commenced business, B's gain was found to be 11257. C's 2107. and D's 2027. 10s. quere, how long were C's and D's money employed in trade, and what did each merchant gain per cent. for his money?

(13.) Two merchants, A and B traded together with a stock of 3157.; A's money was employed 12 months, and B's only 8: when they came to divide the profits of their traffic, they had equal shares.-Pray what money did each person put into the stock?

(14.) A certain village is possessed by three proprietors, who are desirous of having it enclosed for their mutual benefit. A's property, upon a survey of the quantity and quality, is 394a. 3r. 34p. at 18s. per acre; B has 417a. 1r. 14p. at an average of 198. 6d. per acre; and C has 714a. 3r. at a guinea an acre. Out of these an allowance of 5s. 6d. in the pound is to be made for the tithes. What quantity of land must be allotted for these tithes, at an average quality of 19s. 9 d. per acre?

LOSS AND GAIN.

Definition. Loss and Gain is a rule that discovers what is gained or lost in the buying or selling of goods; and instructs the merchant, or trader, to raise or lower the price of his goods so as to gain or lose so much per cent. &c.

Note. By the prime cost, or selling price of an integer, in the following propositions and rules, is meant the prime cost, or selling price, per yard, pair, dozen, pound, cwt. gallon, tun, &c. of any quantity of goods, or it may signify the whole value in any of the propositions, except the first, fifth, and sixth.

Proposition 1. Given the prime cost and selling price of an integer of any quantity of goods to find the whole gain or loss.

Rule. Calculate the value of the goods at the prime cost and selling price of an integer, by the Rule of Three, or Practice, and the difference of these values will be the gain or loss.

Prop. 2. Given the prime cost and selling price of an integer of any quantity of goods, to find the gain or loss per cent.

Rule. As the prime cost of an integer is to 1007. so is the advanced or reduced price of such integer to a fourth

number; which, if greater than 100%. the excess will be the gain; but, if less than 1007. the defect will be the loss per cent.

Prop. 3. Given the prime cost of an integer, and the proposed gain or loss per cent. to find the selling price of such integer.

Rule. As 100%. is to 100. with the gain added to, or the loss subtracted from, it, so is the prime cost of an integer to the required price per integer.

Prop. 4. Given the price of an integer, with the gain or loss per cent. by such a price, to find the gain or loss at any other price.

Rule. As the given price of an integer is to 1007. with the gain per cent. added to, or loss subtracted from, it, so is the proposed price to a fourth number. If this fourth number be greater than 1007. the excess will be the gain ; but, if it be less, take it from 1007. and the remainder will be the loss per cent.

Prop. 5. Given the price at which an integer of any quantity of goods is sold, and the gain or loss per cent. by such sale, to find the whole gain or loss.

Rule. Find the whole value of the goods at the selling price per integer. Then, as 100%. with the gain per cent. added to, or loss subtracted from, it, is to 1007. so is the whole value at which the goods were sold to the whole prime cost. The difference between the whole value at which the goods were sold and the whole prime cost will give the whole gain or loss.

Prop. 6. Given the prime cost of an integer of any quantity of goods, and the gain or loss per cent. by the whole quantity, to find the whole gain or loss.

Rule. Find the whole value of the goods at the prime cost per integer. Then, as 100l. is to 1007. with the gain added to, or loss subtracted from, it, so is the whole value of the goods, at the price they cost, to the whole value at the gain or loss per cent. proposed. The difference between these values will give the whole gain or loss..

Note. More propositions and rules may be given; but, if the scholar thoroughly understand the rules already laid down, and their application, it is presumed he will not meet with any embarrassment in Loss and Gain, however complicated the examples may be.

Examples to Proposition 1.

(1.) Bought 119/cwt. of sugar at 17. 15s. per cwt. whether shall I gain or lose if I sell it by retail for 6d. per lb.? 1cwt. : 11. 15s. :: 119cwt. : 209l. 11s. 3d. prime cost. 6d. :: 119cwt. : 3351. 6s. sold for. Then 3351. 6s.-209l. 11s. 3d.=125l. 14s. 9d. gain.

1lb.

:

(2.) Bought 15cwt. of cheese at 17. 11s. 6d. per cwt. which I sell by retail at 44d. per lb. what shall I gain or lose by so doing?

(3.) I bought 77cwt. 3qr. 14lbs. of sugar at 21. 7s. 10d. per cwt. and sold it again for 6d. per lb. whether did I gain or lose, and how much?

(4.) A merchant bought 12 tuns of wine at 757. 12s. per tun, which he sold at 7s. per gallon; but, by misfortune, a pipe was staved, and rendered unsaleable. Whether did the merchant gain or lose, and how much by such sale?

(5.) Bought 340 yards of cloth at 5s. 4d. a yard, and sold it again at 7s. 6d. per yard; what did I gain in the whole?

Examples to Prop. 2.

(6.) If wine be bought at 7s. 6d. per gallon, and sold for 10s. what is gained per cent. by such sale?

