SECTION IV. MISCELLANEOUS QUESTIONS. Ans. 1440. 339. 1. What number taken from the square of 48 will leave 16 times 54 ? 2. What number added to the 31st part of 3813, will make the sum 200? 3. What will 14 cwt. of beef cost, at 5 cents per pound? 4. How much in length that is make a square foot? 5. What number is that to which the sum will be 1? Ans. 77. Ans. $78.40. 83 inches wide, will Ans. 17 inches. if of § be added, Ans. 3. 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 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. 55 m 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, 530 yds. 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 ::: 55: 300-500, Ans. 1:1 13. 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? Ans. 5. pears, 15. In an orchardthe trees bear apples, plums, and 50 of them cherries; how many trees are there in all ? Ans. 600. 16. A can do a piece of work alone in 10 days, B can do it in 13, in what time will both together do it? Ans. 515 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 33. 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 ? 12×12×12 .25.25 -27648in-2304ft. Ans. 21. A lent B a solid stack of hay, measuring 20 feet every way; sometime 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. 340. 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? RULE. From the square of the length, of the pole, (i. e. the sum of the hypothe- 75 75-5555-71 ft. Ans. nuse and perpendicular) take the square 75x2 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 135 leagues; what is the distance sailed, and the latitude come to? 135X 135-45 135 2 45 lea. m. Ans. 341. 25. Four men bought a grindstone 60 inches in diame ter; 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 allow ance for the eye? RULE.-Divide the square of the diameter by the number of men, suhtract the quotient from the square, aud 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, 60×60÷4=900, the subtrahend. 3600-900-51.96+ 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. and 30, 4th's 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+502=8064, and 8064><3.1416-25333.8624 its circumference. Then 25333.862420-1266.69312s. 21' 6" 41" 35""" 13" 55""" Ans. 27. When first the marriage knot was tied betwixt my wife and me. My age with hers 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. What were our ages at marriage? Ans. 57 and 33. 28. A body weighing 30lb. 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.=1131 miles. 30. 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? 30x30x40-36000, the solidity in inches. 24000, and is 12000. Therefore, as 36000: 120x120x120 :: 3 1152000 Now of this is {12000: 576000} Then, ✓31152000=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. 1825. PETER PINDLE, Dr. $cts.|| 1825. PETER PINDLE, Cr.lg❘cts. Jan. 1. To 3 cords of wood. Jan. 1. By 12lb. shingle-nails 4 50 at 10 cts. 1 20 19 To 7 bush. of oats, at 30 cts. 3 00 24 By 6yds. black silk, 123 55 i5 40 123155 346. Either of the foregoing methods may answer for farmers, and for mechanics generally, but to the retail merchant, and others whose business is extensive, an acquaintance with book-keeping by the day-book and leger, called SINGLE ENTRY, or by the day-book, journal and leger, called DOUBLE ENTRY, is indispensible. The latter is much the most perfect system, and far best for wholesale dealers, but as it is more complicated and seldom used, we shall confine our attention to the former, which is generally adopted by merchants and others in this country. BOOK-KEEPING BY SINGLE ENTRY. Single Entry requires two principal books, the day book, or waste book, and the leger, and one auxiliary book, the cash book. 1. THE DAY BOOK. 347. This book is ruled with two columns on the right hand for dollars and cents, one coluinn on the left, for inserting the folio or page of the leger to which the account is transferred, and a top line over which is written the month, date and year. The articles are separated from each other by a line drawn across the page, and the transactions of one day from those of another by a double line, in the centre of which is the day of the month. This book commences with an account of all the property, debts, &c. of the person, and is followed by a distinct record of all the transactions in trade in the order of time in which they occur, with every circumstance necessary to render the transaction plain and intelligible.* In entering accounts in the day-book, the following order should be ob served: 1, the date; 2, the name of the person, with the abbreviation Dr. or Cr. at the right hand as he is debtor or creditor, by the transaction; 3, the article or articles with the price annexed, and the value carried out into the ruled columns, with the amount placed directly under, when there is more than one article charged; and 4, the page to which the account is transferred in the leger. For the better understanding of the day-book, see the specimen annexed. As the day book is the decisive book of reference, in case of any sup, posed mistake, or error, in the accounts in the leger, it is of the greatest importance that every transaction be noted in it with particular perspicui By and accuracy. 2. THE LEGER. 348. Each page of the leger is ruled with a top line, on which is written the name of the person, and marked Dr. on the left hand for receiving the debited articles, and Cr. on the right for receiving the credited articles of the day-book. On the right hand of both Dr. and Cr. sides, are ruled two columns for dollars and cents, and on their left, thrée columns, one for the page of the day-book, one for the month, and one for the date. The leger has an index, in which the names of persons are arranged under their initial letters, with the page in the leger, where the account may be found. 349. Rule for Posting.-Under the name of the person, enter the several transactions on the Dr. or Cr. side in the leger, as they stand debited or credited in the day book. When several things are included in the same transaction, they are distinguished by the term "sundries." Some accountants enter in the leger only the page of the dry-book and the amount of the transaction, without specifying the items, but the former is thought to be the most correct method. 350. Balancing Accounts.-When all the articles are correctly posted into the leger, each account is balanced by subtracting the less side from the greater, and entering the balance on the less side, by which both sides are made equal. The excess of all the balances on the Dr. over those on the Cr. sides, being added to the cash on hand and the value of the goods unsold, the sum is the net. of the estate, which, compared with the stock at the commencement of business, exhibits the merchant's gain. 351. When the place assigned to any person's account is filled with items, the person's name must not be entered the second time, but may be transferred to another page in the following manner, viz. Add up the Dr. and Cr. columns and against the sums write, Amount transferred to page ―, here inserting the page where the new account is opened. Begin the new account by entering on the Dr. side, To amount brought from page —, inserting the page of the old account, and on the Cr. side, By amount brought from page - inserting the page of the old account, placing, the sums in their proper columns. As several day-books and legers may be necessary in the progress of business, they should be distinguished by lettering them, as follows: daybook A. day-book B. &c.-Leger A. leger B, &c. and in posting accounts into the leger, there must be a reference to day-book A or B, &c. as the account is found in one or another. 3. CASH-BOOK. 352. In the cash-book are recorded the daily receipt and payment of money. For this purpose it is ruled with separate columns, one for money received, and the other for money paid, in which should be recorded merely the date, to or by whom paid, and the sum. The cash-book is convenient, but not absolutely necessary. Other auxiliary books are sometimes used, and are important in some kinds of business, but the accountand will readily form these for himself, as circumstances render them ne cessary. |