147. A principal of £10000 is lent at compound interest. At what rate per cent. per annum must it be lent to amount to £11576. 4s. in three years?

148. If a man earn 3s. 6d. a day by mowing grass at 5s. 8d. per acre, when he works 12 hours a day, how long must he work a day, and what quantity must he mow to earn 3s. 9d. a day, when he is allowed 5s. an acre?

149. How many revolutions will the driving wheel of a locomotive 18 feet in circumference make between London and Birmingham, a distance of 1124 miles? And how many times will the cylinder discharge its steam on the journey (the cylinder discharges steam 4 times in each revolution.) Also how long will it be going, supposing it to move at an average rate of 30 miles an hour when at work, and stopping at 12 stations; at the first station 1 minute, and at the twelfth 15 minutes, increasing the period of stopping in arithmetical progression? Also how much coke will the engine consume supposing that while in motion it requires 6 bushels per hour, and when stopping 4 bushels per hour? And to what sum will the price of the coke amount at 5d. per bushel ?

How

150. The rent of a house is £120 per annum. It is assessed at the rate of the rent, the poor rate is 7s. 6d. in the pound, the paving rate is 1s. 9d. and the church rate 4d. much does the tenant pay altogether for his residence? 151. A person increases his estate annually by £100 more than the quarter of its value, and at the end of 4 years he found his estate amounted to £10342. 3s. 9d. What had he at first? 152. A person after paying an income tax of 7d. in the pound, and a rate equal to of of it, has £458. 10s. left. Find his income

153. Prove that the simple interest of £260 for 4 months at 37 per cent. per annum, is equal to the discount of £263 7s. 2d. for the same time at the same rate.

154. What is the difference between the true and bankers' discount, on a bill of £1209. 12s., drawn October 13th, at 4 months, and discounted December 5th, at 4 per cent. per annum, C. I. ?

155. A cubic foot of wood weighs 1140 lbs. What is the weight of a beam, 24 feet long, 23 feet wide, and 2 feet thick; and what is its value at 2s. 2d. per cubic foot?

156. A wishes to buy property that will cost £50000, for which purpose he sells the following stocks, of which he is the holder, viz.: £1750 income in the 5 per cent., at 121.40, and £800 in the 3 per cent., at 83.50. How much had he left after he bought the property?

157. A has 3 lumps of metal of the same volume, but of different weights: 5 cubic inches of the 1st weigh 693 oz., 31⁄2 cubic inches of the 2nd weigh 41 oz., and 4 cubic inches of the 3rd weigh 91 oz. Find the weight of 1 cubic inch of the mixture of these metals.

158. Brass contains 3 parts of copper to 7 of zinc; copper costs 1.60s., and zinc .30d. per lb. Find the price of 1 cwt. of brass.

159. A bought oil for £240; of the payment is to be made in 3 months, 1⁄2 in 6 months, and the rest in 10 months. In what time should the whole sum be paid in one payment? 160. Divide 20s. among 6 men, so that each shall have 24d. more than the other.

161. In a field of 12 acres there are grazing 2 horses, 3 cows, 12 sheep, and 1 ass; each horse eats as much as 1 cow, 1 sheep, as 1 ass; each cow as much as 1 sheep and 1 ass, and 1 sheep one-third part of the ass. What part of the pasture does each kind of animal eat?

162. The united weight of two persons is 148 lbs., their difference 48lbs. Find the weight of each in ounces; and also how many cubic inches each contains, the specific gravity of living men being .891.

163. The relation of two magnitudes is expressed by the continued fraction:

Find the converging fractions showing the approximate ratio of these magnitudes.

164. I bought goods for £150, upon which I want to gain 10 per cent. and allow 12 per cent. discount to the purchaser. What will be the selling price?

165. A, B and C perform of a work together in 24 days, but if A or B, who do the same work in equal times, had been taken away, then of it would only be accomplished in 28 days. In what time can each do it separately?

166. What is the vulgar fraction equivalent to .08134765625 ? 167. The advance of the hour hand of a watch beyond the

minute hand is measured by 24% of the minute divisions, and the time is between 6 and 7 o'clock. Find the time by the watch.

168. A work is to be performed by 15 workmen in 24 days; after having been 9 days working, 4 men fell ill, who returned after being absent 7 days. How long were they doing the work?

