Ex. 11. If the carriage of 37 stone, 6 lbs. for 7 miles cost £2. 5s., what weight should be carried 12 miles for £3. 10s.? Our arrangement may be the following: where the producing quantities in the first line will be the 37 st., 6 lbs., and the 7 miles, since these together, that is, the weight carried over the distance, produce the £2. 5s. to the carrier. Reducing the quantities according to the Rule, the arrangement becomes Instead of reducing the quantities to lower denominations, as in the above operation, we might have kept them in the higher denominations, by reducing any part which was expressed in a lower to a fraction of the higher denomination. Thus, observing that 6 lbs st. st., and 58.= £1, and 10s. = £1, we have 6 = Dividend =37 × 7×31=292 × 7×1=131 × 7=917. Divisor = 12 × 21=12×2=3×9=27. Required weight=247 stones =33 st.,13 lbs., 7 oz., 1177 drs. Note. It will be observed throughout the above Examples, that in the first line of our arrangement, we have put down first the causes, and then, after them, the effect or effects; thus determining of course the places of the numbers in the second line also. This order was adopted for each line, not because it is necessary, but because it enables us more readily to distinguish between the causes and the effects, when we require them in the subsequent process. Ex. LVII. 1. If 7 men can reap 6 acres in 12 hours, how many men will reap 15 acres in 14 hours? 2. If 3 men earn £15 in 20 days, how many men will earn 15 guineas in 9 days, at the same rate? 3. If 16 horses eat 96 bushels of corn in 42 days, in how many days will 7 horses eat 66 bushels? 4. If 800 soldiers consume 5 sacks of flour in 6 days, how many will consume 15 sacks in 2 days? 5. If 17 bushels be consumed by 6 horses in 13 days, what quantity will 8 horses eat in 11 days, at the same rate? 6. 16 horses can plough 1280 acres in 8 days, how many acres will 12 horses plough in 5 days? 7. If 11 cwt. can be carried 12 miles for £1. 5 c. how far can. 36 cwt., 23 lbs. be carried for £5. 2 fl. 5 c.? 8. If the carriage of 8 cwt. of goods for 124 miles be 6 guineas, what weight ought to be carried 53 miles for half the money? 9. If 5 men on a tour of 11 months, spend £641. 13s. 4d., how much at the same rate would it cost a party of 7 men for 4 months? 10. If with a capital of £1000 a tradesman gain £ 100 in 5 months, in what time will he gain £49. 5 fl. with a capital of £225 ? 11. If it cost £59. 28. 14d. to keep 3 horses for 7 months, what will it cost to keep 2 horses for 11 months? 12. The carriage of 4 cwt., 3 qrs., for 160 miles costs £3. 8 fl. 5 c. what weight ought to be carried 100 miles for £6. Os. 32d.? 13. If 1 man can reap 3455 sq. yds. in an hour, how long will 7 such men take to reap 6 acres? 14. If 20 men in 3 weeks earn £90., in what time will 12 men earn £150? 15. If the carriage of 1 cwt., 3 qrs., 21 lbs. for 52 miles come to 178. 5d., what will be charged for 21 tons for 461 miles ? 16. If 10 men can reap a field of 7 acres in 3 days of 12 hours each, how long will it take 8 men to reap 9 acres, working 16 hours a-day? 17. If 25 men can do a piece of work in 24 days, working 8 hours aday, how many hours a-day would 30 men have to work in order to do the same piece of work in 16 days? 18. If the rent of a farm of 17 ac., 3 ro., 2 po. be £ 39. 4s. 7d., what would be the rent of another farm, containing 26 ac., 2 ro., 33 po. if 6 acres of the former be worth 7 acres of the latter? 19. If 1500 copies of a book of 11 sheets require 66 reams of paper, how much paper will be required for 5000 copies of a book of 25 sheets, of the same size as the former? 20. If 5 men can reap a rectangular field whose length is 800 ft. and breadth 700 ft. in 3 days of 14 hours each; in how many days of 12 hours each can 7 men reap a field whose length is 1800 ft. and breadth 960 ft.? 21. If a thousand men besieged in a town with provisions for 5 weeks, allowing each man 16 oz. a-day, be reinforced with 500 men more, and have their daily allowance reduced to 63 oz ; how long will the provisions last them? 22. If 20 masons build a wall 50 feet long, 2 feet thick, and 14 feet high, in 12 days of 7 hrs. each, in how many days of 10 hrs. each will 60 masons build a wall 500 feet long, 4 thick, and 16 high? 23. If 10 men can perform a piece of work in 24 days, how many men will perform another piece of work 7 times as great, in one-fifth of the time? 24. If 125 men can make an embankment 100 yards long, 20 feet wide, and 4 feet high, in 4 days, working 12 hours a-day, how many men must be employed to make an embankment 1000 yards long, 16 feet wide, and 6 feet high, in 3 days, working 10 hours a-day? 25. What is the weight of a block of stone 12 ft. 6 in. long, 6 ft. 6 in. broad, and 8 ft., 3 in. deep, when a block of the same stone 5 ft. long, 3 ft., 9 in. broad, and 2 ft., 6 in. deep, weighs 7500 lbs. ? 