7s. 6d. : 1001. :: 10s. : 1331. 6s. 8d.

Then 133t. 6s. 8d.-100l.-331. 6s. 8d. the gain per cent.

Or, 10s.-7s. 6d.—2s. 6d. and 2s. 6d.={ of 7s. 6d. therefore 100÷S 331. 6s. 8d. answer.

(7.) A merchant has a quantity of damaged tobacco, which, including all expences, stands him in 174d. per lb. what will he lose per cent. by a sale at 131⁄2d. per lb.?

(8.) Bought 27 yards of cloth for 17 guineas, and sold them again at 9s. 10d. per yard; what was the gain or loss per cent.?

(9.) Bought a quantity of goods for 607. and sold them again for 757. what was the gain per cent.?

(10.) Bought a quantity of cloth at 7s. 6d. per yard, which, upon examination, I find not so good as I expected. Now, if I sell it at 6s, 24d. per yard, what shall I lose per cent, by it?

Examples to Prop. 3.

(11.) Bought muslin at 4s. 8d. per yard; at what price must I sell it per yard to gain 121⁄2 per cent.?

100l. : 112/. 10s. :: 4s. 8d. : 5s. 3d. answer.

Or, 12l. 10s. of 100l. and of 4s. 8d.=74. Hence 4s. 8d.+7d. 5s. 3d, as before.

(12.) If I buy cloth at 11s. 6d. per yard, how must I sell it to gain 201. per cent.?

(13.) A Manchester man bought a quantity of yarn at 6s. per bundle, which not proving so good as he expected, he sold it so as to lose 6 per cent. by it; what was the selling price?

(14.) If I buy tobacco at 12 guineas per cwt. at what rate must I sell it per cwt. to gain 157. per cent.?

(15.) Bought a quantity of cloth at 7s. 6d. per yard, which, not proving so good as I expected, I have resolved to lose 17. per cent. by it; how must I sell it per yard?

Examples to Prop. 4.

(16.) A stationer sold quills at 11s. per thousand, by which he cleared 607. per cent. but they growing scarce, he raised them to 13s. 6d. per thousand; what was his gain per cent. by the latter price?

11s. : 1601. :: 13s. 6d. :: 1961. 7s. 3rd.

Then 1961. 7s. 32d.—100t.—961. 7s. 3. answer.

(17.) If, when I sell cloth at 8s. 9d. per yard, I gain 127. per cent. what will be the gain per cent. when it is sold for 10s. 6d. per yard?

(18.) A woollen-draper in London had a quantity of black cloth by him, and, being afraid of its being damaged, he sold it at 15s. per yard, and, by so doing, lost 147. per cent. but a general mourning coming unexpectedly, he was enabled to advance his cloth to a guinea per yard; what did he gain or lose per cent. by the latter sale?

(19.) If a plumber gain 127. 10s. per cent. when lead is sold at 201.9s. 6d. a fother, what would he gain or lose per cent. when it is sold only at 177. 1s. 3d. the fother?

Examples to Prop. 5.

(20.) A merchant sold 5t. 3hhds. 53 gall. of wine at 6s. 8d. per gallon, and by so doing gained 647. per cent. What was the prime cost of his wine, and what did he gain in the whole?

1 gall. 6s. 8d. :: 5t. 3hhd. 524g.: 5001. 16s. 8d. sold for. Again, 1061. 10s. : 100l. :: 500l. 16s. 8d. : 470k. 53. 3181d. prime

cost.

Then 500l. 16s. 8d.-4701. 5s. 318d=301. 11s. 4. whole gain.

(21.) A merchant sold 15cwt. 3qr. 18lb. of sugar at 71d. per lb. and his profit per cent. was 257. what did he gain in the whole?

(22.) If I sell 500 deals at 15d. a piece, and 97. per cent. loss, what do I lose in the whole quantity?

(23.) A had 15 pipes of Malaga wine, which he parted with to B at 441. per cent. profit, who sold them to C for 387. 11s. 6d. advantage; C made them over to D for 5007. 16s. 8d. and cleared thereby 6 per cent. what did this wine cost A per gallon?

Examples to Prop. 6.

(24.) Bought 60 reams of paper at 15s. per ream, by the sale of which I lost 47. per cent. what did I lose in 'the whole?

1r.

15s.: 60г. : 451. prine cost.

100 96: 451.: 431. 4s. selling price.

Then 451-431. 4s.=1l. 16s. whole loss.

(25.) Sold 7 pieces of cloth, each containing 354 yards, 'on account of damage, at a loss of 101. per cent, what did I lose in the whole, the prime cost being 15s. per yard?

(26.) Bought 475 yards of cloth at 10s. 6d. per yard, by which I gained 30l. per cent. what did I gain in the whole?

(27.) Bought 127hhds. of sugar, each containing 4 cwt. at 31. Os. 8d. per cwt. how must I sell the sugar per lb. to gain 50 guineas by the whole?

(28.) A merchant bought 1400 casks of tallow, at 21, 5s. per cask, and sold one half of it at 21. 15s. per