169. A wall can be built in 83 days by 16 men. The first day all the men take part in the work, and every succeeding day their number is diminished by one. How long will it take building the wall?

170. 21204 yards of stuff are to be woven in 20 days by 21 men, working 8 hours a day, when they had been 13 days working, 9 of the men ceased attending. How many hours per day must the remaining weavers work, in order to have performed their task in the required time?

171. What principal must be lent at 4 per cent. per annum, so that its interest after 7 months, being lent at 5 per cent. for six months, shall bring £8. 15s.?

172. A bought for £1200, merchandise which he sold to B at 5 per cent. profit; B sold it to C, at 4 per cent. profit; C to D, at 4 per cent. profit; D to E, at 34 per cent. profit. What did the goods cost each man? How much is the profit of

each individual?

173. P had goods to the amount of £25640 prime cost, which he disposed of during the year. At how much per cent. did

he retail his goods, having covered the prime cost, his annual expenses of £2460, and increased his capital by £1680?

174. The latitude of Greenwich is 51° 28′ 40′′, and at the solstices the sun is 23° 27′ 34′′ from the equator. Find the zenith distances of the sun at both solstices.

175. Find the meridian altitude of the sun at the summer and winter solstices, in the latitude of Greenwich.

176. The proportion of the solid area of our planet is to that of the liquid parts as 10 to 27. If the mean depth of the sea were 484 yards, what would be the weight of the water, and what would be the weight of the salt and other impurities wherewith it is impregnated?

177. A cloth merchant values his cloth at 18s. per yard in bartering with B, which is 124 per cent. above his invoice price. Required, how B should rate his goods, which cost 2s. 6d. per yard, to be even with him, and the prime cost of the cloth. 178. I have a case of liquors in bond on which I wish to pay the duty; the case contains 48 bottles of 33 gills, each bottle weighs 14 ounces. What is the duty, knowing that the duty on foreign liquors is £1. 10s. 4d. per gallon, and on glass 3s. per cwt.

179. A lever is an inflexible rod turning upon a fixed point, called a fulcrum. Levers are of three kinds according to the relative situations of the power and weight:

the

Now in every lever the power the units in its arm= weight the units in its arm; or in other words, the momentum of the power the momentum of the weight. Suppose

the weight is 20 lbs., its arm 3 feet, and the power's arm 5 feet, what must the power be in case of equilibrium?

Power-Weight's arm × Weight__ 3×20

Power's arm

5

= 12 lbs.

180. A weight at the end of its arm 9 inches in length, balances 2 lb. 14 oz. at the end of the other arm 5 inches in length. Find that weight.

181. Five persons of equal strength hold the ends of a pole 10 feet long, to which a weight is hung. Two persons are at one end, and three at the other. Where must this load be fixed, so that every bearer may have the same weight to carry? 182. In a false balance, (one in which the arms are of unequal length,) a body appears to weigh when in one scale, and the weight in the other, 24 lbs., but when weighed in the other 18 lbs. The real weight is required.

In this question we have 24 × a=Wxb, and 183×6=W×a. .. 24 ×a× 181 × 6=W2 ×a×6, &c, &c.

183. It is required to make a steel-yard with a rod, the unvariable

arm of which is 4 inches, and the moveable weight used 2 lbs. At what distances from the fulcrum must the weight be placed so as to equipoise 1,2,3,4,...12 lbs.

184. There is a cistern whose length is of its breadth which is

of its depth and whose solidity is 1157 cubic feet. Required its length, breadth, and depth, as well as how many imperial gallons it contains. Also what difference is there in the weight of water it contains, allowing a cubic foot to weigh 1000 oz. and the imperial gallon to weigh 10 lbs.?

185. Divide £2293 between A, B, and C so that for every 53 shares taken by A, B takes 43; and for every 41 shares taken by B, C takes 33; what did each man receive?

186. A received £2100 which was of B's money, now three times B's money was half C's; what was C's money?

187. Suppose I plant a bean, and its produce be 21 the first year, how much land (allowing 6 inches for each bean) will it take to plant 10 years' produce?

188. A garden roller 38 inches long, outside diameter 22 inches, and the thickness 2 inches, is made at the rate of 3d. per lb.