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having lost 163% in weight, he sold of it at 36 cents a bushel : at what rate must he sell the remainder so as to realize a net profit of 20% ?

13. B owes C $1,324; C offers to allow 4% for ready money. If B pays $960 immediately, how much does he still owe ?

14. A man bought 10 books at the rate of $9 a dozen, and sold them for 85 cents each : what % was gained ?

15. A man bought 60 tons of coal at $54 a ton, 163% of which was lost by the sinking of the boat : for how much per ton must he sell the remainder so that he may neither lose nor gain ?

16. The premium on an insurance of $1,250 was $22.50 : what was the rate ?

17. A and B rented a pasture for $18.66. A put in 20 cows for 11 days, and B 23 cows for 31 days: how much rent should each pay ?

18. A, B and C enter into partnership; A puts in $500 for 8 months, B $600 for a year, and C $800 for a year-anda-half. They lose $512 : how should the loss be apportioned ?

19. C and D form a partnership ; C put in $4,000, and at the end of 6 months put in $2,000 more; D put in $8,000, and at the end of 8 months withdrew $3,000. At the close of the year they had gained $1,320 : what was each one's share ?

20. A certain piece of work was to be done by 240 men in 64 days, but a number having been sent away, it was performed in 120 days : what was the number of men sent away?

21. How much more is the compound interest than the simple interest of $1,500 for 5 years at 6% ?

22. A cistern centaining 480 gallons can be emptied by two pipes in 4 and 5 minutes respectively : if both pipes are left open, in what time will they empty the cistern?

23. When 9 barrels of onions are worth $33.75, what are 28.50 barrels worth ?

24. A man bought 358 bushels of corn at 78 cents a bushel; he distributed 38 bushels among his poor neighbors, and sold the rest at 93 cents a bushel : how much did he make ?

25. Bought a house and a farm of 48 acres for $9,456. The house cost $4,320: what was the value of the land

per acre ?

26. A farmer sold 143 acres of land at $45.75, and 125 acres at $61 : what was the average price to the nearest cent of each acre ?

27. I bought land for $2,450.75, and sold 48.5 acres at $35.50 an acre. The value of the remaining land was $36.45 an acre : how many acres did I buy ?

28. If 24,500 bricks are sold for $134.75, what is the price per M. ?

29. What is the cost of 4,250 feet of planking at $35

per M. ?

30. What are 1,480 melons worth at $8.75 per hundred ?

31. A man bought 4,000 bushels of wheat at $1.10 per bushel ; he sold 10% at 5% loss, 40% at 10% gain, and the remainder at 8% gain : what did he gain by the transaction ?

32. If you sell a house for $5,000 and lose 12%, for what price should you sell another at an advance of 121%, so as to cover the loss on the former house ?

33. Sold property for $2,400, 25% of which was gain. I was able to collect only 80% of the proceeds of the sale : what was the actual gain ?

34. A grocer after losing 19% of his apples had 153.9 barrels left: if they cost $3.50 a barrel, for what must they be sold so that he may neither gain nor lose ?

35. What is the difference in net cash value between a bill of $1,200 less a discount of 25% and 10% off the remainder, and the bill less a discount of 35% ?

36. I wish to purchase a 5% bond, so as to make the investment yield me 7% : how much can I pay for the bond, including brokerage at %?

37. A piece of property was worth $5,000 in gold, when the premium on gold was 12%: what was the value of the same in currency?

38. A man borrowed $5,000, which he invested in real estate. „Six months later he sold the property on a credit of 12 months, with interest, for $7,500: money being worth 6%, what was his profit ?

39. A man sold a quantity of wheat at $1.08 per bushel, at a profit of 20%; he afterward sold a lot of the same for $31.05, at a profit of 50% : how many bushels were there in the last lot ?

40. A man sold at a gain of 30% and took a note for the amount of the sale. He sold the note at 15% less than its face value : what was his gain per cent. ?

41. A farmer llows one acre pasture for every 5 sheep, and one acre of plowed land for every 8 sheep : how many sheep can be kept on 325 acres ?

42. If a gallon measure is d'y too small, how much will a dealer filch from his customers in a year, if he sells 150 gallons of milk daily at 13 cents a gallon ?

43. A certain man owns 7 of a tract of land, and sells 14% of it to one man, 25% of the remainder to another, and 284% of what he then had to a third person, when he has 15 acres remaining: how many acres in the tract of land ?

44. A merchant bought on 12 mo. time, 5 casks of wine, each containing 125 gallons, at 90 cents a gallon, and sold it at 95 cents a gallon on 6 mo. time. If money is worth 10%, how much does he gain ?

45. A farmer sold a number of cows and had 21 left, which was } of the number sold; if the number sold be divided by 4 of 81, the quotient will be of the price of each cow : how much did he receive for his cows?

46. A tax of $2,910 is to be raised in a town whose property is valued at $175,000 : what is the rate if there are 276 polls at $2 each, and what is B’s tax, who owns a house valued at $1,200, a watch worth $50, and pays for ono poli?

47. A boy bought an equal number of apples at 2 for 1 cent, and 3 for 1 cent, and, selling them at 5 for 2 cents, thereby lost 1 cent: how many apples did he buy ?

48. A, B, C and D agree to do a piece of work for $152. A, B and C can do it in 5 days; B, C and D, in 31 days; C, D and A, in 4 days; and D, A and B, in 4 days: how long will it take them all to do it ? How long will it take each of them to do it? If they work together, how much should each receive ?

49. At what time after 4 o'clock are the hour and minute hands of a .clock together:

SUGGESTION.— The minute-hand gains 11 of the distance it passes

over.

50. A, B and C were employed to do a piece of work for $29.50. A can do it in 4 days working 9 hr. a day; B in 3 days working y hr. a day, and C in 4 days working 6 hr. a day: if they all work together, what part of the money should each man receive ?

51. A merchant sold 20 stoves for $180. He received $19 for the largest size, $7 for the middle size, and $6 for the smallest size: how many stoves of each size did he sell ?

Involution.

ART. 425.—Every number is the first power of itself; when multiplied once by itself, the product is the square or second power of the number; when the number is used three times as a factor, the product is the cube or third power; when the number is used four times as a factor, the product is the fourth power, and so on.

ART. 426.—An Exponent is a small figure placed to the right and slightly above a number, and shows the power to which the number is to be raised. Thus, 192 means that my is to be raised to the second power ; 93 that 9 is to be raised to the third power; 134 that 13 is to be raised to the fourth power.

ART. 427.—The Root or Base of a number is one of the equal factors of the number.

ART. 428.- Involution is the process of finding the powers of numbers.

Find the value of :
1. 672.
2. 493.
3. 262.
4. 234.
5. 423.
6. 1202.
7. 1.53.
8. (3.2)2.
9. (.44)3.
10. (.01)4.

11. 324.
12. 253.
13. 1212.
14. 1013.
15. (1).
16. (3)3.
17. (3)? ()3.
18. (.25)3 x 24.
19. (.02)2 x 52.
20. (4)" x 3.

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