5. Find the square root of 0.0000001. 6. A merchant sold a quantity of goods for $ 29900. He deducts five per cent from the amount of the bill for cash, and finds that he has made fifteen per cent, on the investment. What did he pay for the goods? 7. What is the compound interest on £ 47 13 s. 6 d. for 3 yrs. 4 mos. 15 ds., at 3| per cent? 8.' How many feet of board in a plank 17 ft. long, 22 inches wide at one end, 13 inches wide at the other, and 4 inches thick? 9. Write the tables for Long Measure and Square Measure. XXI. 1. Eeduce 179487 to the product of its Prime Factors. 2. Find the Greatest Common Divisor of 13212 and 1851. 3. To divide by a Vulgar Fraction: give the rule and the reason of the rule. 4. Find the sum of the following numbers: fifty-seven and three thousandths; three hundred and sixty-four hundred thousandths; forty-seven thousand and eight thousand and seven hundred thousandths; eighty-seven hundred millionths; four hundred and twenty-seven ten thousandths. 5. Divide (2\ X by (2\— If), and reduce the result to a decimal. 6. What is the difference between Bank Discount and True Discount? Give an example. 7. Bought $ 1500 worth of goods, half on 6 months' and half on 9 months' credit. What sum at 7 per cent interest, paid down, would discharge the whole bill? 8. Find the cube root of 0.29 to three places of decimals. 9. The interest on £ 50 12 s. 6 d. for a year is £ 1 15 s. 5\d. What is the rate per cent? 10. A cubical vat measures 9 feet in each direction: what is its capacity in Litres? (Given 1 metre = 39.37 inches.) 11. In the Metric System of Weights and Measures what is the unit of length? of surface? of volume? of weight? How are they related to each other? XXII. 1. Divide four millionths by four millions, and write the quotient in words. 2. The metre = 39.371 inches: compare the kilometre with the mile. 3. Change £ to a decimal, and extract the cube root to four places. 4. Express 38 sq. rods, 21 sq. yards, 5 sq. feet, 108 sq. inches, in decimals of an acre. 5. The capital stock of a certain bank is $500,000, and directors have declared a dividend of 4 per cent. The sum set aside from the profits to meet this dividend is subject 'to a revenue tax of 5 per cent. What sum must be set aside in order that the stockholder may receive a dividend of 4 per cent on his stock? 6. From -~—subtract 5?. 7. A man has a bin 7 ft. long, 2^ ft. wide and 2 ft. deep, which contains 28 bushels of corn; how deep must he build another, which is to be 18 ft. long, 1 ft. lOj in. wide, in order to contain 120 bushels? (Solve this question by analysis, and give your reasoning in full.) /," 8. What is the present worth of $ 10,000, due three years hence, at 7 per cent compound interest? 9. Find the Greatest Common Divisor of 1274, 2002, 2366, foot, and 13013. 10. How do you verify your work when you have multiplied together two large numbers? Give an example to illustrate your method. XXIII. 1. Find the Greatest Common Divisor and the Least Common Multiple of 13860 and 38500. What is the Least Common Multiple of 15,18, and 35? When are two numbers said to be prime to each other? 2. Divide ^ by | of i ^- Simplify by cancelling. 3. Reduce to its lowest terms as a Vulgar Fraction 0.05405. Reduce ^g- to a Circulating Decimal. 4. Find the number of cubic inches (to the nearest tenth) in the British imperial gallon, which contains 10 pounds of water. Given 1 gramme = weight of 1 cubic centimetre of water, 1 cubic metre = 35.3 cubic feet, 1 kilogramme = 2.2 pounds. 5. Find the square root of 0.076 to six significant figures. 6. A rectangular field measures 30 rods and 6 feet by 21 rods and 11 feet. Find its area in acres, roods, rods, and feet. 7. Find the sum on which the interest at 9 per cent for 5 years 1 month and 18 days is $ 947.10. 8. Find the interest on one pound sterling at 5 per cent for one year; for one month. XXIV. 1. What is the Greatest Common Divisor of 1872 and 432? Obtain the answer, if possible, by factoring. 2. What is the smallest sum of money that can be made up either of 2-cent, of 3-cent, of 5-cent, of 10-cent, or of 25-cent pieces? 4. By a pipe of a certain capacity a cistern can be emptied in 3-^ hours; in what time can it be emptied by a pipe the capacity of which is $ greater? 5. Find the value of 7 acres 35 rods 127 feet of land, at $ 108.15 per acre. 6. How many litres are there in a rectangular vat 2.8 m. long, 2 m. wide, 5 dcm. deep? 7. Find the square root of 0.9 to four places of decimals. 8. My agent sells for me 2000 yards of cloth at 24 cents a yard. He allows the purchaser 5 per cent discount for cash, and charges me 2| per cent on the cash receipts. How much money does he pay over to me? 1. Find the Greatest Common Divisor of 187 and 153. Also the Least Common Multiple of the same t fro numbers. 2. Multiply 108 billionths by two thousand, and extract the cube root of the product. 4. A cellar is to be dug 30 feet long and 20 feet wide : at what depth will 50 cubic yards of earth have been removed? 5. What is the amount of $ 340 at 8 per cent for 1 year 3 months, the interest being compounded semiannually? 6. A man receives $ 18 for six days' work of 8 hours XXV. each; what should he receive for 5 days' work of 9 hours each? 7. A cistern is 4 metres long, 24 decimetres wide, and 80 centimetres deep. How much water will it hold in cubic metres? In litres? In cubic centimetres? In grammes? In kilogrammes? 8. I have a rectangular lot of land, 64 rods long and 36 rods wide, and a square lot of the same area; how many more feet of fencing will be needed for the former lot than for the latter? XXVI. 1. Add \ oi~to f|. 2. Multiply 0.145 by 0.297, and give the answer as a Circulating Decimal. 3. Find the Greatest Common Divisor of 43700 and 9430. Also obtain their Least Common Multiple. 4. I buy one fifth of an acre of land for $2178. For how much a square foot must I sell it, in order to gain twenty per cent of the cost? 5. The kilogramme equals 2 lb. 8 oz. 3 dwt. 2 gr. How many centigrammes equal one grain 1 q 6. What is the present worth of $ 678.75, due 3 years 8 months hence, at 7 per cent compound interest? 7. Multiply the square root of 0.173056 by the cube root of mn 8. A can do a certain piece of work in 10 days, working 8 hours a day. B can do the same work in 9 days, working 12 hours a day. They decide to work together, and to finish the work in 6 days. How many hours a day must they work? |