2. A and B have gained by trading 1821. A put into stock 300l. and B 400l. what is each person's share of the profit ? Ans. A 781. and B 1041. persons, so that their 3. Divide 1201. between three shares shall be to each other as 1, 2 and 3, respectively. Ans. 201. 40l. and 601. 4. Three persons make a joint stock; A put in 1841. 10s. B 961. 15s. and C 761. 5s. they trade and gain 2201. 12s. what is each person's share of the gain ? Ans. A 1131. 16s. B 591. 145. 7159 C471.18. 15 5. Three merchants A, B and C, freight a ship with 340 tuns of wine; A loaded 110 tuns, B 97, and C the rest. In a storm the seamen were obliged to throw 85 tuns overboard; how much must each sustain of the loss? : 8 A 27, B 244, and C 33 6. A ship worth 8601. being entirely lost, of which belonged to A, to B, and the rest to C; what loss will each sustain, supposing 500l. of her to be insured ? Ans. A 451. B 90l. and C 2251. 7. A bankrupt is indebted to A 2751. 14s. to B 3041. 7s. to C 1521. and to D 1041. 6s. His estate is worth only 6751. 15s. how must it be divided ?. Ans. A 2221. 158. 2d. B 2451. 18s. Id. 8. A and B, venturing equal sums of money, clear by joint trade 1541. By agreement A was to have 8 per cent. because he spent his time in the execution of the project, and B was to have only 5 per cent. ; what was A allowed for his trouble ? Ans. 351. 105. 9d. DOUBLE FELLOWSHIP. 1 Double Fellowship is when different or equal stocks are employed for different times. S RULE. Multiply each man's stock into the time of its continu ance, then say, As the total sum of all the products is to the whole gain or loss, So is each man's particular product to his particular share of the gain or loss. EXAMPLES. 1. A and B hold a piece of ground in common, for which they are to pay 361. A put in 23 oxen for 27 days, and B 21 oxen for 35 days; what part of the rent ought * Mr. MALCOLM, Mr. WARD, and several other authors, have given an analytical investigation of this rule: but the most general and A 2. Three graziers hired a piece of land for 6ol. ros. put in 5 sheep for 4 months, B put in 8 for 5 months, and C put in 9 for 6 months: how much must each pay of the rent? Ans. A 111. 55. B 20l. and C 291. 55. 3. Two merchants enter into partnership for 18 months; A put into stock at first 2001. and at the end of 8 months he put in 100l. more; B put in at first 550l. and at the end of 4 months took out 1401. Now at the expiration of the time and elegant method, perhaps, is that, which Dr. HUTTON has given in his Arithmetic, viz. When the times are equal, the shares of the gain or loss ate evidently as the stocks, as in Single Fellowship; and when the stocks are equal the shares are as the times; wherefore, when neither are equal, the shares must be as their products. 1. time they find they have gained 5261. what is each man's just share? Ans. A 1921. 19s. od. 672 12542 1254 B 3331. os. 11 II. 4. A, with a capital of 1000l. began trade January 1, 1776, and meeting with success in business he took in B as a partner, with a capital of 1500l. on the first of March following. Three months after that they admit Cas a third partner, who brought into stock 2800l. and after trading together till the first of the next year, they find, there has been gained since A's commencing business, 17761. 105. How must this be divided among the partners ? Ans. A 4571. 95. 4d. B 5711. 16s. 8-d. C 7471. 35. 11-d. ALLIGATION. ALLIGATION teaches how to mix several simples of dif ferent qualities, so that the composition may be of a middle quality; and is commonly distinguished into two prin cipal cases, called Alligation medial and Alligation alternate. ALLIGATION MEDIAL, Alligation medial is the method of finding the rate of the 'compound, from having the rates and quantities of the seve eral simples given. RULE.* Multiply each quantity by its rate; then divide the sum of the products by the sum of the quantities, or the whole composition, * The truth of this rule is too evident to need a demonstration. NOTE. If an ounce or any other quantity of pure gold be reduced into 24 equal parts, these parts are called carats; but gold is composition, and the quotient will be the rate of the compound required. EXAMPLES. 1. Suppose 15 bushels of wheat at 5s. per bushel, and 12 bushels of rye at 3s. 6d. per bushel were mixed together: how must the compound be sold per bushel without loss or gain? 2. A composition being made of 5lb. of tea at 7s. per pound, olb. at 8s. 6d. per pound, and 14 lb. at 5s. Iod. per pound, what is a pound of it worth? Ans. 6s. 10-d. 3. Mixed 4 gallons of wine at 4s. 10d. per gallon, with 7 gallons at 5s. 3d. per gallon, and 94 gallons at 5s. 8d. per gallon; what is a gallon of this composition worth? Ans. 5s. 44d. 4. A goldsmith melts 8lb. 5oz. of gold bullion of 14 carats fine, with 12lb. 8oz. of 18 carats fine: how many carats fine is this mixture ? Ans. 16 carats. 508 5. A is often mixed with some baser metal, which is called the alloy, and the mixture is said to be of, so many carats fine, according to the proportion of pure gold contained in it: thus, if 22 carats of pure gold and 2 of alloy be mixed together, it is said to be 22 carats fine. If any one of the simples be of little or no value with respect to the rest, its rate is supposed to be nothing, as water mixed with wine, and alloy with gold or silver. |