212 QUESTIONS FOR EXERCISE. C's 14s." 4}d. a piece, which were so d at 18d. a yard; re quired the prime cost, what it sold for, and the gain. £. S. d. Prir . e cost, 19. 8 1 Ans. Sold for, 23 5 9 Gair 3 1775 25. Three partners, A, B and C, join their stock, and buy goods to the amount of £1025,5; of which A put in a certain sum; B put in....I know not how much, and C the rest; they gained at the rate of 241. per cent. : A's part of the gain is t, B's }, and C's the rest. Required each man's particular stock. £ S A's stock was 512,75 Ans. 205,1 307,65 26. What is that number which being divided by x, the quotient will be 21 ? Ans. 151. 27. If to my age there added be, One-half, one-third, and three times three, Ans. 66. 28. A gentleman divided his fortune among his three sons, giving A 91. as often as B 51. and to c but 31. as often as B 71. and yet C’s dividend was 25841. ; what did the whole estate amount to? Ans. £19466 2s. 8d. 29. A gentleman left his son a fortune, # of which he spent in three months; of the remainder lasted him 10 months longer, when he had only 2524 dollars left; pray what did his father bequeath him? Ans. 85889, 3Scts. + 30. In an orchard of fruit trees, t of them bear apples, pears, plums, 40 of them peaches, and 10 cherries; how many trees does the orchard contain ? Ans. 600. 31. There is a certain number, which being divided by 7, the quotient resulting multiplied by 3, that product divided by 5, from the quotient 20 being subtracted, and 30 added to the remainder, the half sum shall make 65 ; can you tell me the number? Ans. 1400 32 What part of 25 is of an unit ? Ans. . a 33. If A can do a piece of work alone in 10 days, Bir 20 days, C in 40 days, and D in 80 days ; set all four about it together, in what time will they finish it ? Ans. 51 days. 34. A farmer being asked how many sheep he had, answered, that he had them in five fields, in the first he had of his flock, in the second , in the third , in the fourth ts, and in the fifth 450; how many had he ? Ans. 1200. 35. A and B together can build a boat in 18 days, and with the assistance of C they can do it in 11 days; in what time would C do it alone ? Ans. 28 days. 36. There are three numbers, 23, 25, and 42; what is the difference between the sum of the squares of the first and last, and the cube of the middlemost ? Ans. 13332. 37. Part 1200 acres of land among A, B, and C, so thai B may have 100 more than A, and C 64 more than B. Ans. A 312, B 412, C 476. 38. If 3 dozen pair of gloves be equal in value to 2 pieces of holland, 3 pieces of Holland to 7 yards of satin, 6 yards of satin to 2 pieces of Manders lace, and 3 pieces of Flanders lace to 81 shillings; how many dozen pair of gloves may be bought for 283. ? Ans. 2 dozen pair. 39. A lets B have a hogshead of sugar of 18 cwt. worth 5 dollars, for 7 dollars the cwt. of which he is to pay in cash. B hath paper worth 2 dollars per ream, which he gives A for the rest of his sugar, at 24 dollars per ream; which gained most by the bargain ? Ans. A by $19, 20cts. 40. A father left his two sons (the one 11 and the other 16 years old) 10000 dollars, to be divided so that each share, being put to interest at 5 per cent might amount iv equal sums when they would ve respectively 21 years of age. Required the shares ? Ans. 54546 and 4545- dollars. 41. Bought a certain quantity of broadcloth for 3831. 59. and if the number of shillings which it cost per yard were added to the number oi nyards bought, the sum would be 386; I demand the number of yards bought, and at what price per yard ? Ans. 365 yds. at 21s. per yard. Solved by PROBLEM VI. page 183. 42. Two partners, Peter and John, bought goods to the amount of 1000 dollars; in the purchase of which, Peter paid more than John, and John paid....I know not bow much: They then sold their goods for ready money, and thereby gained at the rate of 200 per cent. on the prime cost: they divided the gain between them in proportion to the purchase money that each paid in buying the goods ; and Peter says to John, My part of the gain is really a handsome sum of money; I wish I had as many such sums as your part contains dollars, I should then have 8960000. I demand each man's particular stock in purchasing the goods. Ans. Peter paid 600 dollars, and John paid 400. THE FOLLOWING QUESTIONS ARE PROPOSED TO SURVEYORS. 1. Required to lay out a lot of land in form of a long square, containing 3 acres, 2 roods, and 29 rods, that shall take just 100 rods of wall to enclose, or fence it round; pray how many rods in length, and how many wide, must said lot be ? Ans. 31 rod's in length, and 19 in breadth. . 183. 2. A tract of land is to be laid out in form of an equal square, and to be enclosed with a post and rail fence 5 rails high ; so that each rod of fence shall contain 10 rails. How large must this noble square be to contain just as many acres as there are rails in the fence that encloses it, so that every rail shall fence an acre ? Ans. the tract of land is 20 miles square, and contains 256000 acres. Thus, 1 mile=320 rods: then 320X320;-160=640 acres: and 320X4x10=12800 rails. As 640 : 12800.:: 12800 : 256000 rails, which will enclose 256000 acres20 miles square. 215 AN APPENDIX, CONTAINING SHORT RULES, FOR CASTING INTEREST AND REBATE; TOGETHER WITH SOME USEFUL RULES, TOR FINDING THE CONTENTS OF SUPERFIOIES, SOLIDS, &c. SHORT RULES, FOR CASTING INTEREST AT SIX PER CENT. 1. To find the interest of any sum of shillings for any number of days less'than a month, at 6 per cent RULE. 1. Multiply the shillings of the principal by the number of days, and that product by 2, and cut off three figures to the right hand, and all above three figures will the interest in pence. 2. Multiply the figures cut off by 4, still striking off three figures to the right hand, and you will have the farthings, very nearly. EXAMPLES 1. Required the interest of 51. 8s. for 25 days. £. 5,8=108 X25X2=5,400, and 400X4=1,600 Ans. 5d. 1,6qrs. 2. What is the interest of 211. 38. for 29 days? Ans. 2s. Od. aqrs. FEDERAL MONEY. II. To find the interest of any number of cents for any number of days less than a month, at 6 per cent. RULE. Multiply the cents by the number of days, divide the product bay 6, and point off two figures to the right, and all the figures at the left hand of the dash, will be the interest in mills, nearly. EXAMPLES. Required the interest of 85 dollars, for 20 days. 8 cts. mills. 85=8500 x 20:6=283,33 Ans. 283 which is 28 cts. 3 mills. 2. What is the interest of 73 dollars 41 cents, or 7341 cents, for 27 days, at 6 per cent. ? Ans. 330 mills, or 33 cts. a III. When the principal is given in pounds, shillings, &c. New-England currency, to find the interest for any number of days, less than a month, in Federal Money. RULE. Multiply the shillings in the principal by the number of days, and divide the product by 36, the quotient will be the interest in mills, for the given time, nearly, omitting fractions. EXAMPLE Required the interest, in Federal Money, of 271. 158. for 27 days, at 6 per cent. 8. Ans. 27 15=555 X 27:-36=416 mills. 41cts. 6m.' IV. When the principal is given in Federal Money, and you want the interest in shillings, pence, &c. Newa England currency, for any number of days less thans months |