Since the present worth of £75, to continue 7 years, at 6 per cent. per annum, is found to be (by Ex. 1) £418. 13s. 6d., and this is to be paid in 10 years; by discounting this sum, at compound interest, for 10 years, we find the present value of it to be £238. 11s. 9d. = the present worth of the annuity in reversion.

298. EXERCISES.

1. If an annuity of £100 continues 5 years, what will it amount to, at 6 per cent. compound interest?

2. Required, the present value of an annuity of £100 per annum, to be continued 5 years, interest at 5 per cent.

3. Required, the present worth of a freehold estate of £6000 a year, to continue for ever, the rent being payable halfyearly, interest at 5 per cent. per annum.

4. The annual rent of a freehold estate, which cost £20000, is £1500. In what time will it clear itself?

5. A freehold estate is sold for 18 years' purchase. What rate of interest is allowed the purchaser?

6. The reversion of a freehold estate of £100, to continue 10 years, but not to commence till the end of 6 years, is to be sold. What is it worth, allowing the purchaser 4 per cent. per annum for his money?

PARTNERSHIP, OR FELLOWSHIP.

299. We often find that two or three persons form an association, in order to carry on some commercial or industrial undertaking, which requires more capital than one person can raise. These associations are called Partnership or Fellowship. Every partner subscribes a certain sum towards the joint-stock, which constitutes his share. After some time, the partners may agree to share the profit or loss among themselves, and it is evident that each partner's portion of the profit or loss will depend upon his share in the concern: if A's share be twice as much as B's, then he will receive twice as much of the profit; if it be half of B's, then his part will be half as much, and so on. The method by which we determine the respective gains or losses of the partners is called Fellowship or Partnership.

Ex. 1. Three merchants, A, B, and C, join in a speculation; A contributes £800; B, £750; and C, £1200. How much is the share of each, in a gain of £1200?

Here the joint-stock is £800+£750+£1200, or £2750.
Then £2750 gained £1200,

Ex. 2. A, B, and C formed a joint-stock for conducting a business, of which A contributed £3000 for 6 years; B, £4000 for 5 years; and C, £8000 for 9 years; and they gained £33000. What is each man's share of the gain?

A £3000 share for 6 years is the same as 6× £3000, or £18000 for 1 year.

A £4000 share for 5 years is the same as 5 × £4000, or £20000 for 1 year.

A £8000 share for 9 years is the same as 9 × £8000, or £72000 for 1 year.

The question is now this: A contributed £18000; B, £20000; and C, £72000. What is each man's share of a gain of £3300 ? The joint capital is = £18000+ £20000+£72000, or £110000. Then 110000 produce 33000,

Ex. 3. Divide £36000 among 4 persons, so that the 2nd gets twice as much as the 1st; the 3rd as much as the first two together, and the 4th three times as much as the 3rd.

By the sense of the question, we perceive that if the 1st person's share be taken as 1 part, the 2nd person's is 2 parts;

the 3rd person's share is 1+2, or 3 parts; and the 4th is 3x3, or 9 parts; therefore, we have to divide £36000 into 1+2+3+9 parts, or 15 parts.

Ex. 4. Bought, equal quantities of coffee and sugar for £20; for the coffee I paid 13d. per lb.. and for the sugar 11d. How much was bought of each, and what did each cost?

For 13d. +11d., or 24d., or 2s., I buy 2 lbs.

...for £20 I buy 200 × 2lbs., or 400 lbs.,

and as there are equal quantities of each, the coffee weighs 200 lbs., and so does the sugar.

Now, I lb. of coffee cost 13d.,

£. S. d.

..200 lbs. of coffee, at 13d., cost 200 × 13d.=10 16 8 And .. 200 lbs. of sugar at 11d.=200 × 11d. = 9 3 4

£20 0 0

Ex. 5. Divide 782 into three parts, which are to one another as the quantities,, and; or in such a manner, that for every share of the 1st, the 2nd gets share, and the 3rd share.

...for

every share of 1st portion, the 2nd has, and the 3rd ;

..782 must be divided into 6+8+9 shares, or 23 shares.

Ex. 6. Divide £3120 among three partners, so that for every £3 A receives, B gets £4, and also for every £7 A receives, C gets £3.

If A receives £5, B receives £4,

It follows that if A receives £7, B must have £53, and C £3;

35,

28, and C 15.

.. 1 part =312°=£40; £.
..35 parts 35 x £40=1400;
..28 parts=28 × £40=1120;

..15 parts=15 × £40 = 600.

£3120

Ex. 7. Three graziers rented a field for £30. 5s.; X keeps there 50 sheep for 4 months; Y, 80 for 5 months; and Z, 90 for 6 months. Find the rent paid by each.

Here we see that 50 sheep grazing 4 months is the same as 4× 50 sheep, or 225 sheep grazing 1 month.

Also, 80 sheep grazing 5 months is the same as 5 × 80 sheep, or 400 sheep grazing 1 month.

And also 90 sheep grazing 6 months is the same as 6×90 sheep, or 585 sheep grazing 1 month.

..225+400+585 sheep, or 1210 sheep grazing 1 month cost £30. 5s.

..1 sheep grazing 1 month cost

£30.5s.

=

-6d.

1210

..225 sheep grazing 1 month cost 225 × 6d.

X's expenses.

..400 sheep grazing 1 month cost 400 × 6d. =10

Y's expenses.

L. S. d.

0 0=

..585 sheep grazing 1 month cost 585 × 6d. = 14 12

Z's expenses.

300. EXERCISES.

1. A ship's cargo belongs to three merchants, A owns £5600; B, £6000; and C, £6400. The whole cargo was sold for £10800. What is each man's share of it?

2. Four person's speculated: A with £7400 for three months; B, £6700 for four months; C, £3540 for 11 months; and

D, £5000 for 15 months: they gained £1000. each man's gain?

What was

3. A ship, worth £2000, was lost; the owners were four persons: N possessed; O, ; P, ; and Q, . She was insured What will each receive, and how much will

for £2500.

each gain? 4. A commenced business on January 1st, 1852, with a capital of £1000; he took in B as a partner, with a capital of £1600, on the 1st of March following; three months after, they admitted C as a partner, who brought into the firm £2400: having carried on business till the end of the year, they found the gain to be £1846. 15s. What was each man's share of the gain?

5. A person had divided among his three sons £1200, so that A got part; B, part; and C, part. Find the share of each.

6. Three persons remained partners for 2 years: the 1st brought in £4000, which remained the whole time; the 2nd began with £300, and 6 months after put in £300 more; the 3rd began with £200, and 1 year after put in £500 more. The whole gain was £6600. Determine each partner's share of it. 7. Three workmen were employed to perform a job; L worked 6 days of 10 hours each; M, 7 days of 8 hours each; N, 9 days of 6 hours each. They receive for their labour £25. 10s. What is each man's wages?

8. Divide £600 among A, B, C, and D, so that B gets as much as A; C, 4 times as much as B; and D, as much as B. How much will each get?

9. Divide £288 into parts, which are to one another as the numbers 3, 5, 4; or in such a manner, that as often as the first person receives £3, the second shall receive £5, and the third £4. How much will each receive?

10. Four persons divide among themselves £249270, in such a manner that for every £ A receives, B has £; for every £ A receives, C has £4; and for every £ A receives, D has £. The share of each man is required.

11. A, B, and C own £800, which are to be divided so that B shall receive £40 more than A, and C £20 more than B. How much is each part ?