8. 48 men can do a piece of work in 30 days, working 10 hours a day; how many additional men will be wanted to complete it in 20 days, working 8 hours a day? 9. If 5 donkeys require as much hay as 3 horses, and each horse's hay cost 45. a week, what must be spent in supplying 85 donkeys with hay for 6 months ? 10. 75,000 flagstones, each 24 inches long and 5 inches broad, are required to lay down a court; how many stones, each 40 inches long and 6 inches broad, would be necessary for the same purpose ? 11. If 9 men can earn £2, ios. 5ļd. a day, how much will 15 men earn in 13 days? 12. If it costs £17, 155. to fill a coal cellar when coal is at £1, 6s. 7}d. a ton, what will be the cost of filling a cellar half the size of the other when coal is 335. per ton? 13. If 8 fires consume 6 tons 8 cwt. of coal in 6 weeks, in what time will 9 fires consume 10 tons 16 cwt. ? 14. If 23 horses can plough 46 acres in 8 days, how many acres will 7 horses plough in 9 days? 15. If 24 oxen require 6 acres of turnips to supply them for 10 weeks, how many acres would supply 6 score of sheep for 15 weeks, 3 oxen eating as much as ten sheep? 16. If 10 men or 14 women can perform a work in 43! days, how long would 8 men and 12 women working together require for double the work? 17. If 6 horses eat 18 guineas worth of hay in 6 weeks when hay is 9d. a stone, what is its price per stone when 15 horses eat £110, 5s. worth in 21 weeks? 18. If 5 men receive £5, 18s. wages for 12 days, what will be the wages of 16 men for 20 days? 19. If 12 men build a wall 60 feet long, 4 feet thick, and 20 feet high, in 24 days, working 12 hours a day, how many men will it take to build a wall 100 feet long, 3 feet thick, and 12 feet high, in 18 days, working 8 hours a day? 20. A man travels 120 miles in 5 days, at the rate of 3 miles an hour; how many hours a day must he travel at the same rate to go 200 miles in 8 days? a 21. If £187, 1os. pay for the education of 20 boys for 6 months, how long will £ 150 pay for 8 boys? 22. If 6 masons, each receiving 31s. 6d. a week (6 days), earn as much as 7 bricklayers in the same time, in how many days at this rate will the wages of 35 bricklayers amount to £141, 15s.? 23. If £ 12 be charged for conveying 21 tons 10 cwts. of iron for 63 miles, how far should 430 tons 5 cwts. be carried for £4? 24. 115 men undertake to make a road 2 miles long in 46 days, but when it is half done at that rate, 69 men go off to another job; how many days altogether were spent in making the road? 25. A 20 horse-power engine pumps 40 gallons of water from a pit 100 yards deep in 3 hours; what quantity of water would an engine of 35 horse-power pump from a depth of 235 feet in 141 days, working night and day? 26. If the carriage of 1 cwt. 3 qrs. 21 lbs. for 104} miles come to £1, 145. rod., what sum would be charged for conveying 21 tons for 237 miles? 27. I get 8 oz. of bread for 6d. when wheat is 155. a bushel ; what ought a bushel of wheat to cost when I get 12 oz. of bread for 4d. ? 28. If 10 men or 15 boys can reap 20 acres of corn in 6 days, working 14 hours a day, how many boys must be employed to assist 3 men. to reap 11 acres in it days of 8 hours a day? 29. If the carriage of 5 tons 5 cwt. 2 qrs. 1 lb. for 50 miles cost £27, 1os., what will be charged for conveying 254 cwt. 117 miles ? 30. If 24 cakes can be made out of 3s. worth of oatmeal when its price is 18d. per peck, how many cakes can be made out of 1os. 3?d. worth when oatmeal is at 13d. per peck ? 31. If 7 men earn £9, ios. 6d. in 10 days, in how many days will 28 men earn £114, 6s. ? 32. If a family of 9 persons spend £120 in 8 months, how much will serve a family of 24 persons 16 months? 33. If a tradesman with a capital of £2000 gain £50 in 3 months, what sum will he gain with a capital of £gooo in a year and two months ? VULGAR FRACTIONS. Reduction to the Fraction of (Money). 