+ 9. Three gardeners working all day can plant a field in 10 days; but one of them having other employment can only work half time. How long will it take them to complete the work ? 10. What fraction of a crown is of 6s. 8d. ? What is the value of of a guinea ? Reduce 11 d. to a decimal of a pound, correct to five places of decimals. 11. Reduce the expressions } + } } }-is Multiply 497% by 507, and add to to the result. Divide (27)3 – 1 by (276)2 + 376. 12. A bankrupt's estate amounts to £910. 3s. 13d., and his debts to £1875. What can he pay in the pound? and what will a creditor lose on a debt of £57 ? 13. A person having invested a sum of money in the Three per Cent. Consols received annually therefrom £233, after deducting the income tax of 7d. in the pound. What is the sum of money? What can the stock be sold for when Consols are at 945. 14. Find the value of :003 X.004, and of :181ttz. 15. Prove the rule for finding the value of a circulating decimal, and divide 4.367 by the circulating decimal 052. 3 + 5 Reduce to its simplest form the quantity 3 15 8 8 + 120 16. Three persons, A, B, C, hold a pasture in common, for which they are to pay £30 per annum. A put in 7 oxen for 3 months; B, 9 oxen for 5 months; and C, 4 oxen for 12 months. How much rent ought each to pay? 17. Calculate to four places of decimals the value of the of :31416 expression .93 .006 120 Х 18. Find the least common multiple of 16, 24, and 30, and explain the method. 19. What should be the price of English standard silver, 37-40ths fine, in order that the par of exchange between England and France should be 25 fr. 22 c.—200 francs being coined from 1 kilogram of silver, 9-10ths fine? (1 kilog. = 15.434 grains). 20. A person buys 100 shares in a company for £3,500; after receiving four half-yearly dividends of 15s. 4d., 20s. 10d., 30s. 4d., and 38s. 9d. per share, he sells at a profit of 43 per cent.; reckoning the simple interest of money at 4 per cent., how much above that interest has he gained? 21. The price of Three per Cent. Consols is 90%; what sum must be invested in order to purchase £24 per annum; and what is the rate of interest on the money invested ? 22. Three partners in trade contribute respectively the sums of £438, £292, £730, with the agreement that each was to receive 5 per cent. on their respective investments, and that the remainder of the gains of the firm, if any, was to be divided between them in the proportion of the sums originally advanced. The whole gain of the firm was £200. What was each man's share ? 23. If 25 tons of goods are purchased for £37. 10s. and sold at 358. a ton, what is the gain per ton ? At what rate per ton should the goods have been sold in order to obtain a profit of £9. 78. 6d. ? 24. Find the value of of £3. 12s. 11 d.; and find the fraction that 3 miles, 2 fur. 100 yards is of 12 leagues, 2 fur. 20 yards. 25. The sum of £9040. 16s. is placed in the Three and a Half per Cents. at 94 ; find the income obtained, allowing on the stock purchased fth per cent. to the broker, and to per cent. for other expenses. 26. Express as a fraction .200123, and express as a recurring decimal 012 4 00132. 27. By the reduction of the income tax from 7d. in the pound to 5d. a person saves £28. 2s. 6d. a year; what is his income? 28. If 81 bushels of wheat are consumed by 56 men in 5 days, how long will 16 men take to consume 28 bushels ? 29. Find the square root of i, and prove that 1.694 = 83. 30. The periods of three planets which move uniformly in circular orbits round the sun are respectively 200, 250, and 300 days. Supposing that their positions relative to each other and to the sun to be given at any moment, determine how many days must elapse before they again have exactly the same relative positions. SECTION II. GEOMETRY EUCLID'S ELEMENTS, BOOK I. Definitions. 1. A point is that which has position, but not magnitude. 2. A line is length without breadth. 3. The extremities of a line are points. 4. A straight line is that which lies evenly between its extreme points. 5. A superficies (or surface) is that which has only length and breadth. 6. The extremities of a superficies are lines. 7. A plane superficies is that in which any two points being taken, the straight line between them lies wholly in that superficies. 8. A plane angle is the inclination of two lines to one another in a plane, which meet together, but are not in the same direction. 9. A plane rectilineal angle is the inclination of two straight lines to one another, which meet together, but are not in the same straight line. NOTE.—When several angles are at one point B, any one of them is expressed by three letters, of which the middle letter is B, and the first letter is on one of the straight lines which contain the angle, and the last letter on the other line. Thus, the angle contained by the straight lines AB and BC is expressed either by ABC or CBA, and the angle contained by AB and BD is expressed either by ABD or DBA. When there is only one angle at any given point, it may be expressed by the letter ať that point, as the angle E. 10. When a straight line standing on another straight line makes the adjacent angles equal to one another, each of the angles is called a right angle; and the straight line which stands on the other is called a perpendicular to it. 11. An obtuse angle is that which is greater than a right angle. 12. An acute angle is that which is less than a right angle. 13. A term or boundary is the extremity of anything. 14. A figure is that which is enclosed by one or more boundaries. 15. A circle is a plane figure contained by one line, which is called the circumference, and is such, that all straight lines drawn from a certain point within the figure to the circumference are equal to one another. 16. And this point is called the centre of the circle, [and any straight line drawn from the centre to the circumference is called a radius of the circle). |