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“153. A ship at sea is pursued by a privateer, which is 15 miles from her when the chace commenced, the privateer advances at the rate of 10 miles an hour, and the ship pursued sails at the rate of 83 miles an hour; in what time will the privateer overtake her ? 154. The distance of Cork from Belfast is, suppose 204 miles: two travellers set out in order to meet, one from Cork the other from Belfast, they meet at the end of 4 days, when it appears, that the traveller from Cork has gone 3 miles per day less than he from Belfast; how many miles did each of them travel per day? , 155. Suppose I bought 2 pieces of grey linen, the one 63 yards, at the rate of 9 yards for a pound, the other 54 yards at the rate of 12 yards for a pound; but unexpectedly being called on for a sum of money, which not having, I sell both pieces at 21 yards for 21; whether do I gain or lose, and how much P 156. If 5 men, or 8 boys, can do a piece of work in 3 days: in what time could one man and one boy together perform it P Here it is plain, that in 3 days one man will perform + of the work, and a boy # of the work in the same time. Therefore, H = 3 days work for a man. + = 3 days work for a boy. 43 = 3 days work for a man and a boy. 13 : 40 : : 3 days. 3

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157. Suppose the proportion of mens’ work to boys to be the same as in the last question, and that 5 men and 8 boys can perform a piece of work in 13 days; in what time would 8 men and 5 boys perform the same piece of work?

158. A person bought 2 baskets of apples, each containing an equal number, for the first he paid at the rate of 6 for a Penny, for the other at the rate of 7 for a penny ; he mixed them together and sold all at the rate of 7 for a penny, by which he lost 2d.; how many were in each basket :

159. If a barrel of beer last a family of 9 persons 7 days; how many barrels will be used by 16 persons in 91 days, diicking at the same rate *

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160. Two merchants entered into partnership, and each put in 20 pieces of cloth; but one of them had a better quality than the other, and cost 4l more per piece; the cloth being sold, they find they have gained 1021 10s. of which he that had the worst quality received 461 5s. for his part of the gain; how much per piece was each of their cloths valued at 7 161. Two merchants buy certain goods, the one advances 80l, the other 105l, they gain on sale of them 741; what is each man's part of the gain :

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162. Three persons went into trade, with the respective cas pitals of 26300, 250, and 350; their joint profit at the end bf the year was 5001; what was each man's part of the gain? 163. Two merchants made a stock of 1200l., of which one contributed 750l and the other the remainder, they gain 300l; what is the share of each 164. Divide 1541 in the proportions 2, 3 and 4 respectively. 165. Divide 1541 in the proportions +, + and + respectively. 166. A piece of ground of 45a. 2r. 20p. is to be divided between 3 sons, of which the eldest is to get #, and the remainder to be equally divided between the other two: what is the share of each * 167. A ship, worth £1960 being lost, of which A had #, B #, C or and D the remainder: what will each partner lose if £1200 of the value be insured? 168. Three persons, A, B and C purchase a ship, of which A advanced #, B 3 and Cthe remainder, which was 350l; what part of the vessel had C, and what money did each of the others put in P 169. Divide £240 between 3 persons, in the proportions of 1, 2, 3, respectively. 170. Three merchants enter into partnership, their joint stock was £3440, they gain 4051, which they divide equally; what did each put in, having continued in trade 5, 6 and 9 months respectively :

Here, as the gains are equal and the stocks required, no notice need be taken of the gain, in solving this question, and it is evident, that the less time each man’s money was in trade, the greater the sum of money he should employ, therefore, proceed thus ; find the least common multiples of the numbers 5, 6 and 9, which is 90. --Whence, 90 + 5 = 18.) The direct propor90 -i- 6 = #} tions of the respec90 -i- 9 - 10 J tive stocks. Then, as 18 + 15 + 10 = 43 : 18 :: 3440 : 1440 43 : 15 : : 3440 : 1200 43 : 10 :: 3440 : . 800 And the answers are 1440l., 1200I, and 800l respectively. Or, by taking the gain into consideration, 405 + 3 = 135 each man's gain.

