30. Six men purchased 640 acres of land; the first is to have 63%, the second 85%, the third 10%, the fourth 121%, the fifth 16%, the sixth the balance ; how many acres ? Ans. 293} acres. 31. Sold a lot of grain, and after deducting commissions of 41% for selling and 21% for buying, I invested the proceeds $7640 .in sugar ; what was the grain sold for? Ans. $8200. 100 $7640 x Х 100 953 1021 32. Sold goods 40% off the marked price, and thereby lost $1200, which was 10% of cost; what was the marked price and cost ? Ans. Marked price $18000; cost $12000. 33. What is the cost of a draft on New York for $2000, at 1% premium ? Ans. $2015. 34. What is the cost of a draft on New Orleans for $2500, at 1% discount? Ans. $24871 35. A merchant entered business with $5000; the first year he gained 20%, which he added to his capital ; the second year he gained 20%, and added it to his capital; the third year he lost 25%; what had he then ? Ans. $5400. 36. Sold goods for $375, thereby losing $25; what per cent did I lose ? Ans. 62% 37. After selling 25 sheep there remained 225; what per cent were sold ? Ans. 10%. 38. A tax collector gets 5% additional on the taxes which he collects; the cost on property valued at $56000 was $294; .what was the rate per cent of the tax ? Ans. 3% 9 39. In a storm 20% of the cargo was thrown overboard; at what rate of gain must the remaining cargo be disposed of so that no loss is sustained ? Ans. 25%. 40. A merchant commenced business with $3000 and closed with $4500; what per cent did he gain ? Ans. 50%. 41. What per cent of £3 10s. is 14s. ? Ans. 20% 42. What per cent of 5 lb. Avoirdupois is 8 oz. ? Ans. 10%. 43. What per cent of 5 Ib. Avoirdupois is 14 pwt. 14 gr.? Ans. 1%. 44. What per cent of 1 ton is 1 cwt. ? Ans. 5%. 45. One quart is what per cent of 1 bushel ? Ans. 31%. 46. What is the cost of a draft on New Orleans for $2000, at sixty days, with grace, discount %, and interest allowed at 6% ? Ans. $1969. 47. 2 is what per cent of 5 ? Ans. 40%. 48. 31 is what per cent of 53 ? 7 631 = 631%, Ans. 11 100 49. 13} is what per cent of 94 ? 27 142 1423%, Ans. 100 19 REM.-A common fraction is reduced to hundredths by multi. plying both terms of the fraction by the quotient obtained by dividing 100 by the denominator of the fraction. ALLIG ATION. Alligation is the mixing of different qualities of grain, groceries, liquors, etc., in order to get an article of a certain price; thus, sugar at 5 cts. and 9 cts. per lb. may be mixed together in such proportions as to make an article of any value between the two given prices. COR.- The mixture cannot be made of less value than 5 cts. nör more than 9 cts.; for if a quantity be taken at 5 cts., and some of 9 cts. be added, it will increase the value above 5 cts.; and if 5 ct. sugar be added to the 9 ct., it will diminish the value. REM.-If both kinds are either above or below the required price, the mixture cannot be made PROBLEM. 1. What relative quantity of each must be taken of two kinds of sugar, the one worth 5 cts. per Ib., and the other 11 cts., in order that the mixture be worth y cts. EXEMPLIFICATION.–For every lb. at 5 cts. there is a gain of 2 cts., and for 1 lb. a gain of 1 ct.; for every lb. at 11 cts. there is a loss of 4 cts., and of 7 lb. the loss is 1 ct.; hence, if 1 lb. at 5 cts. be taken, and 7 lb. at 11 cts., the gain and loss will be equal ; this is then the ratio ; or, reducing the fractions to a common denominator and canceling the denominators, the ratio is 2 at 5 to 1 at 11. REM.-It matters not how many different qualities are to be mixed, only two at a time can be mixed ; . the principle developed in the above problem is the only principle in alligation. 2. Mix together coffee worth 17 cts., 19 cts., 21 cts., and 24 cts., so that the mixture shall be worth 20 cts. It is evident that 117 and 19 cannot make a mixture worth as much as 20 cents; it is also evident that 21 and 24 cannot make a mixture worth as little as 20 cts.; but 17 and 21, 19 and 24, 17 and 24, and 19 and 21 may be mixed so as to be worth 20 cts. By the first is taken 1. at 17 to 3 at 21; and 4 at 19 to 1 at 24 ; again, 4 at 17 to 3 at 24; and 1 at 19 to 1 at 21. All the mixtures being of the same value, may be put together, and the whole will be worth 20 cts. ; thus, The result is the same; that is, the whole mixture is worth 20 cts. Take the same articles to form a mixture, and place them together thus: COR.—The same relative portions of each is obtained by taking the difference between each price and the mean price, and placing this difference opposite the price to which each one is connected. Solve the next one according to this corollary. 8. A vintner has four qualities of wine, viz., at $1.30, $1.50, $1.75, and $1.95 per gallon; he has an order for wine at $1.60; what relative quantity of each must be put into the mixture ? |