E.— la.

4. If 5-6531 cwt. of lead cost £2-87, what must be given for 3-954 lb. ? (Answer to three places of decimals of a penny.) 5. If 144 lb. of one tea is mixed with 541b. of another tea valued at 2s. Ofd. a pound more, and if the mixture is worth Is. llfd. a pound, how much a pound is each tea worth? 6. If, when the bank rate is five per cent, per annum, the difference between the true discount and the banker's discount on a bill due six months hence is £1 55., what is the amount of the bill ? 7. The outside diameter of a circular bicycle track 5 yards wide is 190 yards : what will it cost to asphalt the track at 2s. 6d. a square metre ? (Answer to the nearest penny.) 8. A and B working together can get through a task in 4f days, A and C can do the same work in 3f days, and B and C in 6 days : in what time ought each man to get through it working by himself? 9. A goods train is 18 miles ahead of an express train which travels at the rate of 75 miles an hour and overtakes it in 25 minutes : find the speed of the goods train. 10. A corn merchant bought 2100 quarters of wheat, which he sold so as to gain 30 per cent, on 925 quarters and 12-| per cent, on the remainder. He had previously tried to sell the whole at a uniform advance of 25 per cent., which would have brought him in £176 Is. more than he actually received. How much a quarter did the wheat cost him ? 11. If the total surface of a cube of coal amounts to 937-5 square decimetres, find its value, in decimal money, at £1 6 florins 2 cents a cubic metre.

Arithmetic and Algebra. — For Civil Service Senior. Time allowed : Three hours. 1. Find the number of pounds in a kilogramme (1000 grammes), given that a gramme is the mass of a cubic centimetre of water, that the mass of a cubic foot of water is 1000 ounces, and that 1 centimetre = 0-3937 inch. 2. If the mean velocity of a rifle bullet over a range of 1000 yards is 1342 feet a second, and that of sound is 1122 feet a second, what time will elapse between the moment when the bullet strikes the target and the moment when the report of the rifle reaches the target ? 3. In 1888 an investor bought £10,000 of New Zealand 4 % stock at In 1898 he sold out at 116-| and invested the proceeds in at 103. Find the alteration in his income. 4. A merchant took from a customer a bill for £56 10s., dated 3rd March, due in 100 days (without grace), at 6%, and his banker discounted the bill on Ist June. How much did the merchant get from the banker ? 5. A man wrote to London for a suit of clothes. The postage for his letter and for the parcel cost him 3s. Id., and he paid a duty of 25% ad valorem. How much did the tailor get if his customer paid £7 10s. in all ? 6. Find the quotient and the remainder when x 6 + \xf + fx* + 1 is divided by a; 2 + _■ + 2; and find m so that 2a; 4 — 3* 3 + mx 1 — 9x + 1 may be exactly divisible by x — 3 7. Simplify:— ... a+ x x 3 -y 2 _j_ im- n_ x+ y 1 *"' (m +nf x 12~~ ' \(m +nf 6(m 2 -» 2 )j ... . a? fe 2 & (11 (c -a)(a-b)+(a-b)(b-c) + (b - c) (c - a) 8. Solve— (i.) x 1 — x + vAc 2 — Ix + 8 = 5x — 6 (explain the introduction of extraneous roots) (ii.) 3a; 4 - 20a; 3 - 94a; 2 - 20a; + 3 = 0 ..... (x*+xy = 2i/ 2 . { ' (a; 2 + 2xy + 3y* + 4a; +by= 15 and find what condition must be fulfilled in order that the equations px + q =rx -+- p and qx + p = px + f may be satisfied by the same value of x. 9. Find the relations between the roots and the coefficients of a quadratic equation, and the condition that must be fulfilled in order that the equation may have equal roots. If x 1 and a; 2 are the roots of x 2— x—l = 0, form the equation whose roots are (x* + ay*) and W + x~i) Show that the pair of equations j/ 2 = 4ax and y = mx + — has equal roots whatever be the value of to, 10. A man's net income, after paying income-tax of 6d. on every pound over £300, is £700 : what would be his net income if the tax were raised to 6-J-d. ? 11. A swimming-bath is 44 feet longer than it is broad. There is a distance of 9 feet from the edge to the dressing-rooms, which are all round the bath, and are themselves 9 feet deep. The whole floor space, together with the space occupied by the bath, has an area of 928 square yards. What are the dimensions of the bath ?

Algebra. — For Class D. Time allowed : Three hours. , 1. Find the value of— (JL _ JL\ (JL _ jL\ + /-£-_ _£_\ (JL_ JL\ + (JL_ JL\ (-JL_ l\ \sy p / \zs p ) "*" \zs p / \xs p } \ ass p}\ ys p ) where s = x + y + z, p 2 = xyz, and x = — 1, y = 2, z — — 4. 2. Multiply the sum of to 2 — Stow + 2» 2 , 3ra 2 — to' 2 , and bmn — 3re 2 + 2w 2 by m— n.

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