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Arithmetic. — For Class D. Time allowed: 3 hours. 1. Explain the reason of the process you adopt in multiplying two vulgar fractions together : e.g., f x f 2. Simplify ' 78571 f l + 1^ f| * l*ft + (2A--066 of 3f) X (16»-B* of 4|). n , • , * V 3-1 3. Find the value correct to four places of decimals of ,» - + /g , 2 ' 4. A passenger from New Zealand to England takes a return-ticket, for which he pays 50 per cent, more than he would have paid for a single ticket. Finding that he cannot return so soon as he expected, he gets the time for which his ticket is available extended, and for this privilege he pays an advance of 10 per cent, on the price which the return-ticket originally cost him; he finds that his return fare is now £115 10s. Find the price of the single fare to England. 5. A man has been in the habit of paying property-tax to the extent of a penny in each pound of his capital. A change is made in the system of taxation, and he is now called upon to pay a shilling in the pound on his income. If his capital earn 8 per cent., compare the effects on him of the two systems of taxation. 6. A well, whose horizontal section is everywhere a circle 6ft. in diameter, contains 10,000 gallons of water : find the depth of the water, assuming that a gallon contains 27725 cubic inches. (N.B.—The area of a circle is formed by multiplying the square of its radius by 3-1416.) 7. If the mass of the moon be -012345679 times that of the earth, and the mass of Jupiter's third satellite be -0297 times that of the earth, find the ratio of the mass of the moon to that of Jupiter's third satellite. 8. If the discount on £1,545 2s. 6d. due 2>\ years hence be £230 2s. 6d., find the rate per cent., simple interest. 9. Find the present worth of £3,087 due three years hence at 5 per cent, compound interest. - 10. A metre being equal to 39-37 inches, express an acre as a fraction of a hectare, a hectare being a square whose side is 100 metres. 11. The pendulum of one clock vibrates in 1-05 seconds, and that of another in -95 second: if the clocks are started at 9 in the morning of Monday, 2nd January, when will they be together again ? How often in the first 24 hours will the pendulums begin a vibration together ? 12. Divide £182 8s 9d. among 5 men, 6 women, 3 boys, and 10 girls in such a way that for every florin each man gets, each woman gets eighteen pence ; that for every half-crown a man gets, a boy gets a shilling ; and for every half-crown a boy gets, a girl gets a florin. 13. A person has £1,583 17s. lid. stock in the 3-per-cents, and £982 12s. 6d. stock in the 3i_per-cents. He transfers a certain sum from the former to the latter when the stocks are at 91 and 98 respectively, and thus makes the income derived from each the same. How much stock has he finally in the 3-per-cents ? Arithmetic. — For Class E, and for Junior Civil Service. Time allowed: 3 hours. rjST.B. The working must be shown. Simplicity and directness of method, clearness of explanation, and neatness of work will be taken into account.] 1. Express in words, 42146675; and, if the quotient obtained by dividing it by a certain number be 743, determine the number. 2. Simplify — (*•) 1 1--5-X IS A 2 I 16 11111 SI- IS (ii ) Uof 2+3 + 4 xSt if • W 24-31+4} X 3 4i 4| + 3 3. Divide £29 into an equal number of half-sovereigns, crowns, half-crowns, shillings, sixpences, and fourpences. 4. If a herring and a half cost 2Jd. how many will you get for 12s. 3d. ? 5. There was a yard, 10ft. square, paved with 1,000 bricks. One edge of each brick was long : what was the length of the other edge ? 6. Express If of 33 qr. 7 bus. 7 gal. as a fraction of 9 qr. 4 bus. 1 gal. 7. A regiment of a thousand men are to have new coats; each coat is to contain 2-J yards of cloth of 1J yards wide, and to be lined with shalloon § yard wide : how many yards of shalloon will be required ? 8. What is the difference between £ of a guinea and § of a pound? 9. How many persons can be paid lis. 6d. each out of a sum of £170 10s. 2d.? And, if the balance be also distributed equally among them, how much more will each receive ? 10. Divide 1-9517 by 673000, and 64000 by -0008; multiply each quotient by 3-2. 11. Find, by Practice, the cost of 2 tons 7 cwt. 221b. soz. at £32 per ton. 12. The interest on a certain sum of money for two years is £71 16s. 7-J-d., and the discount on the same sum for the same time is £63 175., simple interest being reckoned in both cases. Find the rate per cent, per annum and the sum.