Quest. 66. The gain on 70£ at 10 per cent. is given by the proportion 100£ : 70£ :: 10£ : 70 × 10 100 =7£. Therefore the wine ought to be sold at 126 gal. for 77£. .*. 126 gal. : 1 gal.::77£ : 7£=12s. 23d.=price required. Examples. 11. How much per cent. is gained at the rate of 2d. on a shilling? 2. Three pounds of tobacco are bought for 5s. 9d., and sold for 78. 6d.; what is the gain upon the sale of that quantity which cost 100€ ? 3. A silk mercer bought 100 yd. of riband at 3 yd. for a shilling, and 100 yd. at 2 yd. for a shilling; and sold the whole at the rate of 5 yd. for 2s.: whether did he gain or lose, and how much? 177. Barter. Quest. 67. The value of 500 yd. of broad cloth at 6125£ per yd., is given by the proportion 1 yd. 500 yd. :: 6125£: 6125 x 500-306-25£. And the number of gallons of port which can be bought for 306-25£ at 425€ per gal. is given by the proportion 425£ 306 25£::1 gal.: 306.25 =720-5882 gal. In this instance the exchange of commodities is made by means of their money values. In Quest. 69. the money values are not given. But, since 5 apples are worth 3 oranges, 1 apple is worth orange. And since 4 apples are worth 7 pears, 1 apple is worth pears. orange is worth pears. ... 1 pear is worth 3×4 orange. ...1 pear 360 pears :: orange: 360 x 12 =1232 oranges. 35 Ex. How many pounds of coffee at 5s. 9d. per lb. must be given in exchange for 426 lb. of tea at 13s. 4d. per lb. ? 178. Exchange.-The answer of Question 68. is given by the proportion 4s. 2 d. 100£::1 dol.: 48000 Other Examples. 48000=475,25 dol. 1. How many francs at 9.69 pence each ought to be received in exchange for 100£? 2. How much British money must be given in exchange for 10,000 francs at 9.69 pence each. Hence 16 cwt. 2 cwt.: 710s.: 710=883s.=4£ 8s. 9d. 180. Miscellaneous Examples. 1. Divide the least common multiple of 2, 5, 6, 10, and 12 by the greatest common measure of 1500 and 4284. 2. Which is the greatest, and which the least of the fractions, and ? 3. Divide the sum of 1,, and by the difference between and }. 4. What number, being divided by 5, will give ğ for quotient? 5. Divide the sum of 14.4 and 1·44 by the difference. 6. Find the continual product of 1, 01, 001, and 1000. 7. Reduce 08, 00125, and 0078125 to equivalent vulgar fractions expressed in the lowest terms. 8. Reduce the periodic decimal ·3945945 to an equivalent vulgar fraction. 9. Extract the square root and also the cube root of '068÷00005. 10. Reduce 14s. 3d. to the vulgar and also to the decimal fraction of 1£. 11. What is the sum (in troy and also in av. weight) of 33 lb. troy, and 16 lb. av. ? 12. If 1 lb. troy of gold is coined into 46 sovereigns, and 1 lb. av. of copper into 48 halfpence; what is the difference of weight between a sovereign and a halfpenny ? 13. Add together 16 mi., 30 po., 1073 fathoms, and 509 yd. 14. 4 hhd. of water are poured into a cistern, the capacity of which is 80 cubic feet; how much more water is required to fill the cistern? 15. Multiply 14s. 8d. by 7251.25. 16. Divide £61 4s. 7d. by 267.1875. 17. How many packages of 4 cwt. 2 qr. 10 lb. each are contained in 2 t. 17 cwt. I qr. 13 lb. ? 18. Find, by aliquot parts, the price of 37 cwt. 2 qr. 13 lb., at £4 14s. 6d. per cwt. 19. Multiply 34 ft. 4 in. by 13 ft. 3 in. 20. A bankrupt pays 11s. 7d. in the pound; how much ought a creditor to receive on a debt of £1246 16s. ? 21. If 4 men reap a field of 9 ac. 2 ro. in 6 days; in how many days ought 9 men to reap a field of 14 ac.? 22. If 180 men, in 6 days of 10 hours each, dig a trench 200 yd. long, 3 yd. wide, and 2 yd. deep; in how many days of 8 hours each ought 100 men to dig a trench 360 yd. long, 4 yd. wide, and 3 yd. deep, at the same hourly rate for each man? 23. In how many days ought 15 horses to consume 75 bu. of oats, if 60 bu. serve 6 horses for 50 days? 24. A gentleman, whose yearly income is 1500£, runs 2000£ in debt in 4 years; by how much do his daily expences exceed his daily income? 25. If 30 men reap 120 ac. in 16 days of 12 hr. each; in how many days of 10 hr. each ought 60 women to reap 294 ac., 14 men being able to reap as much as 16 women? 26. If, at 1s. 2d. in the pound, the income tax produces 10,000,000£; how much more would it produce at the rate of 6£ per cent. ? 27. What is the interest of £194 5 fl. 7 c. 5 m. (£194.575 or £195 11s. 6d.) for 315 days, at 4 per cent. per annum? 28. What is the present worth of 450£, due in 3 months, allowing discount at the rate of 5 per cent. per annum ? 29. What is the difference between the simple interest and the discount on 1000£ for 1 year, at 4 per cent.? 30. What is the compound interest of 520£ for 1 yr., at 3 guineas per cent., the interest being payable half yearly? 31. What amount of stock must be purchased in the 3 per cent. consols, at 80, to produce an income of 150£ a year? 32. What sum of money must be invested in the 3 per cent. consols, at 80, to produce an income of 150£ a year? 33. If 27 yd. of cloth are bought for 17 guineas, and sold at the rate of 9s. 10d. per yd.; what is the gain or loss per cent. ? 34. If 18 qt. of water are mixed with 27 gal. of rum, at 15s. 9d. per gal.; what is 1 pint of the mixture worth? 35. What is the price of 1 cwt. of the following mixture, viz., 7 cwt. at £3 4s. 6d. per cwt., 10 cwt. at £1 19s. 10d. per cwt., 6 cwt. at £2 10s per cwt., and 12 cwt. at 5€ per cwt.? 36. Gunpowder is composed of nitre, charcoal, and sulphur, in the proportion of the numbers 15, 3, and 2 respectively; how many lb. of each ingredient are required to make 1 cwt. of gunpowder? 37. Three merchants, A, B, and C, traded together; A contributed 500£ for 2 months; B, 350£ for 5 months; and C, 400£ for 2 months. C received £29 12s. 7d. as his share of the profit; what were the shares of A and B ? 38. What does the broker receive for selling 8000£, three per cent. stock, at 913; the brokerage being per cent. ? 39. Supposing that the 3 per cents. are at 841, and the 3 per cents. at 87; into which of the two is it preferable to buy? 40. A and B barter; A has 2 cwt. of tea, at 5s. 3d. per lb. : for this B gives 300 lb. of coffee at 2s. 1d. per lb., and as many lb. of sugar at 51d. per lb. as are required to pay the balance; how many pounds of sugar must B give? THE END. |