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4. A, B, and C enter into partnership for a year, with a jointstock of £8900 : A contributes £4000; B, £2140 ; and C the remainder. At the end of the year, their gain is found to be £1483, 6s. 8d. C managed the business, and was to have a salary of £445 for his trouble. What portion of the gain belongs to each partner? Ans. A, £466, 13s. 4d.; B, £249, 13s. 4d. ; C, £767.
II. COMPOUND PARTNERSHIP.
RULE.—Multiply each share by the time it has been employed in the business, and add together the products: then state and work the question for each partner, as in Simple Partnership; only use the products of the sums instead of the sums themselves.
Example.—Three partners, A, B, C, invested the following sums in business :—A, £400, for 6 months; B, £600, for 9 months; C, £1000, for 12 months; and they gained £300 : what is each partner's share of the profits ?
Months. A. £400 x 6 £2,400 B. 600 X 95,400 c. 1000 X 12 12,000 € Total products, £19,800 : 300 :: 2,400 : £36 7 31 } A's share.
5,400 : 81 16 41 5 B's , 12,000 : 181 16 41 6 C's
£300 0 0 Total profit. Here each share is multiplied by the time it is employed, and the products are then added together : in order to find A's share, we say, 'If £19,800, the total products, gain £300, what will £2400, the product of A's share, gain ?' It is then calculated as in Simple Proportion. B and C's shares are found in the same way.
Exercises. 1. A's stock of £340 was 4 months in trade; B's, of £510, was eight months; and C's, of £850, was 10 months; they gain £270, 13s. Od. : what was each partner's share of the gain ? Ans. A's, £26, 8s. 1 d. 11; B's, £79, s. 51d. ;
C's, £165, Os. 10 d. 37 2. Two merchants, A and B, entered into partnership for 2 years : A contributed to the capital £960, and B £1500. After 8 months of the time had elapsed, they admit C, with a capital of £720. On balancing their books at the end of the period, they found that their nett gain amounted to £847, 15s. How must this gain be divided among them ? Ans. A's, £276, 16s. 3 d. 38;
B's, £432, 10s. 6 d. 14; C's, £138, 8s. 1 d. 11 3. A, B, and Center into partnership for 2 years : A put in at first £700, and after 8 months £250 more; B put in £650, and after 15 months he took out £300; C put in £850, and after 10 months £400 more, but at the end of 18 months he withdrew £900. During their copartnership the gains amounted to £1684, 12s.; what was each man's share ?
Ans. A, £645, 5s. 11 d. 10; B, £400, 4s. 2 d. 18; C, £639, 1s. 10 d. 13
EQUATION OF PAYMENTS.
EQUATION is the rule for ascertaining the time at which two or more sums payable at different dates, by one person to another, may be paid at one equivalent date, without loss to either party.
Rule.-1. Write the different sums or debts below one another, and multiply each of them by the time that has to elapse before it is due, placing the products opposite each sum.
2. Add the debts in one sum for a divisor, and their products in another sum for a dividend : then divide the one by the otherthat is, the sum of the products by the sum of the debts-and the quotient is the equated or average time required for paying the whole at once.
Example.- A gentleman owes £60, payable in 72 days ; £85, in 128 days; £70, in 176 days; and £105, in 320 days. Required the average time at which the whole ought to be paid. £ Days. Products,
Here we multiply 60 X 72 = 4320
£60 by 72, the num85 X 128 = 10880
ber of days before it 70 x 176 = 12320
is due; £85 by 128; 105 X 320 = 33600
£70 by 176; and £105
by 320. We then 320 320 ) 61120 191 days. Ans. divide 61120, the sum
of the products, by 320, the amount of the debts; and the quotient, 191, is the average number of days.
Exercises. 1. A gentleman owes £56, payable in 40 days; £72, in 108 days; £106, in 175 days; £230, in 241 days; and £960, in 342 days. Required the average time at which the whole ought to be paid,
Ans. 289153 days. 2. If a person owe £100, payable in 2 months, and £750, payable in 7 months; what is the just time for the payment of the two debts ? . . . . . . . Ans. 61 months.
