3 22. Reduce of a guinea + 3 of a crown +3 of 7s. 6d. - 3 of 8 4 Ans. 22. I 23. Reduce + + + Ans. 1'45. them together as fractions; secondly, by reducing them separately to decimals, and then adding them. 24. Express £32 16s. 54d. in decimal coinage. Ans. £32 8 fl. 2 cents 1875 mils. 25. Add together '0016, 1'75, '02, and subtract the sum from 2′i. Ans. *33193375. 26. Divide 76.57 by 0019, and multiply the quotient by ✯ of *0008568. Ans. 14'79816. 27. Express £67 fl. 1 cent o'416 mils in ordinary coinage. Ans. £6 14s. 2 d. 28. Simplify 172 × ‘04 + ('03 +502) × ·08. Ans. *04944. 29. Divide 738 by 0018, and multiply the quotient by of *0009747. Ans. 6.3099. 30. Simplify 12.4 +064 *066 '002 Ans. 6199. 31. If a rupee be worth 2s. 4d., express £6·944 in rupees. Ans. 59'52 rupees. 32. Reduce 8.4987 rupees to the decimal of a guinea. Ans. '9443. 33. Find the value of 375 of a guinea +54 of 8s. 3d. +027 of £2 158. Ans. 138. 10d. 34. What is the length of a tropical year which contains 365 242218 days? Ans. 365 days 5 hrs. 48 min. 47'6352 sec. 35. Express as a decimal the sum of 3 hundredths, 5 tenthousandths, and 7 hundred-thousandths of unity. 37. From 3 of £2 148. 6d. take 375 of 278. Ans. 6s. 27d. 38. Find the difference of 346 of £1, and 295 of a guinea. 39. Simplify (37 ÷ 1'17) × ('052 ÷ 1·8). Ans. 8.7d. Ans. '008. 40. Multiply 6.307692, 1-428571, and 2.3 together. Ans. 21025641. 41. If the length of a degree of latitude is 365000 feet, and a metre is one ten-millionth of 90 degrees, find its length in feet. Ans. 3 ft. 3:42 inches. 42. Supposing a French metre to contain 3'28 feet, find the lowest number of metres which contain an exact number of English feet. Ans. 25 metres equal 82 feet. 43. If a gallon contains 277 27 cubic inches, and water weighs 62.42 lbs. a cubic foot, find the weight of a pint of water. 44. Divide ‘014904 by 39. Ans. 125 lbs. nearly. 45. Convert £1 138. 4d. into the decimal of £100, and reconvert 7 times the result into pounds, &c. Ans. 016; £11 138. 4d. 46. Add together 57, 25 of 47, and '00375. Ans. 34'656527. 39 50. A man's weekly wages are £2.125, on which he pays an income tax of 5 cents in the pound; find his net yearly income (52 wks. in the year). Ans. £104 19s. 6d. EXERCISE LXI. 1. What is the area of a room whose length is 23 ft. 6 in., and breadth 17 ft. 3 inches ? Ans. 45 sq. yds. 54 sq. inches. 2. What is the size of a field whose length is 275 yds., and breadth Ans. 9 ac. I rood 10 pls. 27 yds. 164 yds.? 3. What is the size of a garden, whose length is 43'75 metres, Ans. 10 ares 13:25 centiares. and breadth 23.16 metres? 4. What is the width of a field which contains 89.6 ares, and is 160 metres in length ? Ans. 56 metres. 5. What is the size of a field whose length is 8 chains 42 links, and breadth 3 chains 73 links? Ans. 3 ac. 22.5056 poles. 6. What length must be cut off a board 63 inches wide, that the area may be a square foot ? Ans. 21 inches. 7. Find the expense of painting a wall 22 ft. 6 in. long, and 10 ft. 8 in. high, at 2s. 6d. a square yard. Ans. £3 6s. 8d. in., 8. What is the cost of carpeting a room 18 ft. 4 in. by 16 ft. 9 at 4s. 6d. a square yard? Ans. £7 13s. 6d. 9. Find the area of a room 17 yds. 2 ft. 4 in. long, and 22 feet wide. Ans. 133 sq. yds. 3 ft. 10. Find the cost of a marble slab whose length is 5 ft. 7. in. and breadth 1 ft. 10 in., at 6s. a square foot. Ans. £3 18. 5d. II. Find the cost of carpeting a room 7.3 metres long, 4'5 metres wide, at 2 florins 4 cents a square metre. Ans. £7 8 fl. 8 cents 4 mils. 12. Find the cost of carpeting a room 13 ft. 4 in. wide, 15 ft. 9 in. long, at 6s. 3d. a sq. yd. Ans. £7 5s. 1od. 13. A room is 16 ft. 8 in. long, and costs £7 148. 