4001. for 2 months, by which he received 297. 12s. 7žd· profit. What must A and B receive for their respective stocks, and what did they gain in the whole?

(7.) Three merchants traded together in this manner, A's money continued 8 months, for which he received 441. 4s. gain; B's continued 6 months, for which he had 421. 16s. 93d.; and C's 12 months, by which he was entitled to receive 797. 11s. 23d.—Their whole stock was 2277. hence is required each person's particular stock?

(8.) A, B, and C, are in company, and put in together 38221. A's money was in 3 months, B's money was in 5 months, and C's money was in 7 months; they gained 2341. which was so divided, that of A's gain was equal to of B's gain, and of B's gain was equal to 4 of C's 1 / 3 gain; what did each merchant gain and put in?

of

(9.) X, Y, Z, in company, make one common stock of 42621. X's money was in 4 months, Y's 6 months, and Z's 9 months. They gained 4207, which was to be divided in the following manner, viz. of X's gain to be equal to of Y's, and of Y's gain to be equal to Z's. Quere, what each person gained and put in? (10.) Four merchants, A, B, C, and D, trade together; A clears 761. 4s. in 6 months, B 577. 10s. in 5 months, C 100 guineas in 12 months, and D (with a stock of 200 guineas) 787. 158. in 9 months. Required each man's particular stock?

(11.) Three persons, A, B, and C, traded together; A's stock was 891. 5s. B's 92/. 15s. and C's 381. 10s. Their respective gains were 25/. 10s., 377. 2s. and 247. 4s.; also, if the times that each person's stock was employed in trade be added together, the sum will be 23 months; pray how long was each man's stock in trade?

(12.) A merchant (B) in trade, with a capital of 50007. after a certain time, agreed to take a friend (C) into partnership, who was to have a share in the profits accord. ing to the money he advanced, and the time of its continuance. Now C put 14007. into the stock, and they traded together in this manner, till, willing to enlarge their sphere of trade, they admitted another person (D) as a partner with a stock of 18007.-At the end of 3 years (or 36 months) reckoning from the time that B

commenced business, B's gain was found to be 1125l. C's 210l. 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 315l.; 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 19s. 6d. per acre; and C has 714a. 3r. at a guinea per 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, puir, 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, of 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 1007. 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 1007. is to 1007. 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 1007. 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 1007. 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 1192cwt. of sugar at 17. 15s. per cwt. whether shall I gain or lose if I sell it by retail for 6d. per lb. ? 1cwt. : 1l. 15s. :: 119 cwt. : 209l. 11s. 3d. prime cost. 1lb. : 6d. :: 1192cwt. : 3351. 6s. sold for.

Then 3351. 6s.-209l. 11s. 3d.—125l. 14s. 9d. gain.

(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 27. 78. 10d. per cwt. and sold it again for 63d. per lb. whether did I gain or lose, and how much?

(4.) A merchant bought 12 tuns of wine at 75l. 12s. per tun, which he sold for 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 78. 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?

Then 1331. 6s. 8d.-100l.—337. 6s. 8d. the gain per cent. Or, 10s.-7s. 6d.=2s. 6d. and 2s. 6d. of 7s. 6d. therefore 100÷3 -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 13 d. 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 751., what was the gain per cent.?

(10.) Bought a quantity of cloth at 7s. 6d. per yard, which, upon examination, I found 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 12 per cent. ?

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

Or, 124. 10s.} of 100l. and } of 4s. 8d.=7d. 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 1747. per cent. by it; how must I sell it per yard?

Examples to Prop. 4.

(12.) A stationer sold quills at 11s. per thousand, by which he cleared 60l. 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. 3 d.

Then 1961. 7s. 3&d.—1001.=96l. 7s. 3d, answer.

(17.) If, when I sell cloth at 8s. 9d. per yard, I gain 121 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 da maged, 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?