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4. A farmer threshes 6 qr. 5 bush, of wheat per acre from a field of 28 acres, and he sells it at £1 11s. 6d. a quarter : find, by the method of practice, the value of the crop. 5. What is the interest on £1,253 15s. from November 14th, 1904, to February 14th, 1905, at 6| per cent, per annum ? 6. A coal-merchant buys a cargo of 297 tons 12 cwt. of coal for £223 4s. ; he reckons that it will cost him Bs. 4d. a ton to sell it in truck-loads of 4 tons 16 cwt. each: if he charges £6 10s. a truck, what is his total profit ? 7. A can do a piece of work in 10 days ; B can do it in 6 days : how long will it take them, working together, to do a piece of work twice as great ? 8. Assuming that 396 inches = 1008 centimeters, express 2 miles 14 chains in centimeters. 9. A farmer sends 260 sheep to the saleyards, and they are sold at 15s. 9d. a head : if the auctioneer charges a commission of 2 J per cent., how much does the farmer receive for his sheep ? 10. Express 2 roods 16 perches as the decimal of an acre, and find the value of a farm of 164 acres 2 roods 16 perches at £8 an acre. 11. Gold-leaf is sold in packets of 500 sheets, each sheet measuring 3£ inches square, at £2 10s. a packet; the quantity required to cover a cubical block costs £3 : find the length of the edge of the block. 12. The working of the sum " How long will 16 reapers take to cut 120 acres of wheat if 12 reapers cut 84 acres in 7 hours ? " was set out in two steps, without explanation, as follows : — Hours. „ 12 120 ' X 16 X 84 State as clearly as you can the reasoning on which these two steps are based.

Ao. 30. — Arithmetic. — For Civil Service Junior. Time allowed: Three hours. [The full working of the questions should in all cases be given.] 1. By what factor less than 1000 must 4389 be multiplied so that the last three figures of the product may be 438 ? 2 A + ± 2. Simplify 1| of + + + \of S-S 4* + 3 3. Eeduce 3 cwt. 3 qr. 5 lb. 4 oz. to the decimal of a ton. 4. Show how to obtain the product of 275406 and 8347 to five places of decimals by contracted multiplication, and test your answer by multiplying in the ordinary way. 5. A vessel whose speed was 9} miles an hour started at 8 o'clock to go a distance of 74 miles; a second vessel whose speed was to that of the first as 8 to 5, starting from the same place, arrived 5 minutes before the first: when did the second vessel start ? 6. Two rectangular fields are enclosed by fences each 3,796 feet in total length, the first field being square, and the second 624 feet longer than the first: what length of fencing would it take to enclose a square field equal in area to the second ? 7. A Lyons merchant could sell silk at home at 7 fr. 10 c. a meter, making a profit of %; but at Vienna he could sell it at 10 fl. 25 kr. (100 kreutzer = 1 florin) for 3 meters, gaining 8J % : find the rate of exchange between Austria and France in florins for 200 fr. 8. If the interest on £253 2s. 6d. at 5 % be equal to the true discount on £257 6s. IOJd. for the same time at the same rate, when is the latter sum due ? 9. A rents a house for a year at £93 125., and at the end of four months takes in B as a co-tenant, and they admit C in like manner for the last 2f months : how much of the rent should each pay ? 10. Given that 7 women are paid as much as 4 men, and that 24 men and 7 women working together earn 726 guineas in 51 days, what number of women should work with 20 men so that the earnings of the 20 men and the women together for 17 days may amount to £254 2s. ? 11. If the length of the minute hand of a clock is 11 it., find to the nearest yard the distance that the end of it will travel in 365J days, taking the ratio of the diameter of a circle to its circumference as 7 to 22. 12. The area of a coalfield is 937£ square miles, and the average thickness of the coal is 70 ft. : if a cubic yard of coal weigh a ton, and the annual output be 70,000,000 tons, how many years will it take to exhaust the coal ?

No. 31. — Arithmetic. — For Class D. Time allowed: Three hours. [All the work by which a result is obtained must be clearly shown, as no credit can be allowed for any result, however correct it may be, unless the method of obtaining it is given.] 1. (a.) Divide 3879769 by 56, short division, by factors ; and explain the reason for your method of finding the remainder. (6.) Find the G.C.M. of 441441 and 844272, and explain the principles involved in the working