and ; .# = # The direct proportions

135 + 9 = 15 of the respective stocks

Which numbers being in the same proportion as the former will give the same result. - - 171. A, B and C have had capitals of 2000l., 3000l, and 4000l., in trade 12, 9 and 7 months respectively, at the years end they have to divide 2133 l ; what is each man's part? 172. Three merchants, C, D and E have gained 340l when the profit of C is multiplied by 2, that of D divided by 3 and that of E increased by 20, the results will be equal; what was the share of each 2. Here it is plain that D's part is six times A's, and E’s onethird of C's less 20l. - - - Then C will have 1 part D will have 6 parts and E will have 2 parts less 20!. . . and adding 201 to the given sum, we have to divide 360l into parts as 1, 6 and 2 respectively. * : Whence C's part is 401, D's part 2401, and E’s 80–20= 60l the answer required 2 : 173. Suppose, as in last question, but the share of C to be divided by 2, that of D to be multiplied by 3, and E’s increased by 20 as before; what is the share of each P 173. In this question the parts are 6, 1, and 3-20; therefore, adding

20 to the given sum and proceeding as above, the answers are readily obtained.

174. Three merchants, A, B and C are in trade 12, 9 and 7+ months respectively, they gain 300, which they divide equally; what did each put in, their gains being at the rate of 15 per cent 2

175. Bought goods for 115, 10s. which I sold for 126, 1s. what is my gain per cent? -

176. Bought 45 pieces of coarse cloth for 1351; how must they be sold per piece to gain 15 per cent?

177. If I buy cloth at 17s. 6d. per yard; what shall I gain per cent, if I sell it at 19s. 6d. per yard; if I lose 1 yard to 100 by remeasuring 2 178. Sold 500 barrels of oats, at 12s. 6d. per barrel, by which I lost 4 per cent; what do I gain per cent when I sell 500 barrels of the same oats at 15s. 2d. per barrel, and what do I lose by the first, and gain by the last parcel? 179. If I sell a parcel of barley at 18s. per barrel, and I find I have gained 20 per cent; now if I sell a parcel of the same barley, which came to 451; how many barrels were in the last parcel, and at what price did I dispose of them P 180. Received from Lisbon 50 casks of raisins, which stand me in 21 8s. 0d. each, sold them at 51 12s. per cwt. by which I gain 25 per cent. ; what was the weight of each cask? 181. Sold hops at 3, 15s. per cwt. and gained 20 per cent; what would have been gained, if they had been sold at 41 5s. per cwt. P - 182. Bought 1200 yards of muslin at 2s. 8d. per yard, sold one-third at 3s. per yard, one-fourth at 3s. Id. and the remainder at 3s. 2d. per yard; required the whole gain and gain per cent P 183. What was the first cost of flaxseed which being sold at 5 guineas per hbd. the seller clears 20 per cent?

184. If 15 per cent, be lost by selling calico at 15d. per yard ; what was the prime cost?

185. Bought 20 bags of flour at 25s. per cwt. (each bag 2 cwt.), 15 bags more at 23s.6d. per cwt., and 10 more at 20s. 8d. per cwt. which being mixed, were sold at 22s. 9d. per cwt ; what did I gain or lose, and at what rate per cent. ”

186. If whiskey be bought at 9s. per gallon, and that in a puncheon containing 130 gallons I put 8 gallons of water, and then retail the mixture at 1s. 2d. per pint; what was my whole gain and gain per cent? -

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187. If linen which cost 2s. 6d. per yard, be sold so as to gain 10 per ct. ; what money do I receive when I sell 250yds?

188. If linen which cost 2s. 6d. per yard, be sold, one parcel at 3s. and another parcel at 2s. 9d. per yard; how much per cent was gained by the first, and how much per cent by the last sale ;

189. Sold certain goods at 15s. per lb. by which # of the first cost was gained, but growing scarce, the remainder of them was sold at 17s.6d. per lb. ; what was gained per cent by the latter priee * 190. Suppose I bought goods at 31 15s. 0d. ready money, and sold them immediately at £5 payable in 18 months; what

is my gain per cent per annum ?

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191. If goods were sold at 5s, which were bought for 4s.

2d. payable in 8 months; what is the gain # cent # an.” *:

192. If merchandize was sold at 3l 0s. 8d per cwt. ; how must it be sold with 44 months credit to gain 374 per cent per annum ?

193. If spirits which cost 8s. 6d. per gallon be sold at 10s per gallon, with 3 months credit; what is the gain per cent per annum ? -

194. If sugar which cost 98s. per cwt. be sold at 51 10s. per cwt. with 9 months credit; what is gained per cent per am.?

195. When I sell wheat at 32s. per barrel, I lose 8 per cent ; what do I gain per cent when I sell a parcel of the same wheat at 34s. 6d. per barrel ?

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