10. If sixteen be added to a certain number, tha sum is three times sixteen; what is that number? Ans. 32. 11. Divide sixty so that the seventh of one part may equal the eighth of the remainder. Ans. 28 & 32. 12. A post was a certain distance in the water, twice as much was painted, and three times as much as this above was unpainted, the wbole was nine feet long; what was the length of each part separately ? Ans. 1 ft., 2 ft., 6 ft. 13. A father is four times as old as his son, foar years ago the father's age was six times that of his son; what are the respective ages of father and son ? Ans. 40 and 10. 14. Fifty added to five times a number is the same as fifty-six added to four times the number? What is the number? Ans. 6. 15. If I take away eleven from a certain number multiplied by sixteen, the remainder is the same as the sum of seventy and seven times the number; what is the number? Ans. 9. 16. Twenty-eight times the sum of a number and nine, is the same as twenty-seven times the difference of forty-six and the number; what is the number? Ans. 18. 17. A subscribes a certain sum to a charity, B subscribes half as much, and C one third; the total subscription paid by A, B, and C, is £11; what does each subscribe to the charity ? Ans. £6, £3, & £2. 18. One fifth of a post is in the water, one third is painted and outside, and there are seven feet above this unpainted; what is the length of the post? Ans. 15 ft. 19. If I take the half of a number after adding to it three; and the fourth of the number after adding to it five; and the third of the number after four has been added to it, I find the sum of these three quantities is 16; what is the number? Ans. 11. Ans. 20. If in a lottery of 1000 tickets, half the number of prizes, added to one quarter of the blanks, was 262, how many prizes were there in the lottery ? Ans. 48. 21. The ages of a man and his wife together amount to 75 years; and they are in the proportion of 7 to 8; what is each one's age? Ans. 40 and 35. 22. The ages of a man, woman, and child together amount to fifty-five years. The woman is four times as old as the boy, and the man six times as old; what is each one's age ? Ans. 5, 20, and 30. 23. The sum of two numbers is 27 and the difference 3; what are the numbers ? Ans. 12 & 15. 24. The difference of two numbers is six, and the quotient is lz; what are the two numbers ? Ans. 12 and 18. 25. The sum of two numbers is thirty-four, and eir product 280; what are the numbers ? 14 and 20. 26. A floor was relaid for £108, at the value of 5s. per square foot, the length of the room was 120 feet; what was the breadth ? Ans. 3.6 feet. 27. The walls of a room are papered at a cost of £720, being at the rate of ls. per square foot, the height of the room was 24 feet, and the breadth 64 feet; what was the length of the room ? Ans. 236 feet. 28. The content of a room was 1846 cubic feet, the length 16 feet, and the depth 13; what was the breadth of the room ? Ans. 8-9 29. A rectangular field measured 61874 square yards; its length was 6187 yards; what was its breadth ? Ans. 107145 T. 30. If the surface of a rectangular board be 9768 square inches, and the breadth be 84 inches ; what is the length ? Ans. 116. 31. Two men earn together £600; ono earns twice as much as the other; what is each man's earnings ? Ans. £200 and £400. 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 auswer 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 re 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 gave to his father. There was then a shilling over, 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 ? Avs. 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 Is. 6d. The consequence was, that the former had now three times as much as the latter. What did they begin the week with ? Aus. 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, sball 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 ? |