2d. carpeting at the rate of 6s. 9d. a sq. yd. : what is its width? Ans. 12 ft. 4 in. 14. A room is 224 ft. long, and 20 ft. wide; find the cost of carpeting it at 5s. 6d. a sq. yd. Ans. £13 18s. 5d. 15. What is the length of a room whose breadth is 15 feet, and area 28 sq. yds.? Ans. 16 feet. 16. What fraction of a sq. foot is a rectangle whose sides are 3 ft. and feet? Ans.. 17. What is the price of a rectangular piece of ground whose length is 52 ft. 8 in., and breadth 34 ft. 9 in., at 25s. a sq. foot? Ans. £2287 14s. 2d. 18. What is the cost of carpeting a room 18 ft. by 16 ft. 6 in. with carpet 22 inches wide, at 4s. 2d. a yd. ? Ans. £11 5s. 19. In measuring a piece of ground 270 yds. by 230 yds., a man makes a mistake, and estimates it at 271 yds. by 229 it at 5s. a sq. yd. What does he lose? yds., and sells Ans. £10 58. 20. If a piece of land, 2 chains 75 links by 3 chains 25 links, sells for £143, what should a piece of land 47:50 by 86 25 chains sell for? Ans. £65550. 21. A field of 7 acres is planted with potatoes in rows; the distance between each row is 15 inches; how long is the whole number of rows? Ans. 44 miles. 22. A sheet of iron 75 metres long, 24 centimetres wide, expands by heat so that each side is increased by of itself. What is the increase of surface ? Ans. 378 sq. centimetres. 23. Find the difference in area of two rooms, one of which is 12 ft. by 10 ft., and the other is 15 ft. by 11 ft. Ans. 48 ft. 18 sq. in. 24. Find the area of the walls of a room which is 15 ft. 6 in. long, 13 ft. 4 in. wide, and 10 ft. 6 in. high. Ans. 605 sq. feet. 25. The expense of carpeting a room 18 feet long was £7 48., but if the breadth had been 4 ft. less, the expense would have been £5 88. What was the breadth of the room? Ans. 16 feet. 26. There are two equal fields, one is 1344 yds. by 945 yds., and the other is 1134 yds. long. What is its width and area? Ans. 1120 yds.; 262 ac. 1 rood 26 pls. 3 yds. 27. How much paper yd. wide will be sufficient to paper a room 22 ft. 5 in. long, 12 ft. 1 in. wide, and 11 ft. 3 in. high? and what will it cost at 4 d. a yard? Ans. 115 yds.; £2 38. 14d. 28. Find the cost of painting the walls of a room whose length, breadth, and height are respectively 24, 15, 11 feet, at 4s. a sq. foot. Ans. £183 128. 4d. 29. What is the cost of papering a room 21 ft. long, 161⁄2 ft. wide, Ans. £2 13s. 4ğd. 10 ft. high, at 73d. per sq. yd.? 30. A room is 203 ft. long, 15 wide, 16 ft. high; it has 2 doors, each 8 ft. high, 3 ft. wide, and 3 windows, one 5 ft. by 7 ft., and the other two 5 ft. by 4 ft. each. How much paper yard wide will it require ? Ans. 141 yds. 31. A room is 14 ft. 3 in. high, 20 ft. wide, 24 ft. long. What will it cost to paper it with a paper 2 ft. 6 in. wide, at 11 d. a yard, allowing 8 ft. by 5 ft. 3 in. for each of 4 doors, 10 ft. by 6 ft. 8 in. for each of 2 windows, and 6 ft. 6 in. by 5 ft. for a fireplace? Ans. £6 13s. 91d. 32. What is the cost of carpeting a room 21 ft. by 16 ft. 10 in., with carpet yd. wide, at 4s. 6d. a yard? And what would be saved by leaving a border 2 ft. wide all round the room uncarpeted ? Ans. £35 7s.; £8 16s. 8d. 33. The sides of a rectangle contain 12:19 ft. and 37'5 ft.; find its area. If the length of the sides were only known to be correct within 06 of an inch, how much might the true area exceed the approximate one? Ans. 457 sq. ft. 18 in.; 35'7804 sq. inches. 34. What is the circumference of a circle whose diameter is 14 ft.? Ans. 44 feet. 35. What is the area of a circle whose diameter is 21 feet? Ans. 346 sq. ft. 36. What is the diameter of a circle whose circumference is 28 inches ? Ans. 9 inches. 37. The circumference of a circle is 189 inches. What is its area? 38. The largest possible circle is cut out form of a square whose side is 7 inches. remnants ? Ans. 284 sq. inches. of a piece of paper in the What is the area of the Ans. 10 sq. inches. 39. A circle of 2 in. diameter is cut out from one whose diameter is 3 inches. What is the area of the remainder ? Ans. 3 sq. inches. 40. Show that a circle of 5 in. diameter is as large as two others of 4 in. and 3 in. diameter together. 12. Ans. 31; 45; 136. Ans. 342; 359; 327. Ans. 2403; 1858. Ans. 9820; 10129. Ans. 15334; 22764. I Ans. 1; 5 Ans. 3'51; 073; 23*12. Extract the square root of the product of '004 and 15.625. Ans. 25. |