PRACTICAL QUESTIONS.

1. Three brothers on counting their money, found that Joseph had $20, George five dollars more than Joseph, and John as many as the other two; what number of dollars had the three? Ans. $90.

2. The Arabian or Indian method of notation was first known in England about the year 1150; how long is it since to the present year, 1831? Ans. 681 years. 3. There are two numbers, the greater of them is 73 times 109: and their difference 17 times 28; what is their sum and product? Ans. 59526317 their product. § 15438 their sum.

4. Suppose nine thousand men march in a column of seven hundred and fifty deep; how many march abreast? Ans. 12. 5. A merchant would ship 360 bushels of corn in barrels which hold 3 bushels and 3 pecks each; how many barrels does he need? Ans. 96 barrels. 6. A man can perform a certain journey in 35 days, travelling 133 hours a day; how long will it require to perform the same journey when he travels only 11 hours a day? Ans. 40 615 days.

7. A man bought 180 oranges at the rate of 2 for a penuy, and 180 more at the rate of 3 for a penny; after which, he sold them out at the rate of 5 for 2 pence; did he gain or lose by the bargain? Ans. He lost 6 pence.

8. Two men, A and B, being on opposite sides of a wood, which is 536 yards about, they begin to go round it, both the same way, at the same instant of time; A goes at the rate of 11 yards per minute, and B at the rate of 34 yards in 3 minutes; what number of times must the wood be round before B overtakes A?

gone Ans. 17 times.

9. It is required to divide 600 acres of land among three men, A, B and C; so that B may have. 100 acres more than A, and C 64 more than B. Ans. A 112a. B 212a. C 276a. 10. A gentleman divided his fortune among his three sons, giving A £9 as often as B £5, and to C but £3 as often as B £7, and yet C's dividend was £2584; what was the whole estate? Ans. £19466 2s. 8d. 11. The clocks in Italy go on to 24 hours; then how many times does a clock strike, in that country, in performing one complete revolution of the index? Ans. 300 times.

12. What length must be cut off from a board 9 inches broad, to contain, a square foot, or as much as 12 inches in length and 12 in breadth? Ans. 15 inches.

13. If 14 men can finish a job in 15 days; how many men must be added to complete it in 2 days? Ans. 91 men.

14. The top of a liberty-pole, being broken off by a gust of wind, struck the ground on a horizontal plane, at the distance of 10 feet from the foot of the pole; what was the heigh of the whole pole, allowing the length of the broken piece to be 26 feet?'

*

Ans. 50 feet.

15. Suppose a pole 90 feet high, to stand on a horizontal plane; at what height must it be cut off so that the top may fall touching the ground 30 feet from the bottom, and the other end of the part cut off may rest on the stump or upright part? Ans. 40 feet.

* From the square of the length of the pole, (that is, the sum of the parts forming the hypotenuse and perpendicular,) take the square of the base, (that is, the square of the distance between the bottom of the pole and the top resting on the ground,) then divide the remainder by thrice the length of the pole, and the quotient will express the height at which the pole must be cut off.

16. There are three horses belonging to different men, employed to draw a load from Watertown to Albany for $35, A and B are supposed to do of the work, A and C 153 and B and C of the work. They are to be paid proportional; will you by your work find out what each man is entitled to receive? A's share $13271

17. A man has a room 19 feet long, and 121 feet broad; he wishes to have the floor laid with hard bricks, each 6 inches long, and 3 inches wide; how many bricks will it take? Ans. 1950 bricks.

18. Three towns, A, B and C, are so situate that B lies 30 miles directly east of A, and C lies 40 miles directly south of A; what is the distance from B to`C? Ans. 50mi.

19. In working a sum in Division, I found the remainder to be 649, the quotient was 113, the divisor was a sum equal to both and 24 more; what was the dividend? Ans. 89467.

20. A circular fish-pond is to be made in a garden, that shall take up just half an acre; what length of cord will it require to reach from the centre to the circumference ?

Ans. 27 yards.

