32. Two men put money into the savings' bank; one man puts in £150 more than the other, and their joint savings are £970; what does each invest? Ans. £410 and £560. 33. Three men together walk a distance of 600 miles; one walks twice and the other three times as far as the first; what is the distance travelled by each? Ans. 100, 200, and 300 miles. 34. What is that number which, with 17 added to it, will make 55? Ans. 38. 35. What number is that whose half exceeds its third part by 17? Ans. 102. A. Determine a number which, when 365 is taken from it, shall leave 214. B. What is the number whose third part and fourth part added together make 91 ? 36. What number is that which is as much short of 100 as its double exceeds 100? Ans. 663. C. A farmer had three times as many cows as horses, and ten times as many sheep as cows. The whole number of his live stock (horses, cows, and sheep) was 306. How many horses had he? 37. A boy being asked how many marbles he had, said he would answer no such question, but that it was a matter of indifference to him whether he gained 15 more, or doubled what he had and then lost 10. Can you compute from that hint how many he actually had? Ans. 25. D. Two tradesmen began business with equal sums of money. The first gained £142, and the second lost £150. The first was then twice as rich as the second. What sum had each at the commencement? 38. Divide 1000 into two such parts, that 9 times the larger shall exceed 13 times the smaller by 970. Ans. 635 and 365. 39. The sum of two numbers is 154, and their difference 42. What are they? Ans. 98 and 56. E. Divide 100 into two such parts that 25 times the less may exceed 24 times the greater by 1. F. Divide 100 into two such parts, that half the one added to one-seventh of the other shall just make 20. 40. An election, at which there were only two candidates, was gained by Mr. Smith, who had a majority of 75 votes over Mr. Jones: the number of voters in the interest of Jones was just two-thirds of the number who supported Smith. What was the whole number of voters? Ans. 375. G. A charitable gentleman distributed the contents of his purse, which contained 23 shillings, among a poor family, consisting of a man, his wife, and two children. He gave the man twice as much as his wife, and to the oldest child one-third of what he to his father. There was then a shilling over, gave which he gave to the youngest child: How much did each receive? 41. In the House of Commons there are 654 members, Scotland sending half as many as Ireland and half a member more, and England contributing 29 short of 5 times the number of Irish members. What are the respective numbers? Ans. 496, 105, and 53. H. Four persons engaged in a speculation requiring an outlay of £2400. Of that sum, A contributed twice as much as B, and £10 more; C contributed £20 less than A; and D only two-thirds of C. What sums did they separately contribute? 42. Two boys, who made their living by selling nuts, commenced the week with the same sum; but, when they met on the Saturday night, the one found that, after paying for his maintenance, he had gained a half-crown; and the other that he had lost 1s. 6d. The consequence was, that the former had now three times as much as the latter. What did they begin the week with? Ans. 3s. 6d. each. I. Two fields were purchased at £43 and £28 per acre respectively. Their united area was 12 acres, and their united price £411. What were the sizes of the fields separately? 43. A gentleman, after travelling 12 hours without stopping, found that, if he had travelled 3 miles an hour faster, he would have accomplished the journey in two hours less of time. At what rate did he travel? Ans. 15 miles per hour. J. Two friends, living at Walton and Middleton, 24 miles apart, agreed to meet on an angling excursion between the two places. The one from Walton set out an hour after the other, but, having no encumbrance, got on at the rate of 4 miles an hour, while his friend, having undertaken to bring fishing-tackle and provisions for both, could only proceed at threefourths of that speed. At what point on the road did they meet? K. A man departs on a journey, walking at the uniform rate of 3 miles an hour; and, two hours later, another sets out after him, riding, at 7 miles an hour. At what distance on the road will the latter overtake the former ? 44. If you divide a certain number by 9, and add together divisor, dividend, and quotient, their sum shall be 59. The number is required. Ans. 45. L. Divide the number 100 into four such parts that the first may be equal to half the second, but greater than the third by 6, and less than the fourth by 1. 45. Find three numbers, such that their sums, taken two by two, shall be 11, 12, and 13. Ans. 5, 6, and 7. M. A man and his wife were married at the respective ages of 40 and 20 years. How old will the man be when his wife's age becomes three-fourths of his own? 46. A certain reading-room is maintained at the joint expense of the subscribers. At the end of the first year they find they have each £1 4s. to pay; but one of them remarked correctly that, if there had been seven more of them, the expenditure would not have been increased, and they would have got off at the rate of a sovereign a piece. Compute the number of members. Ans. 35. N. Half the difference of two numbers added to half the sum is 93 5, and half the difference taken from half the sum is 77.4. What are the two numbers? 47. What are the two numbers, whose sum is 133, and quotient 18? Ans. 126 and 7. O. Find two numbers whose difference shall be 1, and the difference of their squares 19. P. Divide 100 into two such parts that the difference of their squares may be 200. Q. What fraction is that which will be = if 3 be added to its numerator, and if 2 be subtracted from its denominator? 48. A lady, on her birthday, presented all the wives and children of her cottagers with donations of money. She gave the women a sovereign each, and the children a half-crown. Having done so, she found that she had bestowed 200 donations, and expended £58 5s. What were the respective numbers of women and children? Ans. 38 and 162. R. Two servants lived together 40 years in the service of the same master, and at the same wages, viz., £12 per annum. The one spent 10 shillings less every year than the other, and found at the end of the 40 years, that she had saved twice as much as her fellow-servant, and half-a-year's wages besides. What did they severally save in the year ? 49. A broker bought two cabinets at a sale, suspecting that a £10 note was hid in one of the two. If in the one, he thought, it should be worth twice the other; but if in the other, it ought to be three times the value of the first. What values did he put upon the cabinets without the note? Ans. £6 and £8. S. Two foolish young gentlemen began to play against each other with equal sums of money. After playing 12 hours, and incurring 15 shillings each of expenses, the one remained with twice as much money as the other, having gained from him £15. What had each when they began? 50. A lady's ring cost 7 guineas; her brooch cost as much as her ring and half her bracelets, and the bracelets cost as much as the ring and brooch together. What was the cost of the whole? Ans. 56 guineas. T. On examining a meteorological table for a particular locality, it was found that the whole fall of rain for the year was 22.8 inches, that the quantity which fell in the first and last quarters together was just equal to that which fell in the second and third, that the fall in the first quarter was two-thirds of that in the fourth, and that the third exceeded the second by 2 inches. What were the depths of fall in the respective quarters ? 51. A tea-dealer considers that 2 lb. of his best green tea is worth three of his best black. He mixes them together in equal proportions, and sells the mixture at 6s. 3d. per pound. At what rate would he sell the black and green separately? Ans. at 5s. and 7s. 6d. U. A lady, going to purchase a carpet, found that if she took the best quality in the shop, at 8 shillings the yard, it would take £1 more than the money she brought with her. She therefore contented herself with the second, at 7s. 6d., and found that she had then £2 left. What did the carpet cost? 52. There are three numbers such, that the first, with half the sum of the other two, makes 46; the second, with one-third of the other two, makes 30; |