146. How many feet are there in 65% of a mile?

147. A man whose income was $2700 spent $1500; what per cent of his income remained ?

148. Paid $8000 for stock 12% below par, and sold it at 115; what per cent did I gain?

.

149. If A loans B $500 for 6 mo., how long ought B to lend A $800 to requite the favor?

150. The ratio is 31, the antecedent of; what is the consequent ?

151. How long will it take 12 men to do a job which 7 men can do in 15 days?

152. What is the difference between the cube and the cube root of .027?

153. What are the dimensions of a cube equal to a bin 12 ft. 6 in. long, 10 ft. wide, and 5 ft. high?

154. The longitude of Boston is 71° 10' W., and that of New Orleans is 90° 2′ W.; what is the time at New Orleans when it is 7 o'clock 12 min. A. M. at Boston?

155. What will be the wages of 9 men for 11 days, if the wages of 6 men for 14 days be $84?

156. For how much must I make my note at bank for 3 mo. at 6%, in order to get from the bank just $300?

157. Bought a horse for $125, and sold it for 20% advance; sold a carriage for $125, gaining 25%; sold a yoke of oxen for $125, losing 20%; bought ten sheep for $125, and sold them at a loss of 25%. What did I gain or lose on the whole?

158. Of two pieces of land, the one a circle 18 rods in diameter, the other a triangle whose hypothenuse is 30 rods, and whose base is 24 rods, which is the larger, and how much?

159. The length of a block of marble containing 105 cu. in. is 7 inches; find the length of a similar block containing 22680 cubic inches.

160. The sum of two fractions is 118, and their difference; what are the fractions?

161. A person expended 16% of all he was worth in buying 20% of the stock of a mining company. If the entire stock of the company sold for $100000, what was the person worth?

\162. A trader sold 75 cords of wood for $487.50, thereby losing 10% of the cost; what did the wood cost per cord?

164. Gunpowder being nitre and equal parts of sulphur and charcoal, how many pounds of each of the three are there in a ton?

165. Extract the square root of 1.225784 to four decimals.

166. Divide $4600 into parts which are to each other as,, and .

167. What capital must be invested in 5 per cents at 95, to secure an income of $10000 ?

168. Find the present worth of a note for $175, payable in 8 mo., interest being computed at 7% ?

169. is what per cent of ?

170. If a merchant sells goods which cost him $1620 for $1800 on a 9 mo. credit without interest, money being worth 6 per cent, how much does he gain?

171. A furrier asked 40% more for a set of mink furs than they cost him; but he afterwards sold them at a reduction of 10% from the price asked, thus realizing from the sale $12.22 profit. What did the furs cost him?

172. In what time will $560, at 8% per annum, produce $106.40 interest?

173. I owe a debt of $325.50, due in 1 yr. 5 mo., without interest; what will pay the debt now, money being worth 6% per

annum?

174. If 15 men, working 6 hours a day, can dig a cellar 80 ft. long, 60 ft. wide, and 10 ft. deep, in 25 da., how many days will it take 25 men, working 8 hr. a day, to dig a cellar 120 ft. long, 70 ft. wide, and 8 ft. deep?

175. If by selling a house for $12500 a builder gains 25%, what per cent would he gain or lose by selling it for $9000 ? 176. What is the area of a right-angled triangle, whose perpendicular is 32 ft., and its hypothenuse 40 ft. ?

177. Find the value of .000238328.

178. How much must be paid for making 52 rd. 14 ft. 8 in. f fence, at $.75 per foot?

179. A traveler, on reaching a certain place, found that his watch, which gave the correct time for the place he left, was 2 hr. 22 min. slower than the local time. Had he traveled eastward or westward, and how many degrees?

180. Find the sum of

.06.03 1 of 24.

31-21

and

.5+

181. What number diminished by 36% of itself = 336? 182. What is the value of a meadow 70 rd. long and 20 rd. wide, at $47.25 per acre?

183. What is the area of a triangle whose sides are respectively 10 ft., 12 ft., and 16 ft.?

184. What is the area of a triangle whose sides are each 24 yards?

185. A man bought a garden 3 rods wide and 4 rods long, and agreed to pay 1 cent for the first square rod, 4 cents for the second, 16 cents for the third, and so on, quadrupling each sq. rod; how much did his garden cost him?

