MATHEMATICAL EXAMINATION QUESTIONS. I. ARITHMETIC. 1. SUPPOSING that a person can count two hundred in a minute, and that after counting incessantly for 30 years he dies, and his son goes on counting for 30 years and then dies, and so on; how many generations must elapse before one billion be counted? 2. A party of five persons agree to travel abroad, and they find that, after they have been absent from England a fortnight, they have expended 1000 francs; two of them are then obliged to return home; how long can the other three continue their tour with their remaining fund of 1500 francs?. 3. An estate is to be divided between A, B and C, in the ratios of 1: 2: 3, subject to the proviso that each of them pay to D one-eleventh of the whole; what would D receive, supposing A's share to be £550. 4. If a watch be two minutes and a half too fast by the clock of the R. M. Academy when the bell rings at 4 P.M. on Wednesday, what will be the time by that watch when the bell rings at noon on Monday? the daily rate of the watch being - 20 sec., and that of the clock + 18 sec. 5. If 6580 shot of 24 lbs. cost £725, how many 42 lb. shot can be purchased for £2100 when iron is five per cent. dearer ? 6. If 30 miles of iron rails cost £15580 when iron was at £10. 58. 6d. per ton, what would be the expense of 1573 miles of the same rails when iron is at £12. 4s. 2d. per ton? 7. If a battery of 6 guns, firing three rounds in ten minutes, will breach a certain work in 60 hours, how many guns must be employed for the same purpose, firing two rounds in five minutes, in order that the breach may be made practicable in 15 hours? 8. A can run at the rate of eight miles an hour and B at the rate of seven and a half miles an hour; what is the greatest number of yards start that A may give B so as to beat him in a race of 440 yards? 9. If two 32-pounders can render a breach practicable in fifty hours, in how many hours can three 24-pounders, two 18-pounders, and one 12-pounder render practicable a breach requiring double the quantity of battering, supposing the effects of the different kinds of shot to be as 6, 5, 2 and 1? 10. A garrison of 1000, men was victualled for 30 days, but after 10 days it was reinforced, and the provisions were, in consequence, exhausted in 5 days: what was the number of men in the reinforcement? 11. A wall 1236 yards in length was to have been built by 60 men in 21 days, but at the end of 15 days it was found that only 824 yards had been completed; how many extra men must be employed in order that the work may be completed in the given time? 12. The proportions of sulphur, charcoal and nitre, in the composition of gunpowder being as 2, 3 and 15 respectively; what is the value of 5460 lbs. of powder, independent of the expense of manufacture, when sulphur is £1. 4s. 6d. per cwt., charcoal £1. 158. 2d. per cwt., and nitre £1. 16s. 8d. per cwt.? 13. What is the value of five pounds Troy of an alloy of silver and gold, in which the weight of the gold is the weight of the silver, gold being £4. 5s. and silver 6s. per oz.? 14. Gunpowder being composed of 75 per cent. of nitre, 12.5 of charcoal, and 12.5 of sulphur, how much of each of these substances is there in 5 tons of powder ? 15. If two ounces of gun-cotton produce the same effect as five ounces of gunpowder, and the spaces occupied by the same weight of each be as 10 to 3 (the cotton being the more bulky); what must be the length of a musketry cartridge, filled with cotton, which is to be used instead of a gunpowder cartridge two inches long? 16. If 25 labourers can dig a trench 220 yards long, 3 feet 4 inches wide, and 2 feet 6 inches deep, in 32 days of 9 hours each; how many would it require to dig a trench half-a-mile long, 2 feet 4 inches deep, and 3 feet 6 inches wide, in 36 days of 8 hours each? 17. Supposing the rates of marching of two columns of infantry to be as 4 to 3, and the one to be three miles in advance of the other and marching at the rate of 24 miles per hour; in what time will the column in the rear overtake the other? 18. If five bricklayers can lay 45 bricks in five minutes, and the bricks made use of be 10 inches long, 4 inches broad, and 3 inches thick; how long (with such bricks) will it take 8 bricklayers to build a wall which would contain 95000 bricks 8 inches long, 5 inches broad, and 3 inches thick; the day being 12 hours long? 19. Six thousand of a certain kind of shot weigh 64 tons 5 cwt. 2 qrs. 24 lbs., how many 9 lb. shot will weigh as much as 3810 such shot? 20. What is the time when the hour and minute hands of a watch are exactly together between 9 and 10 o'clock? 21. Find the time, between three and four o'clock, when the hour and minute hands of a watch are (1) coincident, (2) in exactly opposite directions, and (3) at right angles to each other. |