18. On the supposition of 5 digits only, what is the import of the digit 5 thrice expressed in the series? 19. How many half-guineas, quarter-guineas, and of each an equal number, are there in £37. 10s. 6d. ? 20. How much will £392. 18s. be worth in Ireland; one shilling being worth 13d. in Ireland? 21. How many English miles are equivalent to 375 geographical miles, 694 of the former being equal to 60 of the latter? 22. How long would 100 men take to count a billion of guineas, supposing each man to count 100 guineas in a minute, and to work 12 hours per day? 23. How many crowns, half-crowns, and groats, and of each an equal number, are there in 46 guineas ? 24. A spring of water, which furnishes 5 gallons, 5 pints each minute, supplies a town of 1500 families. How much water has each family daily? 25. How many turns do the wheels of a carriage, 18 feet in circumference, make in passing over 5 miles? SIMPLE PROPORTION. THE subject of Proportion having been already explained, at page 32, and illustrated by a number of examples, it is, therefore, unnecessary to repeat the rule for stating and solving questions in this place, as the rule delivered at page 34 is general, and applies to all questions that can be solved by Proportion; or, as it is often termed, the Rule of Three*. When the terms are in more denominations than one, if they cau be multiplied and divided, as in Compound Multiplication and Division, this method should be adopted. If not, the terms * As the questions at pages 36 and 40 are not immediately connected with mercantile affairs, those that follow will be confined entirely to such transactious as occur in business. must be reduced to the same denomination, and the first and second to the same name. If all the terms be of the same kind, it is sufficient if either the second or third be reduced to the same name with the first; the fourth term, or answer, is of the same name as the other. Operations may often be shortened, and rendered more easy, by reducing the lower denominations to a vulgar or decimal fraction of the highest denomination. EXAMPLE I. If 5 cwt. 2 qr. 14 lb. of soap be purchased for £28. 14s. 4d., how much may be purchased for £7 6s. 8d.? MISCELLANEOUS EXERCISES. 1. If 11 lb. of sugar cost 9s. 74d. what will 28 lb of the same cost? 2. Required the value of 87 lb. iron, at £25. 15s. a ton ? 3. Required the value of 2 cwt. 1 qr. 14 lb. tea, at 7s. 9d. a lb.? 4. Bought 4 cwt. 3 qr. 14 lb cheese, at £3. 5s. 4d. a cwt.; required the amount of my bill? 5. Required the value of 15 casks, qt. 53 cwt. 1 qr. 21 lb. Montreal potashes, at £2. 5s. a cwt.? 6. Required the value of 5 bundles of Riga Rhine hemp, weighing 3 tons, 6 cwt. 2 qr. 7 lb. at £63. 10s. a ton? 7. A piece of linen is worth £5. 10s. 6d. at 4s. 3d. a yard; how many yards does it contain? 8. I have received £7. 16s. for part of a piece of broad cloth, containing at first 37 yards, value £29. 12s. how much remains unsold? 9. A bankrupt's debts amount to £1565. 10s. and his effects to £853. 15s. 6d.; how much will his creditors receive per pound? 10. A bankrupt, whose debts amount to £830. 10s. 6d. compounds with his creditors for 14s. 3d. per £, how much do they receive in all ? 11. A merchant bought a quantity of Holland, at 4s. 6d. ell Flemish, what is that per ell English? per 12. A linendraper has on hand a quantity of linen, for which he paid at the rate of 2s. 94d. a yard, and means to retail it so as to gain 1d. on each shilling it cost him; how much must he charge for a yard of it? 13. If a merchant, who charges 1d. profit on every shilling prime cost, draw £900 in the course of a year; what is his yearly income? 14. If 2d. be charged on a shilling prime cost, to what extent must a merchant deal, to clear £100.? 15. Required the value of 18 yards of sarsenet, at 6s. 9d. a yard? 16. If the interest of £100 for a year be £5, what is the interest of £316. 10s. 6d. for a year? 17. A gentleman buys an estate for £7500, by which he has 4 per cent for his money. Required the yearly rent of the estate? 18. If 3 cwt. 13 lb. of curd soap cost £14. 2s. 9d. what will 7 cwt. 2 qr. 25 lb. cost? 19. If 5 cwt 2 qr. 15 lb. of ashes cost £7. 3s. 54d. how much may be bought for £9. 10s. 54d.? 20. Bought 2 cwt. 3 qr. 14 lb. of sugar for £13. 2s. 7d.; at what must I retail it a lb. to clear £2. 6s. on the whole? 21. Bought 52 ells English of broad cloth at 20s. 6d. per ell, how may I retail it per yard to clear 7 guineas on the whole? 22. Bought a quantity of linen at the rate of 9s. 6d. for 3 yards, by selling which at the rate of 24s. 6d. for 7 yards, I gained as much as 24 yards cost me. Required the quantity i 23. If 18 cwt. of sugar cost £76, what will 32 cwt. cost? ? 24. If 7 ounces of silver be worth 38s. 6d. what is the value of 3 lb. 9 oz. 23 dwt.? 25. If 50 yards cloth be purchased for £36. 17s. 6d.; how much may be purchased for £76? 26. If one gain £1. 15s. on a hogshead of wine worth £15, how many must he sell, and to what extent must he deal, in order to gain £100.? 27. Bought 7 yards of cloth for 17s. Sd.; what must be given for 5 pieces, each containing 27 yards? |