186. Find the balance due March 4, 1882, on a note dated Jan. 1, 1879, for $580 at 5%, on which a payment of $85 had been made every 6 months; using the U. S. rule.

187. A and B enter into partnership; A furnished $240 for mo., and B $559 for 5 mo. They lost $118; how much did each man lose?

8

188. In 25 kilogrammes how many pounds, Troy weight?

190. What is the area in acres of a triangle whose base is 156 rods and its altitude 63 rods?

191. Suppose a certain township is 6 miles long and 41 miles wide, how many lots of land of 90 acres each does it contain? 192. How many strokes would a clock which goes to 24 o'clock, strike in a day?

193. The extremes are 3 and 19, the number of terms 9; what is the com. dif., and the sum of the series?

194. A man spent $3 the first holiday, $45 the last, and each day $3 more than on the preceding; how many holidays did he have, and how much did he spend?

195. What is the area of a circle whose diameter is 120 rd. ?

196. How much should be discounted on a bill of $3725.87, due in 8 mo. 10 da., if paid immediately, money being worth 5 per cent?

197. Bought bonds at 115 and sold at 110, losing $300. How many bonds of $1000 each did I buy?

198. What is the amount of $225, at 6 per cent compound interest for 4 years?

199. A steamer goes due north at the rate of 15 miles an hour, and another due west 18 miles an hour; how far apart will they be in 24 hours?

200. Find the cost, at 30 cts. per sq. yd., of plastering the bottom and sides of a cubical cistern that will hold 300 bbls. 201. Find the surface and the diagonal of a cube of granite containing 162144 cu. inches.

202. What is the area of a circle whose circumference is 160 yards?

203. What is the solidity of a prism whose height is 25 ft., and its base an equilateral triangle whose side is 12 feet?

204. What is the solidity of a prism whose base is 6 ft. square and its height 15 feet?

205. What is the solidity of a triangular prism whose height is 20 feet, and the area of whose base is 460 square feet?

206. Required the solidity of a square pyramid, the side of whose base is 25 feet, and whose height is 66 feet.

207. Required the solidity of a cone, the diameter of whose base is 30 feet, and whose height is 96 feet.

208. Required the solidity of a cylinder 20 feet in diameter and 65 feet long.

209. How many acres in a triangular field whose base is 325 yd. and its altitude 160 yd. ?

210. If a scholar receive 1 credit mark for the first example he solves, 2 for the second, 4 for the third, and so on, the number being doubled for each example, how many marks will he receive for the twelfth ?

211. What rate of income will U. S. 34% bonds yield, if bought at 102, and payable at par in 25 years?

212. What per cent income will Alabama 9's yield, bought at 85 and paid at par in 15 years?

III. PROBLEMS

FROM ENTRANCE EXAMINATION PAPERS OF VARIOUS COLLEGES.

Harvard University, 1880, '81.

859. 1. Find the greatest common divisor of 315, 504, 441. 2. Find the square root of 2 to the nearest ten-thousandth. 3. A wall which was to be 36 feet high was raised 9 feet in 6 days by 16 men; how many men will be needed to finish the work in 4 days?

4. A tradesman marks his goods at 25 per cent above cost, and deducts 12 per cent of the amount of any customer's bill, for cash. What per cent does he make?

5. A tunnel is 2 miles 21 chains 13.2 yards long. Find its length in meters. [1 mile 1.61 kilometres.]

6. Simplify

1731⁄2 — 93 + 45
5×924

7. Find the value in cubic decimeters of 1 of 87 cu. meters 62 cu. decimeters 300 cu. centimeters.

8. If 27 men, working 10 hours a day, do a piece of work in 14 days, how many hours a day must 12 men work, to do the same amount in 45 days?

9. What sum of money, at 6 per cent annually compounded interest, will amount to $2703 in 1 yr. 4 months?

10. Arrange in order of magnitude, 3, 4, 0.89.

13. Find the fourth term of a proportion of which the first, second, and third terms are, respectively, 3.81, 0.056, 1.67.

14. Reduce 133 sq. rd. 8 sq. ft. to a decimal of an acre. 15. In a board 4 meters long and 0.4 meters wide, how many square decimeters?

16. Divide (off of §) by

34

and add the quotient to