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, 905 18 The direct propor

tions of the respec

906
909

15

10.

tive stocks.

And the answers are 14407, 12007, and 8007 respectively.
Or, by taking the gain into consideration,

4053 135 each man's gain.

=

and 135,5 = 27

The direct proportions 15 of the respective stocks

135+ 6 22/
1359

Which numbers being in the same proportion as the former will give the same result.

171. A, B and C have had capitals of 20007, 30001, and 40007, in trade 12, 9 and 7 months respectively, at the years end they have to divide 21337; what is each man's part?

172. Three merchants, C, D and E have gained 3401 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?

१

Here it is plain that D's part is six times A's, and E's onethird of C's less 201.

Then C will have 1 part

D will have 6 parts and
E will have 2 parts less 201.

and adding 201 to the given sum, we have to divide 3607 into parts as 1, 6 and 2 respectively.

Whence C's part is 401, D's part 2407, and E's 80-20= 601 the answer required?

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 ?

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 3007 which they divide equally; what did each put in, their gains being at the rate of 15 per cent?

175. Bought goods for 1157 10s. which I sold for 1267 is. 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 100 by remeasuring?

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?

180. Received from Lisbon 50 casks of raisins, which stand me in 21 88. Od. 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 31 15s. per cwt. and gained 20 per cent; what would have been gained, if they had been sold at 41 5s. per cwt. ?

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?

183. What was the first cost of flaxseed which being sold at 5 guineas per hhd. the seller clears 20 per cent?

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

per

185. Bought 20 bags of flour at 25 s. 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 Is. 2d. per pint; what was my whole gain and gain per cent?

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 250 yds?

188. If linen which cost 2s. 6d. per yard, be sold, one par cel 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 price?

190. Suppose I bought goods at 37 15s. Od. ready money, and sold them immediately at £5 payable in 18 months; what is my gain per cent per annum?

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 31 Os. 8d per cwt.; how must it be sold with 4 months credit to gain 37 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 an.?

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?

196. Sold a parcel of cloth at 8s. 6d. per yard, and 3 months credit, and gained 25 per cent per annum; what did the cloth cost per yard?

197. Suppose 9 lb of tea a 6s. 8d., 51ba7s., 7 a 8s. and 214 a 10s. per fb were mixed together; what is a Ħ of it worth?

198. Bought 1000 barrels of wheat at 22s. 6d. per barrel, and 1000 barrels more at 23s. 4d. per barrel, which having Jost in preparing 4 per cent, and on which I have paid sundry charges, amounting to 127 10s. Od. when 1 sell what remains at 27s. per barrel; what is my whole gain and gain per cent?

199. Bought at Clonroad fair ten pieces of canvass, measuring 729 Clare bandles, each yard, which stood me în 1s. 2d. for every 3 bandles; sold the same in Limerick at 44d. per bandle, 3 bandles there being 2 yards; whether did 1 gain or lose, and how much?

-200. If steel which stands me in £38 per ton, be retailed at 6d. per lb.; what do I gain on 2 tons if 14 cwt. be lost on the whole by cutting and weighing in small draughts?

201. Bought 1700 barrels of wheat, barley and oats, which together stood me in 17751; for every 5 barrels of oats I had 3 of barley, and for every 8 of barley I had 7 of wheat; how many barrels of each had I, and what did each cost per barrel, the prices being as 5, 2, and 13 respectively?

202. If a barrel of wheat produce 14 stone of flour, which is rated at as many pence per stone as the wheat is shillings per barrel, now if the bran and other offal pay all charges for manufacturing; what will the miller gain per cent when wheat is 34s. per barrel ?

203. Borrowed from my neighbour on an emergency, 5 gallons of whiskey and 4 guineas, I repaid him by 20 gallons of whiskey of equal strength, and he returned me 31 6s. 6d.; what was the whiskey per gallon?

204. Bought 20 pieces of grey linen measuring 520 yards. which average Is. 44d. per yard; paid for bleaching 4d. per yard; sundry charges came to 17 2s. 6d. ; at what rate per yard must I sell them one with another, to gain 15 per cent. and pay myself at the rate of 6 per cent per annum, for 3 months time out of cash, while they were at the bleach-green?

205. Bought a puncheon of spirits containing 120 gallons, which stands me in 11s. 3d. per gallon; of this I sell 80 gallons unadulterated, at 12s. 6d. per gallon, with the remainder I mix 10 gallons of water, and then retail the mixture at 10s, per gallon; at what rate per cent is the difference of my profits, on what I sell at full strength and after reducing?

206. If I buy 28 pieces of stuff at 41 per piece, and sell 15 of them at 51 per piece; at what rate per piece must I sell the remainder so as to gain 17 per cent. by the whole?

207. Sold goods for 631 15s. and lost thereby 15 per cent. sold an equal quantity of the same goods for 801; whether did I gain or lose by the sale of the last parcel, and at what rate per cent?

208. Sold goods for 751 and lost thereby, 10 per eent though I ought to have cleared 124 per cent; how much under their just value were the goods sold?

209. Sold to A 20 hhds. of flaxseed, by which I have gained 74 per cent; these A sold to B at a profit of 24s. per hhd. ; and B sold them to C for 1157 10s. by which he gained 5 per cent; what did 1 pay for the flaxseed per hhd.?

210. If 5 gallons of brandy be worth 8 gallons of rum, and 3 gallons of rum be worth 4 of whiskey; what is the price of each per gallon, the price of 3 gallons, taking one of each, being 21 1s. 104d.?

PRACTICE

Is a compendious method of finding the value of any quantity of goods, by the given price of one of the said quantity. It is performed, by supposing the given quantity to be units of the highest denomination of the given price, and by separating the price into aliquot parts of the integer, of which it is a part or parts, and dividing the given quantity by the denominators of those parts, the answers to such questions as commonly occur in business, are found in an easy and concise manner.

NOTE-An aliquot part of any number is such, that being taken a certain number of times, will exactly make up that number, thus 4 is an aliquot part of 12, and 3s, 4d. or 40d. an aliquot part of a pound sterling.