2. A and B have gained by merchandize 182, ́A- did? put in 3001. and B 400. I demand each of their shares of the profit? Answ. A 78, and B 1041.

3. A merchant being deceased, it is found he owes to A 500l. to B 9001 though he left bt 1100 behind him; I demand how much each is to have in proportion of his debt?: Answ. A 3929, and B 70741

4. A, B and C, freight a ship from the Canaries, for England with 108 tuns of wine, of which - A had 43; Ᏼ 36, and C 24; the mariners meeting with a storm at sea, were constrained for the safety of their lives, to cast 45 tuns thereof overboard: Here the question to be resolved is, how many of the 45 tun every particular mechant has lost according to the rate of his adventure?

Answ. A 20, B 15, and C 10 tun..

5. A chapnian breaking owes unto 4 men the following sums of money, viz.

6. Three butchers pay among them. 401 for a grass in closure, into which they put 30 cows, whereof A had 80, B100, and C 120; how much had each to pay?..

Answ, A 101 13s 4d. B 131 6s, 8d. and C.16!,

7. A father left his estate of 160 1. among 3 sous, in;: such manner that for every 21. that A gets, B shall have. 2, and C.5; how is the estate to be divided ?

Answ. A's share 2001. B 3001. C 5001.

8. Four men traded with a stock of 8001. and they gained in 2 years time twice as much and 401. more; A's stock was 1401. B's 260, C's 300!. I demand D'e stock, and what each man gained by trading?

Answ. D's stock was 1001, aud. A gain'd 2871. B 533,-C615, and D 2051..

9.-A, B

9. A, B and C put in money together; A put in 201. B and C put in 85; they gain'd 631. of which B took up What did A and C gain, and B and C put in? Answ. A gain'd 127. and C 30!.

211.

B put in 251, and C 501.

10. A, B and C put in money together; A put in 201. B 301. C a sum unknown; they gained 367. C took up 161. what did A and B gain, and C put in ?

Answ. A gain'd S. and B 127, and C put in 401.

11. Two merchants have gained 4507, of which A is to have 3 times as much as B. How much is each to have? Ansu. A 3371. 10s B 112. 10s.

SOLUTION.

It is manifest from the question that 4501. is to be divided in proportion as 3 to 1. Therefore

12. Three persons are to share 6007.; A is to have a certain sum, B as much again as A, and C three times as much as B, I demand each man's part?

Answ. A 6631. B 13337. and C 4001€

13. Three persons have gained 13204; now when A takes 6l. B takes 47. and C 21. I demand how much each gets? Answ. A 660, B 440, and C 2201.

14 A, B and C shipped off sundry goods in company to have their gains upon the whole in proportion to ther inputs, viz. A pat in 80 pieces of serge, valued at 57. 10s.

piece; B 70 pieces of frize, at 41. piece; and C90 pieces of stuff, at 27. 10s. C paid charges of shipping on the whole 277. 10s, and consigned them to his correspondent at Lisbon; by whose account of salés 'the neat proceeds appear to be 3116 mil. 600 reas, which he remits to C's correspondent at London at 5s. 6d. millrea; and C draws on London at 73 cent. It is required to divide the neat amount rateably among the ad venturers?

15. A ships off 500 barrels of beef worth 20 P be. longing to B; and 250 casks of batter of his own, we $130, Ogrs, 211 at 21s, od, and it was agreed between then, to run equal risques in the whole, the loss. er gain to be divided in proportion to their outsets; A paid 231. O. 3d. charges on them, which is to be reck. oned as so much stock. The goods he consigned to his gorrespondent in Bourdeaux, who returns account of the neat proceeds amounting to 11425 livres, and by his order sends in return 30 hhds, of wine, which gost 80 livres d and & casks of indigo, wt, grose 2078. Tare 3715. cak, at 2 livres dth neat; when these goods arrive. A pays duty and charges on them 461. 10. 01d, and afs terwards sells the wine at 91. bhd. and the indigo at 58. 10d. th. (100fb. at Bourdeaux being 110 here) and the balance his correspondent in Bourdeaux remits to Amsterdam, at 54d. P crown, which his correspon dent at London draws for at 35s. Flemish sterl. and remits to him here at 8 cent. deducting cent.. for his commission; so that it comes here 1941, 6s. 6d. Aeat. It is required to find what A must pay B for his. share of the neat amount of this adventure, being allow ed 24 cent. commission on the sale of the returns, and what each gained thereby?

