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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?

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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.

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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. 6d. what was each partner's share of the gain? Ans. A's, £26, 8s. 12d.; B's, £79, 4s. 51d. C's, £165, Os. 10 d. 27 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. 33d. 38; B's, £432, 10s. 6d. 44; C's, £138, 8s. 1 d. 4

3. A, B, and C enter 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. 111d.; ; C, £639, 1s. 10d.

B, £400, 4s. 22d.

83

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.

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320, the amount of the debts; and the quotient, number of days.

Exercises.

Here we multiply £60 by 72, the number of days before it is due; £85 by 128; £70 by 176; and £105 by 320. We then divide 61120, the sum of the products, by 191, is the average

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. 28919 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. 6 months.

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3. What is the equated time for the payment of four debtsthe first, £250, due in one year; the second, £560, payable in 11⁄2 years; the third, £490, due in 2 years; and the fourth, £1000, due in 3 years? years.

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Ans. 2

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. 8333 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?

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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

3 X 15s. = 2 5 0 5 X 12s. = 3 0 0 10)6 5 0 Average, 12 6

10

Here each quantity is multiplied by its price; and the sum of the products, £6, 58., is divided by 10, the sum of the quantities.

This rule applies to any other averages in which the quantities and the 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. 101d.

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? Ans. 34.14

3. In a class of 6 boys at school, one was aged 14 years and 3 months; the second, 13 years 11 months; the third, 13 years 1 month; the fourth, 12 years; the fifth, 12 years 6 months; and the sixth, 11 years 9 months; what was the average age of the six boys? Ans. 12 years 11 months. 4. The price of the 4 lb. loaf was in one shop 8d. ; in a second shop, 74d.; in a third, 74d.; and in a fourth, 62d.; what was the average price of the loaf in the four shops? Ans. 74d.

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5. If a person purchase 12 articles, one of which costs 2s.; two, 4s. each; two, 5s. each; and seven, 8s. each; what did he pay on an average for each article? Ans. 6s. 4d.

DIVIDEN D.

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 each 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 to the value of £226, 12s. What dividend per pound can he pay?

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Exercises.

Here the assets are divided by 824, the number of pounds forming the debts.

1. What dividend per pound will a person pay who is owing £1000, and whose assets amount to £800 ? Ans. 16s. per £

2. A person is owing to A, £300; B, £400, 10s.; C, £620, 15s.; D, £150, 15s.; and his whole assets amount to £184, what dividend will he be able to pay? Ans. 2s. 6d. per £

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116

BARTER.

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. 7d. per yard, for which B gives him £32, 7s. 6d. ready-money, and for the rest printed calicoes at 10 d. per yard. How many yards of calico did A receive?

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This sum of £149, 8s. 13d. divided by 10d. the price per yard, will give 3415 yards, the number required.

Example 2.-How much coffee, at £7, 9s. 6d. per cwt. should I get in exchange for 897 cwts. 1 qr. 14 lbs. of sugar, at 6ad. per lb. ?

cwts. qr. lbs.

lbs.

897 1 14 = 100506 at 6ad. = £2826 14 7

£7 963)£2826 14 7

Ans. 378 cwts.

Here we convert the given quantity of sugar into lbs. and find the value at 6 d. a lb. The amount, £2826, 14s. 74d. is then divided by £7, 9s. 6d. the price per cwt. of the coffee, and the quotient is the number of cwts. of coffee required.

Exercises.

1. How much tobacco, at £5, 5s. per cwt. must be bartered for 6 cwts. 1 qr. 14 lbs. of snuff, at 4s. 6d. per lb. ?

Ans. 30 cwts. 2 qrs. 11 lbs. 2. I exchanged 172 yards of black cloth, at £1, 2s. 8d. per yard, for 688 pair of silk stockings; what was the price of the stockings per pair?

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Ans. 5s. 8d.

3. A delivers to B 314 yards of cloth, at 5s. 6d., and 78 yards of cassimer, at 7s. 8d., in barter for wool at 1s. 3d. per lb.; what quantity of wool does A receive? Ans. 615 lb.

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4. Exchanged 67 cwts. of tobacco, at 8 guineas per cwt. for 600 lbs. of tea, at 7s. 4d., and stockings at 2s. 8d. per pair; how many pair of stockings did I receive? Ans. 2571 pair.

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