, if one grind his share first, and then another, till the stone is ground away, making no allowance for the eye?

RULE.-Divide the square of the diameter by the number of men, subtract the quotient from the square, and extract the square root of the remainder, which is the length of the diameter after the first share is taken off, and by repeating the latter part of the process, all the several shares may be found.

60 x 60 4900 the subtrahend.

5600-900-51.96+ and 60-51.96-8.04 1st share. √2700—900—42.42+ and 51.96-42.42-9.54 2d share. 1800-900=30. and 42.42—30-12.42 3d share.

26. Suppose one of those meteors called fireballs to move parallel to the earth's surface, and 50 miles above it, at the rate of 20 miles per second; in what time will it move round the earth?

The earth's diameter being 7964 miles, the diameter of the orbit will be 7964+50×2=8064 and 8064 × 3.1416-25333.8624 its circumference. Then 25333.8624 201266.69312s. 21' 6" 41" Ans.

35" 13" 55"

27. When first the marriage knot was tied betwixt my wife and me, My age with her's did so agree as nineteen does with eight and three; But after ten and half ten years, we man and wife had been, Her age came up as near to mine as two times three to nine.

28. A body weighing 3015. is impelled by such a force as to send it 20 rods in a second; with what velocity would a body weighing 12lb. move if it were impelled by the same force?

Ans. 50 rods.

29. In a thunder storm I observed by my clock that it was 6 seconds between the lightning and thunder; at what distance was the explosion ? Ans. 6852ft. 112 miles.

30. I have a square stick of timber 18 inches by 14, but one with a third part of the timber in it, provided it be 8 inches deep, will serve; how wide will it be? Ans. 10 inches.

31. There is a square pyramid, each side of whose base is 30 inches, and whose perpendicular height is 120 inches, to be divided into three equal parts by sections parallel to its base; what will be the perpendicular height of each part?

3

3

30 × 30×40=36000 the solidity in inches. Now of this is 24000, and is 12000. Therefore, as 36000: 120×120×120 :: S24000: 1152000 12000: 576000 Then, 1152000=104.8. Also, 576000 83.2. Then 120-104.8-15.2, length of the thickest part, and 104.8-83.2-21.6, length of the middle part; consequently, 83.2 is the length of the top part.

32. There are 4 spheres, each 4 inches in diameter, lying so as to touch each other, in the form of a square, and on the middle of this square is put a fifth ball of the same diameter; what is the distance between the two horizontal planes passing through the centres of

the balls?

33. There are two balls, each 4 inches in diameter, which touch each other, and another ball of the same diameter is so placed between them that their centres are in the same vertical plane; what is the distance between the horizontal planes which pass through their centres ?

2 2

√ + −2=3.46+ inches, Ans.

34. A military officer drew up his soldiers in rank and file, having the number in rank and file equal; on being reinforced with three times his first number of men, he placed them all in the same form, and then the number in rank and file was just double what it was at first; he was again reinforced with three times his number of men, and after placing the whole in the same form as at first, his number in rank and file was 40 men each; how many men had he at first ?

Ans. 100.

35. If a weight of 1440 lb. be placed 1 foot from the prop, at what distance from the prop must a power of 160 lb. be applied to balAns. 9 feet.

ance it ?

36. Tubes may be made of gold weighing not more than at the rate of 5 of a grain per foot; what would be the weight of such a tube, which would extend across the Atlantic from Boston to London, estimating the distance at 3000 miles?

Ans. 1 lb. 8 oz. 6pwt 39 gr.

37. Divide 1000 crowns; give A 129 more than B, and B 178 fewer than C. Ans. A 360, B 231, and C 409.

38. A person dying, left his wife with child, and by his will ordered that if she went with a son of the estate should belong to him, and the remainder to his mother; and if she had a daughter, he appointed the mother and the daughter; but it happened she was delivered of both a son and a daughter; by which she lost in equity 2000 more than if it had been only a girl; what would have been her dowry if she had only a son? Ans. £1750.

39. A tradesman increased his estate annually a third, abating £100 which he usually spent in his family, and at the end of 34 years, found that his net estate amounted to £3154 11s. 8d.; what had he at outsetting? Ans. 141112s. 93d.

40. Three persons enter joint trade together, to which A contributed £210, B. 312, they clear £140, whereof £37 10s belongs of right to C, that person's stock and the several gains of the other two are required.

Ans. C's stock £190 19s. 6d. A gained £41 4s. 84d. 41. A, B and C will trench a field in 12 days, B, C and D in 14, C, D and A will do it in 15, and D, A, B, in 18; in what time will it be done by all of them together; and by each of them singly? Ans. together in 10.83 days, by A 47.848, B in 38.969, C in 27.194, D in 111.176 days.

SECTION VI.

1 Book-Keeping.

BOOK-KEEPING is the method of recording a systematick account of mercantile transactions.

Every mercantile transaction consists is giving one thing for another. This change of property should be distinctly recorded in a book, or books prepared for the purpose, so that the man of business may at all times know the true state of his affairs.

FARMERS' BOOK-KEEPING.

FIRST METHOD.

By this method but one book is necessary, which should be ruled with four columns on the right hand side of each page, two for debtor* columns, and two for credit, and one column on the left hand side for the date, as in the following example.

On account of its simplicity, the above method is probably the best which can be recommended to farmers and country mechanics. In keeping books in this way, it will be necessary to leave a considerable blank after each man's account, that it may be continued without transferring it to another part of the book; and also to have a list of the names with the page standing against it, for the more convenient reference to the several accounts.

SECOND METHOD.

By this method the debt and credit are entered on separate pages facing each other, with the debt on the left hand, and the credit on the right hand, as in the following example.

*The person who receives any thing of me is Dr. to me, and the person from whom I receive is Cr. Or, the person who becomes indebted to me, where by receiving goods or money, or by my paying his debts, &c. he must be entered Dr. and the person to whom I become indebted, whether by receiving from him goods or money, or by the payment of my debts, must be entered Cr.