25

E.—la

10. A man invests £3,500, part in 3-per-cent. stock at 97, and the remainder in 4-per-cent. stock at 101: find how much he must invest in each in order that he may have equal returns from the two sources.

Arithmetic. — For Civil Service Senior. (Old Regulations,). Time allowed : 3 Jiours. [Note. —The full working of the quastions, and not merely the results, must in all cases be given.] 1. A man sells a bale of goods at 7 per cent, profit, and another like it at 3 guineas profit, making a mean profit of 11 per cent. : what was the prime cost of one bale ? 2. A business is started by three men with equal capitals : one of them, being manager, is to receive 16 per cent, on the total profits before the division is made : if his share altogether comes to £451, what were the total profits ? 3. Simplify- 5f mi + 9 -| 4. State and prove the rule for reducing a mixed repeating decimal to a vulgar fraction, and reduce to a vulgar fraction in its lowest terms 3-8643018. 5. A piece of land, 220 yards long by 176 yards wide, is rented for £26 19s. : how much is that an acre ? 6. If when A makes a profit of £2, B makes £3 ; and when B makes £4, C makes £5 ; and when G makes £6, D makes £7 : compare the profits of A, B, C, and D. 7. Find, by practice, the area of an estate which can be divided into 347-g- fields, each containing 6a. 3r. 15p. 8. The sea occupies i-£ of the surface of the globe; the surface of Asia is that of Europe ; of Africa, - 2 T 2 - that of Europe ; of America, W- that of Europe ; of Oceania, §4 that of Europe ; and the surface of Africa is 12,006,522 square miles : find the area of the surface of the globe. 9. Explain the meaning of the term, " arbitrated rate of exchange." The rate of exchange between London and Petersburg is 31-g-d. for one rouble ; between Vienna and Petersburg, 95f florins for 60 roubles ; and between Paris and Vienna, florins for 200 francs : find the arbitrated rate between London and Paris in francs for £1. 10. Find the difference between the amount of £494 10s. for two years at 3f per cent., and the present worth of the same sum at the same rate due at the end of two years. 11. The ceiling of a room is whitewashed, at 2-Jd. the square yard; the walls are papered with paper § yard wide, at 6fd. the yard ; and the floor carpeted with carpet f yard wide, at 6s. 9d. the yard : find the total cost, if the room is 17 ft. 3 in. long, 10 ft. wide, and 16 ft. high, allowing for three windows (each 8 ft. by 4 ft.), two doors (each 6 ft. by 3 ft.), and a space (7 ft. high, 3 ft. long, and 1 ft. 4 in. deep) for a stove against the wall. 12. Silk is bought at 14s. 5Jd. the yard : at what price must it be sold to gain a clear profit of 174 per cent., after allowing a discount to the purchaser of 3f per cent.

Arithmetic and Algebra. — For Civil Service Senior (New Regulations). Time allowed : 3 hours. 1. A tram 88 yards long takes 24 seconds to pass a second train 88 yards long, travelling in the same direction, and afterwards passes a third train 44 yards long, travelling in the opposite direction, in 6 seconds: how long will the second train take to pass the third train ? 2. Find to the nearest penny the amount of £100 for 8 years, at 5 per cent, compound interest. Employ the shortest method, but show all your work. Use your result to find the present value of an annuity of £100 for 8 years, 5 per cent, being the current rate of interest. 3. A man has £3,000, which he invests in 3 per cent, stock at 96, and 6 per cent, stock at 108 : what sums must he invest in the respective stocks to make 3J- per cent, on the whole ? 4. The Bastille was stormed on the 14th July, 1789 : what day of the week was that ? 5. Simplify (a + b + cf - 2(b + c) (a + b + c) + 2(7) + cf, and find the value of (x - yf + (x -f yf + 4:(x + y) (x — y) when x = a/2 and y = 6. Define the lowest common multiple of a number of expressions. Find the L.C.M. of 8x 3 + 38a; 2 + 59a; + 30 and 6x s - 13a: 2 - I3x + 30 7. Multiply a* +b*+ c' - - ca? - a 3 b f by 0 s +&* + c 8. Extract the square root of— 121 „ 2 x i + - i + 2a; 8 -- x+ x*+-s+2x--9. Find the factors of — f-pq- 2q\ sxy - x 2 - 6y\ 16x l + 36 xhf + 81?/, and x s + 27y s - z s + 9xyz 10. When is a n —b n divisible by a+ b ? Prove that your answer is true universally. 11. Solve the equations — ... (x-lf (x - 2)° (x -9)(x - 8) (i) —i — + —§— =« - 1 (ii) 13a: 2 - 90a: -7 = 0 (hi) 5a: 2 + 11a; -12 \/(x +4) (5x -9)= 36 x > + ± X y = 35) (1V) 2an/-162/ 2 = If 4—E. la.