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14

3. Simplify 8 + L-— ; and E-« x [j-z%\ . B * +lt+ 6f 4. If -0583 of lcwt. cost -428571 of 3f guineas, what will be the cost of 38-51b. ? 5. A sum of £24 13s. 4d. is made up of half-sovereigns, half-crowns, and fourpenny-pieces. There are twice as many half-crowns as half-sovereigns, and the number of half-sovereigns bears to the number of fourpenny-pieces the ratio of 3to 13. How many are there of each coin ? 6. If I lose 16 per cent, by selling a horse for £21, how much did I give for it; and at what price should it have been sold to gain 12 per cent. ? • ~,,,, 7. If f of a stack of hay sold for £15 2s. 6d. when hay was at £4-4 per ton, what would fa of the same stack fetch, the price having risen to £7-5 a ton ? 8. A passenger train starts from A towards B at 8 o'clock, and a goods tram and a coal tram from B towards Aat 8-30 and 9 respectively. The goods train travels 30 and the coal train 20 miles an hour. The passenger train meets the goods train at 9-55f, and the coal train at 10-20. Find the rate per hour of the passenger train, and the distance between A and B. 9. A person received £5 ss. as interest for one year on two sums of money, one of which was double of the other, at the rate of 5 per cent, on the larger and 4 per cent, on the smaller sum. Find their amounts. . 10. The breadth of a room is 16ft.; the cost of papering the walls at 6d. a square yard is £2 3s. 4d.; and that of carpeting the floor at 6s. a square yard is £9 6s. Bd. : find the height and length of the room. . 11. Find the greatest number that will divide 638443 and 34093, leaving remainders 11 and 13 respectively. 12. Divide 73-8 by -0018, and multiply the quotient by T % of -0009747.

Arithmetic. — For Senior Civil Service. Time allowed: 3 hours. 1. What number must three hundred and seventy-one be multiplied by in order that the product may be the same as the quotient of one thousand and nine million ten thousand one hundred and eighty-four by nine thousand and ninety-six ? 2. What is the cost of 4£ dozen silver spoons, each weighing 3oz. ldwt. 10gr., at 4s. 2d. per ounce ? 3. Find, by Practice, the value of 36cwt. 3qr. 181b. at £47 10s. per ton. 4. A rectangular block, which is twice as long as broad, contains 5 acres: if a person walks round'it in 7| minutes, what is the rate of walking in miles per hour ? 5. Find to five decimal places the value of— 3+ L 15+ j-

6 Express of 5-2083 days as the decimal of 3 days 10 hours. 7. If 5 men or 8 women can do a piece of work in 10 days, how many days will 2 men and 4 women take to do the work ? ._ „, .... 8. Express a pressure of 1 ton per square foot m dynes per square centimetre, [ltt. = 30-48 cm.; lib. = 453-6 grammes; weight of lgrm. = 981 dynes.] 9. Extract the cube root of -3 to three decimal places. 10. Define " interest " and " discount." Show that the interest on the discount is the same as the discount on the interest. 11 What sum will amount to £926 2s. in 3 years at 5 per cent., compound interest? 12! A merchant buys 30 hectolitres of Bordeaux wine at 1 franc 40 centimes the litre, and 50 hectolitres at lfr. 92c. the litre, and mixes them; the freight is 14| francs per hectolitre, and the import duty ss. per gallon. Find the price per gallon, in English money, at which he must sell the mixed wine to make a profit of 40 per cent, on his outlay. [1 hectolitre = 100 litres ; 1 litre = 0-22ga1.; £1 = 25-5 francs.]

Algebra. — For Senior Civil Service. Time allowed: 3 hours. x /l -\- x 1. Find the value of - — V j—^ — when x= \, y\= \. 11 2. Multiply x m + 2/ n - 2s p by x m -y n + 2z*; and divide a - 81& by a* - 36*. 3. Find the highest common measure and the lowest common multiple of 3a; 4 + 14a: 3 + 9x + 2 and 2a: 4 + 9a; 3 + 14a; + 3. 4. Simplify — (a.) a + b 2a a? - a?b ' - a + 'b +6 s - a?b' (b.) ( 1_ Vx 1 ( 1 _ 1 tl + -/x +1 - Vx> ' U- Vx 1 + V%>