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Qu. 4. If 96 pioneers in 24 days. caft,,a trench 96 yards long, how many pioneers will cast a trench 536 yards long in 8 days ? - Ans. 1008 pioneers.
10 men mow 40 acres in $ days, how njaný days will it require 3 meu to mow. 150 acres ? - Ans: 100 days.
This rule may be proved by two single rules.
The following rules in this chapter, except vulgar fraca tions and the extractions of roots, are wrought either by some of the rules of proportion, delivered in the four preçeding sections, or by the rule of practice, hereafter to be fpoken of.
FELLOWSHIP is that rule whereby merchants and others, trading in company, and employing a joint capital stock, are enabled to ascertain each partner's particular loss or gain, according to his share in the same joint stock.
This rule also serves to divide a bankrupt's estate among his creditors; to pay legacies, when there is a deficiency of the testator's effects: and, in fine, to divide the loss or profit of any joint concern among the lofers or proprietors.
The rule of fellowship is either single or double, that is, without regard to time, or with time.
Fellowhip without time, or single fellowship, is when different persons employ their respective stocks for the same time.
Rule.' As the whole stock of all the partners is to the whole gain or loss, so is each man's particular stock to his particular share of the gain or loss.
Proof. By adding each person's gain or loss together.
Therefore, the whole stock of all the partners is to be made the first number in the rule of three, the whole gain or loss the second number, and the particular stock of any one partner the third number; then the fourth number, or answer, is that partner's loss or gain, whose stock was the third number. This operation in the rule of three must be repeated if there be more than two partners, and performed as often as there are partners concerned.
Example 1. Three perfons enter into trade together : A put into the trade iool. B 1701. and C 300l. ; at the making up their accompts, they find they have gained 550l. profit : what is each person's share?
A's stock 4.100
300 Whole stock £.570 Whole Stock. Whole Gain.
A's Stock 5701.
If there be any remainders, such remainders in the proof must be added together (if they be fractions of the same denomination), and divided by the cominon divisor of each question (i, e. the total stock); and the quotient, which is units of the same denomination, added to the particular shares : thus, in the foregoing example, I added the three remainders, 330, 390, and 420, together, and dividing the total by 570, the common divisor, the quotient is 2, which are farthings, as they are fractions of a farthing.
Qu. 2. Four persons place their money in the public funds: A put in 3601. B 4801. C 70cl. and D 86ol. When the capital came to be sold out, the principal and interest amounted to 42001. what is each man's share of the net profit? - Answer, A 2701. B 360l. C 5251. D 6451.
Qu. 3. A bankrupt is indebted to four creditors in the following sums: to A 5511. 6s. to B 6o8l. 145. to C 3041. and to D 2081. 125. The bankrupt's estate is worth only 3371. 175. how much will each creditor receive !--- Arf. A 111l. 75. 5d. B 1221. 185. 101d. C 61l. Es. 01 d. and D 421. 25.71d.
Qu. 4. A mip being lost value 1730l.; of which A paid 3461. B 5191. C 6921. and D 1731. towards building her, she was insured to the amount of 1360. what was each person's lofs -- Answer, A 741. B 111. C 1481. D 371.
In the second example, the whole stock first placed in the funds is to be found by adding each person's stock together, and that made the first number in the rule of three; the whole gain is to be the second number, the particular stock of any one person the third number, and the fourth number is his fhare.
In the third example, the whole amount of the bankrupt's debt is to be made the first number; the value of his effects the second number; and any creditor's real due the third number, and the fourth number is that creditor's share.
Fellorufhip with time, or double fellowship, is when the different stocks are employed for different times.
Rule. Multiply each man's particular stock by the time it is employed for; then fay, by the rule of three, as the total of all these products is to the whole gain or loss, so is each man's particular product to his particular share of the gain or loss.
Thus the rule of three must be repeated as often as there are products or persons concerned, as in the fingle rule.
Example 1. A put 200l. in a certain trade; B five months after put 300l.; at the end of one year they find they have gained 350l. profit, what is each person's share?
2400 !2 months.
140000 2.400 A's product
70 A's Share.
45,00)8400,00(1861. 135. 4d. 300
390 2100 B's product:
360 4500 Total of the products.
300 270 3900