7 193. The length of a rectangle is 128 feet and its breadth 96 feet; what is the length of its diagonal ? Ans. 160 feet. 194. The length of a rectangle is 72 feet and its diagonal 90 feet; what is its width? Ans. 54 feet. I 195. A merchant of St. Louis has a debt of $6000 to pay in New York. Direct exchange is 13% premium on New York, but on New Orleans funds there is a discount of 4%, and at New Orleans the premium on New York is %; what advantage is the circuitous route ? Ans. $75.221 gained by the circuit. 196. A house valued at $12500, is insured for its value at 5%; for what sum is the policy drawn so as to include the premium ? Ans. $105261 .197. If I purchase a city bond at 90% which bears 8% interest, what per cent do I get on my investment? Ans. 88% 198. A merchant being asked at what per cent profit he sold his goods, replied f of my selling price is 25% less than cost ; at what per cent profit did he sell goods? Ans. 12% profit. 199. In the ruins of Persepolis are two columns standing upright; the one is 70 feet above the plane and the other 50 feet; in a straight line between these columns is a small statue 5 feet high, the head of which is 100 feet from the top of the higher and 80 feet from the top of the lower column. What is the distance between the tops of the columns ? Ans. 143.54. 200. What is the rate per cent, when the amount is the principal that had been at interest 3 years ? . Ans. 89% 201. How much more fence will it take to enclose a rectangular lot of land 100 rods long and 36 rods wide, than if the same quantity of land were in the form of a square? Ans. 32 rods. 202. In what direction and at what rate must a man at the equator, having the sun on his meridian, travel, in order that he may always have noon? Ans. He must travel west 10374 miles per hour. 203. Extract the square root of .0043046721. Ans. .06561. 204. When it is 5 A.M. at the Cape of Good Hope, in longitude 18° 24' east, what is the time at Cape Horn, in longitude 67° 21' west? Ans. 11 hr. 17 min., P.M., of the previous day. 205. How do you reduce several fractions to equivalent fractions having the least common denominator. Ans. By multiplying both terms of each fraction by the quotient obtained by dividing its denominator into the least common multiple of all the denominators. 206. How many steps of three feet each would a man take in walking five miles ? - Ans. 8800 steps. 207. The difference in the time of two places is 2 hr. 10 min.; what is the difference of longitude ? Ans. 32° 30'. 208. If 500 copies of a book of 210 pages take 12 reams of paper, how much will 1000 copies of 280 pages require ? Ans. 32 reams. 209. Find the third term of 3 : 8 : : ?.: 12. Ans. 41. 210. If 24 yd. cloth cost $20, what will 18 yd. cost? Ans. $160. 211. Find the greatest common divisor of 492, 744, 1044. Ans. 12. 212. Find the least common multiple of 25, 36, 33, 12, 45. Ans. 9900. 213. When the extremes and the number of terms are given in a series of equal differences, how do you find the sum of the series ? Ans. Multiply the sum of the extremes by one-half the number of terms. 214. Of what factors of several numbers is the greatest common divisor composed ? Ans. The factors common to all the numbers. 215. When are four quantities in proportion ? Ans. When the quotient of the first and second, and that of the third and fourth are equal. 216. How is the rate per cent obtained, when the principal, interest, and time are given ? Ans. Divide the interest by the product of the principal and time. 217. How do you find the time, having given the principal, interest, and rate? Ans. Divide the interest by the product of the principal and rate. 218. Having given the principal, rate, and time, how do you find the interest? Ans. The product of the principal, rate, and time is equal to the interest. 219. How do you find the principal, when the interest, rate, and time are given ? Ans. Divide the interest by the product of the rate and time. 220. How do you find the last term of a series of equal ratios, the first term, ratio, and number of terms being given? Ans. The last term is equal to the ratio raised to the power expressed by the number of terms less one, multiplied by the first term. 221. How do you find the sum of a series of equal ratios ? Ans. The sum is equal to the product of the ratio and last term, diminished by the first term, and divided by the ratio less one. 222. How much will it cost to dig a cellar 60 feet long, 30 feet wide, and 6 feet deep, at 30 cts. per cubic yard ? Ans. $120. 223. A and B enter into business ; A furnishes $600 for 8 months and B $400 for 9 months; they gain $140; what is each one's share ? Ans. A's $80, B's $60. 224. 5 pence is what per cent of 8} shillings? Ans. 5%. 225. What is the greatest common divisor of i, j, , 4? Ans. 226. What is the least common multiple of 1, š, 1, $? Airs. 12. 227. What is the least common multiple of 3, 4, 5, 6, 7, 8? Ans. 840. 228. How is a common fraction reduced to a decimal ? Ans. Perform the division indicated. 229. Find the term omitted in 4:?:: 9:16 ? Ans. 7. 230. What principal will gain $11.20 in 3 years and 6 months at 8%? Ans. $40. 231. How do you change a decimal into a common fraction ? Ans. Make the decimal the numerator, and for the denominator place 1 with as many zeros annexed as there are figures in the decimal. 232. What is the least common multiple of 21, 35, 42? Ans. 210. 233. How many yards of cloth, 4 yd. wide, are equivalent to 24 yards, i yd. wide ? Ans. 224 yd. 234. The difference between f and f of a number is 8; what is the number? Ans. 576. 235. The first term of a series of equal differences is 1, the difference 2, and the number of terms 8; what is the sum of the terms ? Ans. 64. 236. The first term of a series of equal ratios is 1, ratio 3, and the number of terms 6; what is the sum of the series ? Ans. 364. 237. A, B, and C bought a horse for $120 and sold him for $180. A received for his part of the gain $25, and B $20; how much had each paid for the horse ? Ans. A $50, B $40, C $30. 238. Find the sum of 8 terms of the series of equal ratios 3, 6, 12, etc. Ans. 1765. 239. A body of 3600 troops have $ as many cavalry as infantry; what is the number of each ? Ans. 600 cavalry and 3000 infantry. 240. When snow is uniformly 1 foot deep, how many cubic yards on an acre of land ? Ans. 16133 cubic yards. 241. To what number'must 235 be added three times to make 950 ? Ans. 245. |