21. How many 3-inch cubes may be cut out of a 12-inch cube? Ans. 64 cubes.

22. A person goes to a tavern with a certain sum of money in his pocket, where he spends 2 shillings; he then borrows as much money as he had left, and going to another tavern, he there spends 2 shillings also; then borrowing again as much money as he had left, he went to a third tavern, where he likewise spent 2 shillings; and thus again repeating the same at a fourth tavern, he then had nothing remaining; what sum had he at first? Ans. 3s. 9d. 23. What is the area of a right angled triangle, the three sides of which are 30, 40 and 50 rods? Ans. 600 rods. 24. A stationer sold quills at 11s. per thousand, by which he cleared of the money, but quills growing scarce, he raised them to 13s. 6d. per thousand; what did he clear per cent by the latter price? Ans. £96 7s. 3,3d. 25. When Hymen's golden knot was ti'd That made friend Delia thine,

Your age did hers as much exceed
As two times three do three;

But after three and thrice three years
She a bride will have been,

Your

age will be to that of hers,

As eleven are to seven.

Now, Joel, vers'd in numbers, tell

Their true ages on the wedding day?

Ans. Delia's age was 16, yours 32 years.

26. A father left his son a fortune, of which he ran through in 8 months; of the remainder lasted him 12 months longer; after which he had only £820 left; what sum did the father bequeath his son? Ans. £1913 6s. Ed.

27. A, leaves Exeter at 10 o'clock in the morning for London, and goes at the rate of 2 miles an hour without intermission; B sets out from London for Exeter, at 6 o'clock the same evening and rides 3 miles an hour constantly: the

question is, whereabout on the road will they meet, if the distance between the two cities be 130 miles?

Ans. 613 miles from Exeter. 28. There is a certain mast, of its length stands in the ground, 12 feet of it in the water, and 5 of its length in the air, or above water; what is its whole length?

Ans. 216 feet.

29. A lent B one hundred pounds for six months, with a promise from B to do him a like favour whenever he should require it; but when A called on B to requite his kindness, B could only lend him seventy-five ponnds; how long may A keep B's money to recompence himself for his courtesy to B?

Ans. 8 months.

30. Seven-eighths of a certain number exceed four-fifths by 6; what is that number?

Ans. -80.

31. A gentleman lent his friend a sum of money unknown, to receive interest for the same at the rate of 6 per cent, simple interest, and at the end of twelve years, received for principal and interest 860 dollars; what was the sum lent? Ans. $500.

32. Three men, A, B, and C bought a grindstone of 36 inches diameter; how much of its diameter must each grind off, to have an equal share of the stone, if A grind first, B next, and then C, making no allowance for the eye?

A 6,607

Ans. B 8,609 inches. € 20,784

USEFUL FORMS, (WITH REMARKS.) Bills of Exchange or Drafts, Promissory Notes, Receipts, Orders, &c.

A Bill* of Exchange or Draft is an open letter or request, from one person to another, desiring him to pay on account of the former, a sum of money therein mentioned, to a third person; and is the same which we call, in common language, an order or draft, for the payment of money. Its form may be thus:

$100

Watertown, Jane 20, 1831. Three months after date, (or "at sight," or "on demand,” or "at ten days after sight,") pay James Jackson, or order, (or "bearer," or "pay James Jackson," simply omitting "order" and "bearer," if you do not wish to make the Bill negotiable,) one hundred Dollars, for value received.

RICHARD ROE.

To Mr. John Doe, Merchant, Watertown.

A CHECK OF ORDER, is only a shorter Bill, governed by the same law as a regular Bill of Exchange. Its form may be thus:

MR. JOHN DOE,

lars.

Watertown, June 20, 1831.

Pay James Jackson, or bearer, fifty Dol-
RICHARD RÕE.

The one who draws the BILL, Richard Roe, is called the drawer; the one to whom it is directed, John Doe, is called the drawee, the one to whom payable, James Jackson, is called the payee.

A Bill must be accepted in order to bind the drawee.— This may be done by either writing on it, thus:

Accepted, JOHN DOE.

Or the drawee may accept it by parol, by saying that he accepts it, or promising to accept it either before or after it is drawn.

*The definition of the word BILL, as here used, is "a written paper of any kind; an account of money," &c. N. B. The words Bill, Writ and Document, apply with propriety to all kinds of communications among men, whether written or printed, and are somewhat similar in their meaning. Custom will generally suggest which word to use with the greatest propriety.