27. If the scavengers' rate at 14d. 1. comes to 6s. 7d. where they ordinarily assess of the rent: what will the king's tax for that house be, at 4s. in the pound, rated at the full rent? Answ. 131. 58.

28. A tradesman excreased his estate annually a third, abating 1001. which he usually spent in his family, and at the end of 3 years he found that his neat estate amounted to 31541. 11s. 8d. What had he at outsetting?

Answ. 14111. 12s. 93d.

29. A can do a piece of work in 10 days, B alone in 13; set them both about it together, in what time will it be finished?

Answ. in 5

days.

30. A cistern is supplied with water by one pipe of such bigness, that if the cock A at the end of the pipe be set open, the cistern will be filled in hour; but at the bottom of the cistern are two other cocks B and C, whose capacities are such, that by the cock B set open alone (all the rest being stopt) the cistern supposed to be full will be emptied in 1 hour; also by the cock C alone it will be emptied in 2 hours: Now because more water will be infused by the cock A, than can be expelled by the cocks B and C in one and the same time; the question is, in what time the cistern will be filled, if all the said three cocks be set open at once? Answ. T hour.

31. A governor of a certain garrison being desirous to know how much money the port or passage of the garrison did amount to, in certain months, made choice of a loyal servant, giving him orders to receive of every coachman passing with a coach 4d. of every horseman 2d, and of every footman d. Now at the year's end the servant making his account to the governor gives him 941. 15s. 10d. and lets him know that as often as 5 passed with coaches 9 passed on horseback, and as often as 6 passed on horseback 10 passed on foot. The question is, how many coaches, horsemen and footmen passed? Answ. 2500 coaches,

4500 horsemen and 7500 footmen.

32. Twenty knights, 30 merchants, 24 lawyers and 24 citizens spent at a dinner 64 pounds, which sum was divided among them in such a manner that 4 knights paid as much as 5 merchants, 10 merchants as much as 16 lawyers, and 8 lawyers as much as 12 citizens; the question is, to know the sum of money paid by all the knights; also by the merchants, lawyers and citizens? Answ, the 20 knights paid 201. the 30 merchants 241. the 24 lawyers 121, and the 24 citizens 81.

33. There is an island which is 36 miles in compass: Now, if at the same time, and from the same place, two footmen A and B, set forward to travel round about said island, and follow one another in such a manner, that A travels every day 9 miles, and B7 miles; the question is, to find in what space of time they will meet again; and also how many miles and how many times round the island each footman will then have travelled?

Answ. They will meet at the end of 18 days from their first parting; and then A will have travelled 162 miles (or 44 times the compass of the island) and B will have travelled 126 miles (or 3 times the compass of the island.)

34. A man dies and leaves a legacy of 9001. to be disposed of among his relations, viz. A, B, C and D, which legacy is to be disposed of in this order: B is to have twice as much as A, and C thrice as much as B, and D is to have as much and as C: what must each person have?

Answ. A's share is 501. B 1001. C 3001, and D 4501. 35. Five merchants. viz. A, C, B, D and E have gained 20251. which they divide in such sort that of the share of A is equal severally to of the share of B. of C, of D, of E: the question is, what was the share of every merchant? Answ. A 1621, B 3241. C 4051. D 4861. É 6481. 36. Two merchants A and B are in company, the sum of their stocks is 3001. the money of A continuing 9 months, the money of B 11 months; they gain 2001. which they divide equally; the question is, how much each man put

in ?

Answ. A 1651. B 1351.

37. If 3481 soldiers are to be placed in a square battle, how many are to be set in rank, or in file? Answ. 59.

33. If 100. being put forth for interest at a certain rate, will at the end of 2 years be augmented to 112,31 (compound interest, or interest upon interest computed) what principal and interest will be due at the first year's end? Answ, 1061.

39. If 1001. being put forth for interest at a certain rate, will at the end of 3 years be augmented to l. 115.7625 (compound interest being computed) what principal and interest will be due at the first year's end? Answ. 1051. 40. The continual multiplication of the nine digits will give the number of changes that may be rung on 9 bells (as well as of any other combinations) how many are

there?

Answ. 362880.

41. There are 2 numbers; 75 is the less, to which the greater is in proportion as 8 to 5, what is the sum; and the product of their sum and difference; the difference and product of their squares; and the sum of the squares of their two quotes, the greater divided by the less, and the less again by the greater? Answ. Sum 195, sum

and diff. 240, diff. sq. 8775, sum sq. of the two quotes

21521

1600'

42. In a series of proportional numbers the first is 5, the third is 8, the product of the second and third is 78.4, what is the difference of the second and fourth? Answ. 5.88. 43. If by sending pewter to Turkey, and parting with it at 253d. pound, the merchant clears cent cent. what does he clear in Holland where he disposes of the cwt. for 81. ? Answ. 21 Os. 23d.

44. An accomptant told a gentleman who had constantly eight persons at his table, that he would gladly make a ninth, and was willing to give 200 guineas for his board, so long as he could place the said company at dinner differently from any one day before; this being accepted, what did his entertainment cost him a year?

