FELLOWSHIP. 124. FELLOWSHIP is the union of two or more indi viduals in trade, with an agreement to share the losses and profits in the ratio of the amount which each individual puts into the partnership. The money employed is called the capital stock. The loss or gain to be shared is called the dividend. What is Fellowship? What is the capital stock? What is the dividend ? EXAMPLES. 1. A, B, and C, enter into copartnership. A put in $180, B put in $240, and C put in $480. They gained $300. What is each one's part of the gain? Make each partner's stock the numerator of a fraction, and the sum of their stock a common denominator; then multiply the whole gain or loss by each of these fractions, for each partner's share. 2. Five persons, A, B, C, D, and E, are to share between them $2400. A is to have; B is to have ; C is to have ; D and E are to divide the remainder in proportion to the numbers 5 and 7. How much does each one receive? Hence, D must receive of $500-$208.331. 3. There are three horses belonging to three men, ern ployed to draw a load of plaster a certain distance for $26.45. It is estimated that A's and B's horses do of the labor; A's and C's horses; B's and C's horses. They are to be paid proportionally according to these es timates. What ought each man to receive? A's and B's horses do A's and C's horses do 8 B's and C's horses do 18=18. Adding all these fractions together, we shall obtain twice what they all do, according to the above estimate, if we take half the sum, it will give the part supposed to be done by all. Hence, A's, B's, and C's horses do **. If from this fraction we subtract 13, which is B's and C's, we find for the part supposed to be done by A's horse. In the same way we find for the part done by B's horse. will represent the part done by C's horse. Therefore, the parts which the three horses are supposed to do are 18, 0,2%. These fractions, having a common denominator, must be to each other as their numer ators, that is, as 10, 5, 8, whose sum is 23. Hence, A ought to have Cought to have of $26-45-$11.50. of 26·45= 5.75. of 26.45= 9.20. Proof, $26.45. 4. A, B, and C, agree to contribute $365 towards building a church, which is to be at the distance of 2 miles from A, 27 miles from B, and 3 from C. They agree that their shares shall be proportional to the reciprocals of their distances from the church. What ought each to contribute? The reciprocals of the numbers 2, 27, 31, are 1, A, ; these reduced to a common denominator, become 11, ,. Now, we must obviously divide $365 in the proportion of these numerators; their sum is 365. Hence, A must contribute of $365=$161. 5. A person wills to his two sons and a daughter, the following sums: To the elder son $1200, to the younger son $1000, and to his daughter $600; but it is found tha his whole estate amounts to only $800. How much ought each child to receive? The elder son received $342.8574. Ans. The younger son received 2857144. 171.4284. 6. Four persons, A, B, C and D together contribute $500 towards the erection of a school-house, which is located at the distance of of a mile from A's residence, of a mile from B's, 4 of a mile from C's, and 1 mile from D's. They contributed in the reciprocal ratio of their respective distances from the school-house. How much did each give? A gave of $500-$240. 125. WHEN the stock of the several partners continues in trade for unequal periods of time, the profit or loss must be apportioned with reference both to the stock and time. In such cases the fellowship is called DOUBLE FEL LOWSHIP. What is Double Fellowship? EXAMPLES. 1. Three partners, A, B and C, put into trade money as follows: A put in $400 for 2 months; B put in $300 for 4 months; C put in $500 for 3 months. They gained $350. How must they share of this gain? It is evident that $400 for 2 months is the same as $400×2 $800 for one month. = And $300 for 4 months is the same as $300 ×4=$1200 for one month. And $500 for 3 months is the same as $500×3=$1500. for one month. Hence, $800 A's money for one month. 1200 B's money for one month. 1500 C's money for one month. Multiply each partner's stock by the time it was in trade; make each product the numerator of a fraction, and the sum of the products a common denominator; then multiply the whole gain or loss by each of these fractions, for each partner's share. Repeat this Rule. 2. Three farmers hired a pasture for $55.50 for the season. A put in 6 cows for 3 months, B put in 8 cow for 2 months, C put in 10 cows for 4 months. What rent ought each to pay? A ought to pay $13.50. 12.00. 30.00. |