26. If 100 men drink £20 worth of wine at 4s. 6d. per bottle, how many men will drink £72 worth at 5s. per bottle, in the same time, at the same rate of drinking? 27. If 5 horses require as much corn as 8 ponies, and 15 quarters last 12 ponies for 64 days, how long may 25 horses be kept for £41. 58. when corn is 22 shillings a quarter? 28. If 42 yds. of cloth which is 18 in. wide cost £59. 14s. 2d., what will 118 yds. of yard-wide cloth of the same quality cost? 29. 124 men dig a trench 110 yds. long, 3 ft. wide, and 4 ft. deep, in 5 days of 11 hours each; another trench is dug by half the number of men in 7 days of 9 hours each; how many feet of water is it capable of holding? 30. If the fourpenny loaf weigh 3.35 lbs. when wheat is at 4.75s. a bus., what ought to be paid for 474 lbs. of bread when wheat is at 13'4s. a bus.? 31. A pit 24 ft. deep, 14 sq. ft. horizontal section cost £3. to dig out; how deep will a pit be of horizontal section 7 ft. by 9 ft., which costs £4. 10s.? 32. The value of the paper required for papering a room, supposing it yard wide, and 41d. a yard, is £2. 3s. 11d.; what would it come to, if it were 2 feet wide and 4d. a yard? 33. 7 men working 16 days can mow a field of corn 1320 yards long and 880 wide; what will be the length of the side of a field 1320 yards broad which 4 men can mow in 42 days? 34. A beam 16 feet long, 21 feet broad, and 8 inches thick, weighs 1280 lbs. ; what must be the length of another beam of the same material, whose breadth is 31 feet, thickness 71⁄2 inches, and weight 2028 lbs. ? 35. If 12 oxen and 35 sheep eat 12 tons, 12 cwt. of hay in 8 days, how much will it cost per month (of 28 days) to feed 9 oxen and 12 sheep, the price of hay being 4 guineas a ton, and 3 oxen being supposed to eat as much as 7 sheep? 36. If 1 man and 2 women do a piece of work in 10 days, find in how long a time 2 men and 1 woman will do a piece of work 4 times as great, the rates of working of a man and woman being as 3 to 2. 37. A person is able to perform a journey of 142.2 miles in 4 days when the day is 10.164 hours long; how many days will he be in travelling 505.6 miles when the days are 8'4 hours long? 38. If the sixpenny loaf weigh 4:35 lbs. when wheat is at 5·75s. per bushel, what weight of bread, when wheat is at 18:4s. per bushel, ought to be purchased for 18-138.? 39. If a family of 9 people can live comfortably in England for 1560 guineas a year, what will it cost a family of 8 to live in Belgium in the same style for seven months, prices being supposed to be of what they would be in England? INTEREST. 162. DEF. INTEREST is the sum of money paid for the loan or use of some other sum of money, lent for a certain time at a fixed rate; generally at so much for each £100 for one year. The money lent is called THE PRINCIPAL. The interest of £100 for a year is called THE RATE PER CENT. Interest is divided into Simple and Compound. When interest is reckoned only on the original principal, it is called SIMPLE INTEREST. When the interest at the end of the first period, instead of being paid by the borrower, is retained by him and added on as principal to the former principal, interest being calculated on the new principal for the next period, and this interest again, instead of being paid, is retained and added on to the last principal for a new principal, and so on; it is called COMPOUND INTEREST. SIMPLE INTEREST. 163. To find the Interest of a given sum of money at a given rate per cent. for a year. RULE. "Multiply the principal by the rate per cent., and divide the product by 100, as in (Art. 126)." Note 1. The interest for any given number of years will of course be found by multiplying the interest for one year by the number of years; and the interest for any parts of a year may be found from the interest for one year, by Practice, or by the Rule of Three. Note 2. If the interest has to be calculated from one given day to another, as for instance from the 30th of January to the 7th of February, the 30th of January must be left out in the calculation, and the 7th of February must be taken into account, for the borrower will not have had the use of the money for one day till the 31st of January, Note 3. If the amount be required, the interest has first to be found for the given time, and the principal has then to be added to it. Ex. Find the simple interest of £250 for one year at 5 per cent. per annum. |