Answ. 50d. and about

45. It is proposed by an elderly person in trade, desirous. of a little respite, to admit a sober and industrious young fellow to a share in the business, and to encourage him, offers that if his circumstances will allow him to advance 1001. his pay shall be 40. a year; if he shall be able to put 200 into the stock he shall have 531. and if 300 he shall receive 701. annually: In this proposal what was allowed for his attendance simply? Answ. 251. a year.

46. A merry young fellow in a small time got the better of of his fortune, by advice of his friends he then gave 22001. for an exempt's place in the guards, his profu

on continued till he had no more than 880 guineas left, which he found by computation, was just part of his money after the commission was bought; pray what was his fortune at first? Answ. 104501.

47. A has kerseys at 41. 5s, a piece ready money, in barter they are charged by him at 51. 6s. each, and of that required down. B has flax at 3d. & pound, how“ ought he to rate it in truck, not to be hurt by the extortion of A? Answ. 5d. nearly.

48. Put out 3841. to interest, and in 81 years there were 542 8s. found to be due, what rate of interest could then be implied? Answ. 5 cent. Pannum.

49. M of Amsterdam orders N of London to remit ( of Paris, at 34 pence sterling crown, and to draw on P. of Antwerp for the value, at 332s. Flemish pound sterling, but as soon as N received the commission the exchange was on Paris at 54 crown, pray at what rate of exchange ought N to draw on P to execute his orders and be no loser? Answ 33s. 2d.

50. Suppose the sea allowance for the common men to be 55. of beef and 3. of biscuit a day, for a mess of four people, and that the price of the first barrelled to the king be 24d. a b. and of the second 14 such as was a ship's company that their flesh cost the government 121. 12s. day; pray what did it pay for the bread week? Answ. 351. 5s. 7d.

51. Three persons enter joint trade together, to which A contributed 2101. B 3121. they clear 401. whereof 371. 10s. belongs of right to C, that person's stock and the se-veral gains of the other two are required?

Answ. C's stock 190l. 19s. 6d. A gained 411, 4s. 8d. 52. A bond was made on the 7th of August. 1713, at 6 cent. annum, for the sum of 11141. 10s. on the 11th of May, 1718: 140l. was paid off, and a fresh bond entered into for the remainder at 5 cent. annum, at the time the interest of this last was 211. 16s. 8d. there was paid off 871. 11s. 9d. the old bond being then takenup, a new one was then given for the res due, which being paid off on the 1th of September, 1724, the bond owner took no more than 14091. 16s. 8d. in full payment; at what rate did he take interest cent annum upon the last renewal of the bond? Answ. 21. 9s. 6d.

53. A, B and C will trench a field in 12 days, B, C and D in 14, C, D and A will do it in 15, and D, A, B in 18, in what time will it be done by all of them together; and by each of them singly?

Answ. Together in 10.83 days: by A in 47.848, B in 38.969, Cin 27. 194, D in 111.176 days.

54. A, B and C company, A put in share of the stock for 5 months, and laid chaim to of the profit, B put in bs for 8 months, C advanced 4001. for 7 months, and required on the balance of the gain, the stock of the other two adventurers is sought? Answ. A 1681. B 701. 55. If 12041. is to be distributed among 3 persons, A, B, C, in such sort, that as often as A takes 5, В shall take

1 Ee 3

4 and as often as B takes 3, C shall take 2; what will be the share of each of them?

Answ. A 5141. B 411. C 27531.

ਨ

56. Divide 1000 crowns: give A 129 more than B, and, B718 fewer than C

Answ. A 360, B231 and C 409.

57. Part 2501. give A 37 more than B, and let C have 28 fewer? Answ. A11741. B 8041. and C 5211. 58. A father divided his fortune among his sons; he gave A 7 as often as B 4; to C he gave as often 2 as B 5: the dividend of C came to 216631. what was the value of the whole legacy? Answ. 170601. 4s. 03d.

59. A stationer sold quills at 11s. thousand, by which he cleared 3 of the money; but growing scarce raised them to 13s. 6d. thousand; what might he clear cent. by the latter price? Answ. 961. 7s. 373⁄4d. 60. A person was possessed of share of a copper mine, and sold of his interest, therein for 1710. what was the value of the whole property at the same rate?

Answ. 38001.

61. What sum of money at 3

cent. annum, will clear 381: 10s. in a year and quarter's time?

·Answ. 8801.

62. X, Y and Z working together, can complete a staircase in 12 days; Z alone can do it in 24 days; X in 34: In what time then can Y get it done himself?

Answ. 813 days.

63. Two merchants enter into partnership, and each of them put in 12 pieces of cloth; but these of A cost 481. more than those of B; the cloth being sold they find they have gained 27331, of which B has for his share 221. The question is to know at how much a piece each of their cloths was valued? Answ. A's at 211. and B's at 171:

64. If when a hhd of wine is sold for 101, there is lost 6 cent, how much is the gain or loss cent. when 5hhds.. cent. loss.

are sold for 451. 10s.? Answ. 143

65. A person dying left his wife with child, and by his will ordered that if she went with a son, of the estate should belong to him, and the remainder to his mother; and if she had a daughter, he appointed the mother 3 and the daughter but it happened she was delivered of both son and a daughter; by which she lost in equity-20001. more than if it had been only a girl. What would have been her dowry if she had only a son? Answ. 17501.