3. What is the equated time for the payment of four debtsthe first, £250, due in one year; the second, £560, payable in 11 years ; the third, £490, due in 2 years; and the fourth, £1000, due in 34 years ? . . . . . Ans. 27 years.
4. A person has to pay £1750 as follows :-£300 in 4 months ; £125 in 5 months; £365 in 8 months ; £400 in 10 months; and the rest in a year. What is the equated time for the payment of the whole ? . . . . . . Ans. 8398 months.
AVERAGE. AN AVERAGE NUMBER is one that is intermediate between several other given numbers. Thus, if there are 4 numbers, 5, 6, 9, 8, their average is 7, because 4 numbers, each of which is 7, will amount to the same sum, namely, 28, as the four given numbers.
I. TO FIND THE AVERAGE OF SEVERAL GIVEN QUANTITIES.
RULE.--Add together the different quantities, and divide their amount by the number of the quantities; thus, if there are 3 different quantities, divide their amount by 3; and the quotient is the average.
Example.—What is the average of 8, 36, 14, 9, 43 ?
II. TO FIND THE AVERAGE PRICE OF GOODS, &C. WHEN THERE ARE
DIFFERENT QUANTITIES AND DIFFERENT PRICES. RULE.-Multiply each quantity by its price; then add the quantities in one sum and the products in another, and divide the sum of the products by the sum of the quantities: the quotient is the average.
Example.--I have bought two yards of cloth, at 10s. each ; 3 yards at 15s.; and 5 at 12s.; what is the average price ?
2 x 10s. = £1 0 0 Here each quantity is multiplied by 3 x 15s. = 2 5 0
its price; and the sum of the products,
£6, 58., is divided by 10, the sum of the 5 x 12s. = 3 0 0
quantities. 10 10)6 5 0 This rule applies to any other aver
ages in which the quantities and the Average, 12 6 rates both vary.
Exercises. 1. The revenue of a public trust, during three years, was £44,261, Os. 4d., £47,471, 14s. 5d., and £38,006, 5s. 11d.; what was the average yearly revenue ? - Ans. £43,246, 6s. 10 d.
2. The temperature, as indicated by the thermometer on the 1st day of November, was 49:10; on the second, it was 40:06; on the 3d, it was 39.00; on the 4th, it was 27.20 ; on the 5th, 28°; and on the 6th, 21:50; what was the average temperature of the six days ? . . .
A DIVIDEND is a division among the creditors, of the funds of a debtor, who finds himself unable to pay the debts which he has contracted.
On examining his assets—that is, the whole of his property and means--he discovers that he could settle with his creditors, provided
would accept a dividend on the amount of his account: this dividend is generally spoken of as at the rate of so much per pound. Supposing the debtor to be owing £1000, and only to possess assets to the value of £250, then he can pay only 5s. per pound, or 25 per cent. on his debts ; if the creditors are satisfied, the debtor is relieved on making payment to this extent.
THE DIVIDEND is ascertained by dividing the total amount of the assets by the number of pounds that form the amount of the debts. As the assets are less than the debts, their amount requires to be converted into shillings or pence, as the case may be, to admit of the division.
DIVIDEND is also the term applied to the profits, at a certain percentage on the amount of the shares, divided among the proprietors of joint-stock companies, &c.
Example.-A person is unable to pay his debts. He owes to A, £440 ; to B, £160; to C, £224-being in all £824. On examining his affairs, it is found that he possesses property only ta the value of £226, 12s. What dividend per pound can he pay ? £ £ s.
Here the assets are divided £1.
by 824, the number of pounds forming the debts.
BARTER is the exchanging of one kind of goods for another, in such a way that the value of the goods given away, may be equal to the value of those received.
No general rule can be given for the working of such questions : they must be treated according to the nature of each case. The following will serve as examples :
Example 1.-A and B barter as follows: A has 1385 yards of linen, at 2s. 74d. per yard, for which B gives him £32, 7s. Od. ready-money, and for the rest printed calicoes at 10 d. per yard. How many yards of calico did A receive ?
A gives 1385 yards of linen, at 28. 7 d. = £181 15 7