ARITHMETIC. Male Candidates. The solution must be given at such length as to be intelligible to the Examiner, otherwise the answer will be considered of no value. [This direction was repeated in the Arithmetic paper for Female Candidates (p. 20), and in the paper on Algebra (p. 24)]. SECTION I. Express in figures, thirty billion, ninety-five million, seventy thousand and five. Express the year 1988 A.D. in Roman numerals. How many times can 75 be subtracted from 6075 so as to leave a remainder equal to itself? Divide the continued product of 17, 18, 19, 23, 301, 113 by the difference of 259,867 and 126,145. [These form one question.] SECTION II. 1. In a bag are 90 shillings, 100 sixpences, and 120 fourpenny pieces; find the least number of threepenny pieces that must be added, so that the whole may be distributed in sums of eighteenpence, no such sum being made up of any one coin exclusively. 2. An orphan asylum contains 120 children, each of whom consumes 40 oz. of meat per week; find the weekly saving effected by using American beef at 6d. per lb., allowing also 28. 4d. per cwt. for carriage, in place of English beef at 68. 4d. per stone of 8 lbs. 3. The length of the solar year being 365 days 5 hrs. 48 min. 50 sec. and the Chinese civil year consisting of 12 months of 29 and 30 days alternately, how many months of 30 days must be added in the course of 60 years that the Chinese civil year and the solar year may agree most nearly? SECTION III. 1. Make out the duty payable on the following goods: 7000 lbs. of coffee at 148. per cwt. 6252 packs of cards at 3s. 9d. per doz. packs. 670 lbs. of gold plate at 17s. per oz. 90 bushels of malt at £1. 4s. Od. per qr. SECTION IV. Find, by Practice, the value of 1. 15 cub. yds. 21 cub. ft. 648 cub. in. at £4. 48. Cd. per cub. yd. Or 2. 75 miles 5 fur. 9 chains 2 yds. at £56. per mile. SECTION V. 1. A tradesman sold some goods at 15 per cent. above the price at which he bought them, the two prices together amounted to £733. 38. Od., find the price at which the goods were bought. 2. A block of granite 16 ft. long, 8 ft. broad, 4 ft. deep, stands on one of its broadest faces; the other faces are polished at a cost of £16.; find the cost of polishing similarly another block 24 ft. long, 10 ft. broad, 5 ft. deep, similarly placed. 3. The earth's orbit is 446 millions of miles and is traversed in 365 days; the distance of the earth from the sun may be reckoned as 71 millions of miles, and light travels at the rate of 186,000 miles per second; how far will the earth travel on its orbit, while a ray of light is passing from the sun to the earth? 31 = 1 of 613. 2. Reduce 2 cwt. to the fraction of 4 tons, 2 cwt. 14 lbs.; and 19 guineas to the fraction of £14. 98. 3d. Shew that d. and every multiple of it will give a terminating decimal of one pound. 3. If of an estate be worth 200 guineas, and the value of the estate be increased 075 per cent. by improvements, find the value of 23 of the improved estate. SECTION VII. 3 32. 1. Express as decimals, 71, 1, 1. Show that } + 10 + 760 + &c. ad infinitum. 63 2. Find the value of (3+) of four guineas + (09-01) of £2. 18. 3. + (5·05·005) of 58. 3. The rainfall of London in the months of April, May, June, 1876, was 1.90, 0·94, 1.27 inches respectively, being in April, 0.77 above and in May and June 1.46 and 1.78 inches respectively below the averages of those months for the previous six years; find the average for these three months both for the year 1876 and for the whole seven years to two places of decimals. SECTION VIII. 1. Which of the following stocks is most profitable for investment, the 3 per cents. at 911, the 33 per cents. at 10S, the 4 per cents. at 118? Find the yearly income produced by investing £5217. 16s. 3d. in the most advantageous of the three. 2. A tradesman induces customers, who owe £750. and otherwise would not have paid him for 6 months by offer of 5 per cent. discount to pay ready money; at the end of the 6 months instead of £750. he had received £947. 12s. 6d. What is his profit per cent? 3. A commission agent agrees to take 5 per cent. on all sales or of net profit; 35 of his transactions realise 10 per cent. profit, the remainder 19 per cent. What would be the difference on sales of £600,000 according ast all his customers adopt one or other agreement? SECTION IX. 1. Find the square root of 32.7142073 to four places of decimals, and the cube root of 941192. Show that the cube root of every perfect cube less than a million can be determined by inspection. 2. If exchange be at the rate of 25.50 francs for one pound and of 57.75 florins for 119 francs, find the value of £4760. in florins. SECTION X. 1. Find the cost of turfing a ground 10 chains long and 5 chains broad, each turf being 15 in. long and 6 in. broad and 100 turfs costing 1s. 3d. 2. £8. 118. Od. is spent upon the floor of a room 24 ft. long and 18 ft, wide, the centre of the room is covered with carpet 2 ft. wide at 4s. 3d. per yd., leaving a margin of 3 ft. all round the carpet; how much per square foot does the margin cost to paint? ARITHMETIC. Female Candidates. SECTION I. Add together nine millions nine hundred and nine thousands and ninety-nine; seven hundred and forty thousands and forty-seven ; six millions twenty thousands and two hundreds; eight thousands and eighty-eight; thirteen millions one hundred and thirty thousands and four hundreds. From the sum subtract four millions four hundred and six thousands three hundreds and sixtyseven and divide the remainder by ninety-four. SECTION II. Divide £7483192. 28. 74d. by 803, and prove your sum by multiplication. SECTION III. Work out the following bill of parcels :-- SECTION IV. Find, by Practice, the value of 8 trucks of coal, each weighing 9 tons 12 cwts. 21 lbs., at 14s. 7d. per ton. SECTION V. 1. What would be the half-yearly dividend from an investment of £3300 in the 31 per cents., made when the stock was standing at 91? 2. What sum of money must be invested in the 5 per cent. stock at 83, to enable the possessor to realize an income of £64. 3s. 4d, per calendar month? SECTION VI. 1. What would be the expense of painting (at 38. 2d. a yard) the walls of a room 27 feet long, 17 feet broad, and 11 feet high, the dimensions of 4 windows being 7 feet by 4 feet each? 2. What length of carpet, of a yard wide, would be required to cover the above room; and what would be the cost at 5s. 3d. per yard? SECTION VII. 1. Divide £10. 10s. between A and B, so that of A's portion shall equal of B's. 2. If 3 of a yard of French merino cost £1. 14s. 44d., what would of of a yard cost? SECTION VIII. 1. Prove the rule for the multiplication and division of decimals. 2. Find the value of 7·92÷÷3.84 and 1003.53÷1250 and of 8 x 016 × 0032. SECTION IX. 1. What is the per-centage gained by the newspaper boys who buy the daily papers at 9d. per dozen, and sell them at 1d. each? Explain your answer. 2. Describe ratio, and illustrate your definition by an example. 3. If 25 men could set up a mile of telegraph wire in 24 days of 8 hours' work, what length of wire would 20 set up, working 10 hours a day for 20 days? |