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Partnership or Company transactions, (in an Arithmetical sense) is a Rule by which merchants in partnership adjust their accounts in proportion to stock and time.
The gain or loss, with the several sums at hazard given, to find each partners share.
RULE.—Multiply the whole gain by each man's fraction part of the stock -or, agreeably to the Old Method; say, as the whole stock is to the whole gain, so is each man's share of the stock, to each man's share of the gain.
1. Three men, A, B and C, entered into partnership for 2 years, with a capital of $6000, A put in $2500, B $1500 and C $2000, they gain $1080; required, each man's share of the gain?
Solution. As the whole stock in trade is $6000, A's share would be 68% = 11; B's. 4488 = , and C's 389% = $. Again, it of $1080 = $450, A's share, and of $1080 = $270, B's share, and C's of $1080 $360. Proof:-A's share of gain is $450.00
do. do. 270.00 C's do. do. 360.00
Whole gain $1080.00 2. A and B enter into partnership; A has in goods at cash price $3400 worth, and cash $1300: B puts in $1200, and agrees to pay for A, a debt of $1100, for which A gives B a title to that amount of his goods. Now suppose A, agrees to take B's note for what B's funds want, of being equal to his own, (say the note bears legal interest, and is not reckoned in the partnership,)
what amount should the note be drawn for, to make them equal? Solution.--Amount of A's goods $3400.00
$1300.00 difference. A's stock in trade then would be $3600-650 $2950. A and B's equivalent composed of
Apportioning the effects of a Bankrupt. In apportioning the effects of a Bankrupt amongst his creditors, it is more convenient to find the proportion for one dollar, &c. Which will be a constant multiplier for each debt.
1. A Bankrupt owes $5000, his effects sold at auction, amounting to $4000, what will his creditors receive on a dollar?
Ans. 80 cents. 2. A merchant having sustained many losses is obliged to become a bankrupt, his effects are valued at $1728, with which he can pay only 15 cents on the dollar, what did he owe?
Ans. $11520. 3. A, B and C, freighted a ship with 108 tuns of wine, of which A had 48 tuns, B 36, and C 24, but by reason of stormy weather were obliged to cast 45 tuns overboard; how much must each man sustain of the loss?
Ans. A 20 tuns, B 15 and C 10.
4. Three merchants trading together lost goods to the value of $1860. A's stock was $2280, B's $11520 and C's $4800; what share of the loss must each man sustain?
Ans. A $288, B $1152, and C $480. 5. A ship valued at $25200 was lost at sea, of which š belonged to A, 1 to B, and the remainder to C; what is the loss on $1.00, and how much will each man sustain, supposing the owners effected an insurance of $18000?
A's $2400, B's $3600, and C's 1200. The pro-rata share on a dollar is 4.
When stocks have been put in trade for different periods of time, and settled with regard, both to stock and time.
RULE.—Multiply each man's stock and time, and then as the aggregate of products is to the whole gain, so is each man's stock to each man's share of the gain.
1. A, B, and C, join in company: A's stock is $100, for 12 months, B's 120 yards of cloth, for 8 months, and C's 240 bushels of wheat, for 7 months; they gained $1612, of which A had $400, B $512, and C $700; what was the value of B's cloth per yard, and C's wheat per
bushel. Ans. B's cloth $1.60 pr yd, and C's wheat $1.25 pr bush.
2. A, B, and C, enter into partnership with a capital of $1100, of which A put in $250, B put in $300, and C $550; they lost by trading, 5 per cent on their capital, what was each man's share? Ans. A's loss $12 50, B's $15, and C's loss $27.50. company
accounts, when the times and payments are equal, the shares of gain or loss are evidently in proportion to their respective stock—and when the stocks are equal, the shares are in proportion to the times of payment. But when stocks and times are unequal, the shares are in proportion to the products of stock and time.
This may be clearly demonstrated thus:
Suppose $100 in trade 12 months, gain $20; $50 in trade in 6 months, will gain $5, and both together $25;
for, as 100 x 12 : 50 x 6 : : 20 : 5 and 20 + ; again, by composition 100 × 12 + 50 x 6 : 100 x 12 ::: 25 : 20; gain of $100 in 12 ṁonths, and 100 x 12 + 50 x 6 : 50 x 6 : : 25 : 5, gain of $50 in 6 months, from which the truth of the rule is evident.
3. A, B and C having traded together, gain $126.80 what is each man's share, allowing that A put in $50 for 4 months, B $100 for 6 months, and C $150 for 8 months?
Ans. A $12.68, B $38.04, and C $76.08.
EQUATION OF PAYMENTS Is a rule, for finding when any number of notes or bonds due at different times may be all paid at once, without loss to debtor or creditor.
Rule.—Multiply each payment by its time, divide the sum of the products, thence arising by the sum of all the payments, and the quotient will be the equated time required.
1. A. owes B. a bond for $100, due 2 months hence, and one for $500 due 18 months hence, what would be the equated time for paying them at once?
500 x 18 9000
= 15s Ans. 2. C. owes D. $550, of which $100 is to be paid at three months, $200 at 5 months, and $250, in 8 months, but have agreed to make one payment of the whole, at what time must it be paid?
Ans. 6 mos. 3. A man has owing to him $500 to be paid as follows, viz: $250 at 6 months, and $250 at 8 months, but it is agreed that the whole should be paid at one time, when must it be paid?
Ans. 7 mos. 4. A. owes B. 5 bonds, for $945 each, payable at 3, 9, 11, 19, and 29 months, what time might they be all paid at once?
Ans. 14} mos.
AVERAGE TIME OF
1. Sold merchandise at sundry times, and on different terms of credit, as per statement annexed. 1840 January 1st, $1500 at 3 months, due 1st April. February 10th, 250 at 2
66 10th March 19th, 643 at 4
66 19th July. Sept'ber 1st. 1400 at 6
66 1st March. Required the average time of payment.
Ans. 21st August. Statement of the preceding question.
days. Due 1st April $1500 X 0 10th
9 19th July 643 x 109 1st March 1400 x 334
3793)539937(142 142 days from the 1st day of April which will make the average time fall on the 21st day of August. THEOREM and General Rule, to find the average time
that several bills of different dates, or different terms of credit, or both, become due.
D C B
In the above diagram let p, q, r, s, t, &c., be the several payments to be made, and B, C, D, E, F, &c., the different periods of time at which those payments are to be made, and 0, the average point of time, then it is manifest (on the principal of Simple Interest, that p X BO + 4 X CO + r X DO t X FO + s X EO, and putting BO = x, we have p x + 2(x-BC) + r (x BD ) = (BE- x) + t (BF-x) by transposition