Answ. A must pay B 5901. who gains 901.

A gains 641. 16s. and commission 221. 48..74d. N. B. The following questions usually solved by posia tion may be more easily effected by the proceeding problem, viz.

16. The sum of the ages of A, B and C is 15 years; B was as old as A and as old again; and C twice as old as B: I demand each man's sage?.

By considering this, question, I discover that A's age is in proportion to B's as 1 to 1, and to C's as 1 to 3: Therefore it is required to divide 151 in proportion to H. 14, and 3, viz.

17. A gamester loses in 4 turns of dice 160 shillings, and treb ed each turn the sum he put in. How much did he play for the first and last time?

Answ. 4s. and 108.

18. Forty yards of drugget and 50 yards of cloth cost 2. 10. but every yard of cloth double as much as a yard of drugget: I demand what the drugget cost yard? Answ. 3s. 6d.

19. Divide 15 into two such parts, that when the greater is multiplied by 4 and the lesser by 16, their product must be equal? Ansi. 12 and 3.

I discover that the numbers required must have the same proportion to each other, the less to the greater, as 4 to 16, consequently 15 must be divided into parts in pro. portion to 4 and 16, viz. 3 and 2.

20. A master hires a journeyman on this condition, that he shall have 128. a day and his diet for every day he works; but for every day he doth not work he is to pay him 6d. for his diet. Now on the 30th day they come to account, but neither of them receives or pays any money: How many days did he work and how many was he idle? Answ. He worked 10 days and was idle 20.

21. What numbers are they which when added, will make 2663, and when one is multiplied by 3 and the other by 5 the sun shall be equal? Anw. 1663 and 100.

W

FELLOWSHIP WITH TIME.

HEN stocks continue unequal time in company, so that consideration is made of the time as well a stock, this is called Fellowship with Time; for which this is the

Rule.

Multiply each man's stock by his time, and add the produc's into one sum; then divide the total gain or loss in proportion to these products.

Application

1. Suppose two merchants A and B to be partners is traffick, and that A permits his stock of 1001. to be em. ployed in their joint traffick 3 months, and his stock of 501. 8 months, and they gain 281, I demand how much hereof belongs to each?

100 A's

2. Two merchants made a company; A put in 1001. for four months, and B put in 1361. for three months, and they gain 501. I demand each man's share of the profits? Answ. A 241. 151. and B 251. 41575.

3. Three graziers hired a piece of land for 601. 10s. A put in 5 oxen for 4 months; B put in 8 oxen for 5 months; and C put in 9 oxen for o months: I demand how much each must pay?

Answ. A 111. 5s. B 201. and C 291. 5s.

4. Three persons have received 6651. interest, A had put in 40001. for 12 months, B 30001. for 15 months, and C 50001. for 8 months: how much is each man's part of the interest? Answ. A 2401. B 2251. and C 2001.

5. Three persons hired a piece of land for 121. 10s. 6d. A put in 20 sheep for 5 days, B put in 16 sheep for 7 days, and C put in 25 sheep for 4 days: I demand how much each must pay? Answ. A 41. Os. 3d. B 41. 9s.

11, d. and C 41. Os. 3d.

6. Three merchants lost by some dealings 451. 10s. A's stock was 1001, for 6 months, B's stock 1001. for 94 months, and C's 1501. for 83 months; what is each man's part of this loss? Answ. A 101. 3s. B 141. 183s. and C 201.777.

7. Three merchants put in a stock, viz. A puts in the 1st of January 1201. until the 23d of March; B puts in 1761. the 10th of February, until the 12th of April; C puts in 2951. the 2d of February,, until the 25th of April, and they gain 8001. I want to know each man's part of the gain, allowing 25 days to the month of February?

Answ. A 1741. 3s. 42420gd. B 1921. 7s. 618d. and C 4331. gs. 1

1266

CHAP.