2. A span of 16 oxen can draw a load of 4 tons for a distance of 7 miles per day; a man carrying 112 lbs. can travel 21 miles per day; how much more will be carried by 120 men a distance of 147 miles (the men going and returning at a uniform rate) than by two spans of oxen? 3. A railway reduces its fares for first class passengers from 3d. to 2d. per mile, and for second class passengers from 2d. to 14d. per mile; before the change of fares 10,000 persons travel second class daily between two towns and 1600 first class: after the change of fares, ten per cent. of the second class passengers begin to travel first class, but the total number of second class passengers is increased by 50 per cent. Find the total gain per train mile. SECTION III. 1. Prove the rule for division of vulgar fractions. Find the value of 23 + 31 + 712 × 2,3, ÷ (43 of 8.) 38-2 212 2. Find by successive divisions the G. C. M. of 652674 and 1475600. How would you prove to your class without actual division that your G. C. M. will divide any of the divisors you have used? 3. Find the value of 7 of 5 guineas + 4 of £3 -27 of 58., and bring the result to the fraction of 18. 3d. SECTION IV. 90 126. 1. Convert to decimal fractions 5H, 77, 87,1 The length of a metre is 1·09363 yards; convert 150 English miles into kilometres. 2. Prove the rule for multiplication of decimals. Find the value of 1590 of 11 cwt. O qrs. 5 lb. 8 oz. 3. Two sums of money are in the ratio of 52:16, and their difference is £12. 16s. 2d.; find the sums. SECTION V. 1. If 49 men working for 64 days of 7 hours can excavate a pit with vertical sides whose edges form a square (each edge being 14 yds. long), how many hours a day must 128 men work for 29 days to excavate a pit of the same depth, but longer and broader by two yards each way? 2. A company possessing £500,000 capital carries forward at the beginning of the year £1,082 10s.; at the end of the year a dividend of 5 per cent. is paid, and £1178. 188. 8d. is carried forward; find the gross receipts, the cost of working being to the net receipts in the ratio of 53: 47. 3. If a quantity of silver bought at 4s. 8d. per oz. has lost in value £19. 6s. 8d. when silver is sold at £2. 118. 9d. per lb., find the weight of the silver. SECTION VI. 1. What is the relation between discount, present worth and amount? In how many years will £675. 10s. amount to £945. 148. at 4 per cent. simple interest? 2. A bankrupt's debts amount to £3750., he pays 13s. in the pound, and defrauds his creditors by concealing of his assets; find the value of his estate. 3. A man invests £4000. in four sums of £800, £900, £1100, £1200 to produce 24, 3, 34, and 3 per cent. simple interest respectively per annum; find the gain in income if the whole had been invested to produce 37 per annum. SECTION VII. 1. Find the square root of 38259-36, and the cube root of 7077-888. 2. A metal is mixed with each of two others in the ratio of 7:8 and 5: 6 respectively, and its value is to those of the others as 3:1 and 4: 1 respectively; find the value of a quantity of the second mixture equal in weight to a quantity of the first that costs £3190. 3. A charity sells out 10,000 consols at 974, and invests the proceeds in railway debentures at 160; what interest must the debentures pay that the income of the charity may be increased by £89 per annum, no charge being made for brokerage? SECTION VIII. 1. Two rooms whose breadths are 17 and 15 feet, lengths 19 and 16 feet, and heights 10 and 9 feet respectively, are covered with papers of different values, each two feet wide; if the difference in the two costs. be £1. 78. according as the larger room is papered with the dearer or cheaper paper, find the difference in prices per yard of the paper. 2. Copper is 8.96 times as heavy as water; what will a cube of copper whose edge is 9 inches weigh when suspended in water if it lose a weight equal to that of the water displaced, a cubic foot of water weighing 1000 ounces? 3. Three clocks occupy respectively 33, 22, 11 seconds in striking twelve, and lose 36, 24, 12 seconds daily respectively; if they begin to strike together at 4 p.m. on March 31, on what day will they all strike twelve separately for the first time? which two will first strike twelve separately? GRAMMAR AND COMPOSITION. COMPOSITION. Every Candidate must perform the exercise in Compo sition. Candidates are recommended not to take more than half an hour for this exercise. Subjects for Composition. 1. The death of Samson told by an eye-witness. Or 2. The writings of Milton. Or 3. Contrasts of town and country life. Or 4. The cultivation of music. Or 5. Gardening. GRAMMAR. Every Candidate must do the parsing and analysis. SECTION I. Parse the words italicised in the following passages:1. Scarce half I seem to live, dead more than half. Of what now I suffer 2. She was not the prime cause, but I myself. 3. Or peace or not, alike to me he comes. 4. Happen what may, of me expect to hear Nothing dishonourable. 5. Best keep together here, lest running thither We unawares run into danger's mouth. 6. Hitherto, Lords, what your commands imposed I have performed, as reason was, obeying, Not without wonder or delight beheld. 1. SECTION II. Analyse the following passages ;- She pleased Me, not my parents, that I sought to wed 2. But what more oft in nations grown corrupt, Whom God hath of His special favour raised? 3. Down, reason, then! at least vain reasoning down, Though reason here aver 4. 5. 6. That moral verdict quits her of unclean. Whom God has chosen once To worthiest deeds, if he through frailty err, Be it for honour's sake of former deeds. God more accepts Him who, imploring mercy, sues for life, What was set before him, Which without help of eye might be assayed, SECTION III. (Not more than four of these questions to be answered.) 1. Give other words derived from the same roots as the following:- respire - prediction object confine-perverse-succeed; and give the force of the prefixes or suffixes in the examples you select. |