1. Reduce 13s. 4d., 6}d., and £1, os. Id each to the fraction of £2, os. 9d. 2. Express 4} of £2, 55. 3 d. as a fraction of £4, 125. gd. 3. Express 3 of £1, os. 9 d. as the fraction (1) of £1, ios. 1od., and (2) of £5, gs. 7d. 4. Express 's of a shilling as the fraction of £5, and 3 of £1, os. 9 d. as the fraction of £1, 1os. 5. What fraction of 18s. gd. is of of half-a-guinea, and what fraction of £i is ] of i's of 175. 4d.? 6. Reduce 3 of 25. 4}d to the fraction of 2s. 6d., and 9s. 10 d. to the fraction of 13s. 2 d. Reduction to the Fraction of (Weights and Measures). 1. Reduce 12 ft. 4} in. to the fraction of a mile. 2. What fraction of a mile is of; of a mile +of of 2 furlongs +of 4 furlongs +18 poles ? Simplification. Simplify :1. 4 of of 13}} = {(t of ?)+40} +741 2. Either (a) 164 -(33 +10%); or of 1} 59 - } of (6) 37 796 2 3. 17 121 4. + and 21 = 71 - 30 VULGAR FRACTIONS (Miscellaneous). 1. Add together 3), 712, 3, 51; divide their sum by of 41, and subtract the quotient from 20. 2. A gentleman gives 3 s. to one boy, 4 s. to a second, 33;s. to a third, 5js. to a fourth ; how much did he spend altogether, and how much did he give on an average to each boy? 3. A pile is driven through water into the ground below; } of it is buried in the soil, ş is under water, and 15 ft. above the surface of the water : what is the length of the pile ? -4. If 958 yds. of velvet cost £357, what quantity may be bought for £20? 5. From of } of 48 guineas take /s. + 1} of half-a-crown + U0's of a guinea. 6. What fraction added to of 6 of 1'y will make 1? 7. A man possessing five-elevenths of an estate, sold onethird of his share, and divided the remainder among his ten children ; what fraction of the whole estate did each child receive? 8. 2 cwt. cost £46}, what is the cost of 2 lbs.? 9. A boy, after spending of his money upon cakes, finds that 4 of what he has left is is. gd. ; what had he at first ? 10. If 11 acres of land cost £118, 13., what will 10% acres cost at the same rate ? 11. Add 9-16ths of is. 6d. to 73-960ths of 10s., and subtract their sum from 2-15ths of 12s. 6d. 12. If z} bushels can be got for 2+: } 2 of £1, what should 3+ be the cost of 7937" bushels ? 13. Simplify -x7.–3} . 1-x76–3213-93, and take the result + 16 +1}12} + 2' from 1. 14. Find the cost of a dress which required 17 yards of 5 Х . 48 ; cloth at the rate of 41 s. for of a yard, other materials in S., and 23 s. for making. 15. What is the number to which, if we add io of 6%, the result will be equivalent to of 133 ? 16. A shopkeeper having of 58} lbs. of tea, sold } qr., Tiscwt., į gr., io cwt, & qr., and of 11 of 18% lbs. ; 'what quantity had he left ? 17. Multiply 1 ton 3 cwt. I qr. 15 lbs. 10 oz. 6 drs. by 36 and 2, and add the two products together. 18. 41 yds. of cloth fyd. wide cost £2, os. 6d. ; how many yards & yd. wide should be got for 3 guineas ? 19. Take of a guinea from £io, and express their difference as the fraction of half-a-crown. 20. A person owning it of an estate sold of of his 33 share for £120%; what would } of io of the estate sell for at the same rate ? 21. Jf claret be of a guinea per doz., and marsala be of 1 of 10s. a bottle, what fraction of the price of a dozen of the former will be the price of a dozen of the latter? 22. What fraction of £10, together with 31 guineas, is equivalent to 5 guineas ? 23. Subtract } of from j of it, and multiply the result by of 24. If 10 yds. of cloth which is 18 in. wide cost £4, 18s. 6.£d., what will 1231 yds. of yard wide cloth cost ? 25. If of a ton is worth £4, 1os., what is the value of } of a ton? 26. Express 4 bush. 1 pk. y gall. 2 qts. as the fraction of a 4 quarter ; and the sum and difference of sy of £i and of a crown as fractions of a half-sovereign. 27. How many seconds are there in 100,000 part of a day, together with 3.400.000 part of 3 weeks 4 days? 4 28. A farmer has to pay yearly the price of 74 bushels of wheat at 45. 9d. per bushel, and 91 of malt at 5s. 3d., and 6 of a 3 11 7 |