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 $5 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 containing 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 12%, 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 1%?

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 allows one acre of 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 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 of a tract of land, and sells 142% 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 of the number sold; if the number of 8, the quotient will be of the how much did he receive for his

left, which was
sold be divided by
price of
each cow:
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 one 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 3 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 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 7 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, 72 means that 7 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.