E.—la

14

10. By selling tobacco at Is. 3d. per pound a tobacconist gains 35 per cent.: what does his profit amount to on the sale of 4cwt. 111b. ? 11..A man invests £420 in the 3-per-cents at 90, sells out at 81, and reinvests in the 5-per-cents at^loB. What is his last income'? 12. Find the compound interest on £540 for 3 years at 2J per cent. 13". Four merchants, A, B, G, and D, join their capitals in the proportion of §, -J-, J, and -|. At the end of twelve months they lose £120. What are their respective shares of the loss? 14. If 3 men and 11 boys working together can do 5 times as much work per hour as a man and a boy together, compare the work of a boy with that of a man.

Arithmetic. — For Senior Civil Service. Time allowed: 3 hours. 1. Define prime number, quotient, factor, decimal, ratio, power, cube root, discount. 2. A spirit lamp with a salted wick emits five hundred and ten billions of light-waves per second, the length of each wave being the forty-two thousand five hundredth part of an inch. Hence find the velocity of light in miles per second. 3. How many sacks, each containing lcwt. lqr. 61b., are required to make up 40 tons 3cwt. of coal? 4. Find the value of 76 T 9c- bales of wool at £17 16s. Bd. per bale. 5. A sheet of ice is three-fourths of an acre in extent and one inch in thickness: find its weight, taking the weight of a cubic foot of ice to be 918oz. 6. Divide the product of 1} of (2s-li) and (7f-6J) -±- (4f-3f) by their sum. 7. A gentleman's pace is 2ft. 6in., a lady's pace 2^\ft. How often will they step together in walking 1,000 yards? 8. Seduce -09 of 1-83 of £1 6s. to the fraction of -7027 of -336 of £4 Bs. 9. A and B occupied a grass paddock, at a rent of 32 guineas for six months. For four months of the time B's stock was T S T of A's; and for the remaining two months A's stock was T S T of B's. Having given that the number of A's stock remained unaltered during the whole period, find the portion of the rent that each should pay. 10. In a mile race "Sultan" can beat "Khedive" by 80 yards, and "Khedive" can beat " Mahdi" by 88 yards. By how much can " Sultan " beat " Mahdi" in a race of the same length ? 11. Find the amount, at compound interest, of £1,829 ss. for three years, at 3-J per cent. 12. A fruiterer, having bought a case of oranges at 4-J-d. per dozen, found, on opening the case, one-fifth of the whole to be unsaleable. He divided the rest into two equal portions, which he sold at the rates of eight for a shilling and twelve for a shilling respectively. Find his gain per cent. 13. A person finds that he will have an income of £99 16s. Bd. a year more by investing his capital in New Zealand 3-J-per-cents at 97J than in the Seduced 2f-per-eent. Consols at 98. How much capital has he to invest ? 14. An English merchant bought, at Bordeaux, 84 hectolitres of wine at 150fr. per hectolitre. He paid, for freight and charges, 22J per cent, on the cost price, and 2s. per gallon duty. At what price per dozen bottles must he sell the wine in order to make a profit of 32 per cent. ? [1 hectolitre =22 gallons; 1 gallon = 6 bottles; course of exchange, 25'16fr. for £I.]

Algebra. — Alternative with Arithmetic for Senior Civil Service. Time allowed : 3 hours. 1. If a-§=a+b = a-2c =0, find the value of (7> 2-c 2). [b i+c i-b{a-c)}. - 2. Divide \x 3-\-\x\j-%y% by ix+y. 3. If s = i(a+b+c), show that 3«(s-5) (.s-c) = [(s-6) + (s-c)] s- [(s-Z>) 3+(s-c) 3]. 4. Eesolve x s+x 2, x 5 —x, and x s+x s-}-x into simple factors, and write down their lowest common multiple. 5. Simplify— (b.) { sH»»I ..(., .jtol. («•) 1 x+ l + I——1 —— 3*+l+Bs 6. Find the square root of 46 + 12\/i4; also of I—xi to four places. 7. Solve the following equations:— (a.) a b _a ~b. x-a x~b~ x ( b-) 5 X 2L = iq'; x-(x -7) y = 13. (c.) A-iP B+je_2(6-iB) i i+x~*~3-x~ I+x 8. Divide M pounds among three persons, giving the first a pounds more than the second, and the second b pounds more than the third. 9. A passenger train and a goods train start from a station at the same hour for another station 180 miles distant, and the passenger train, by travelling 8 miles an hour faster than the other, reaches its destination 3f hours before it. Find the speed of each train.