It is customary, as a precaution against accidents or miscarriage, to draw three copies of a foreign bill, and to send them by different posts. They are denominated the first, second, and third of exchange, and when any one of them is paid, the rest become void and of no value. 1. A merchant in Philadelphia imports goods from London, amounting per invoice to £1525 16s. 9d. sterling; what sum in money of the United States must be given for the bill of exchange to that amount, exchange being at $4.84 per pound sterling? £ Thus, 80 122067×121 14768.107 Ans. $7384.05% 2. A merchant in Boston exports goods to France, which are sold there for 7576 francs; what is the value of a draft on his factor for that amount at 183 cents per franc? Ans. $1409.133. 3. Taylor & Co. of Philadelphia, have purchased goods in Liverpool, to the amount of £18,761 10s.; what is the value of the goods in Federal money, the par value of the pound sterling ($40) being at a premium of 8 per cent.? Ans. $90,472.123. 4. United States on London.-Change £4109 11s. Ï0d. sterling to United States currency, exchange at 7 per cent. above par. Ans. $19,543.3947. 5. London on the United States. Change $4287.50 to sterling; exchange at 4 per cent. above par. Ans. £1003 5s. 6d. 6. An English gentleman died in Philadelphia, and left an estate of $176,984, which his executors wish to remit to London; for how many pounds sterling must a bill of exchange be drawn, at 8 per cent. premium, in favour of England? Ans. £36,871 13s. 4d. 7. A merchant in Philadelphia wishes to remit to London £9648; what must he pay for a bill of exchange, when sterling money is at a premium of 12 per cent.? Ans. $48,025.60. 8. New York on Paris.-Change 48,764 francs to Federal money, exchange being 5 francs, 25 centimes per dollar? Ans. $9288.38. NOTE.-1 franc-100 centimes. 9. Paris on the United States.-Change $4093.80 to money of France; exchange at 5 francs 30 centimes per $1. Ans. $21,697 francs 14 centimes. 10. United States on France.-Change 20,828 francs 67 centimes to Federal money; exchange at $1 for 5 francs 38 centimes. Ans. $3871.50. AMSTERDAM AND ANTWERP. Accounts are kept throughout the kingdom of the Netherlands in florins or guilders, and cents. 100 cents=1 florin or guilder. The par value of the florin in Federal money is 40 cents. 11. United States on Amsterdam.-Change 47,395 florins to Federal money; exchange at par. Ans. $18,958. 12. United States on Antwerp.-Change 6281 florins, 88 cents to Federal money; exchange at par. Ans. $2512.75}. 13. Antwerp on the United States.-Change $47,632.78 to Dutch money; exchange at 39 cents per florin. Ans. $122,135 florins. 14. United States on Antwerp.-Change 21,883 florins, 50 cents to Federal money; exchange at 42 cents per florin. Ans. $9191.07. 15. Amsterdam on the United States.-Change $1362.68 to money of Amsterdam; exchange at 38 cents per florin. Ans. 3586 florins. RUSSIA. In Russia accounts are kept in roubles and copecks. 10 copecks=1 gruvener, 10 gruveners, or 100 copecks=1 rouble. 16. United States on Russia.-Change 32,499 roubles to Federal money; the value of the rouble in the United States being 75 cents. Ans. $24,374.25. 17. Russia on the United States.-What is the value of $5763.60 in Russian currency? Ans. 7684 roubles 80 copecks. 18. A of New York draws on B of St. Petersburg for 2347 roubles, 50 copecks; what is the value in Federal money, at 62 cents per rouble? Ans. 1467.18. 19. Boston on St. Petersburg.-Change 4952 roubles 25 copecks to Federal money; exchange being 77 cents per rouble. Ans. $3813.231. PRUSSIA. Accounts are kept in Prussia in thalers or rix dollars, good groschens, and pfenings. 12 pfenings=1 good groschen, 24 good groschens=1 rix dollar. 20. United States on Prussia.-Change 4285 rix dollars, 18 good groschens to Federal money; exchange at 67 cents per rix dollar. Ans. $2871.45. NOTE. The par value of the rix dollar in the United States is 66% cents. 21. Prussia on the United States.-Change $15,741.60 to Prussian money, exchange at 64 cents per rix dollar. Ans. 24,596 rix dollars, 6 good groschens. PERMUTATION. Permutation or variation means the different ways in which the order or relative position of any given number of things may be changed; thus a and b are susceptible of the two positions ab and ba, which may be expressed by 1×2; a, b, and c, are susceptible of six different relative positions, thus, abc, acb, bac, bca, cab, and cba, and this number of variations is expressed by 1x2x3=6; hence the following RULE. Multiply the terms of the natural series of numbers, from 1 up to the given number of things continually together, and the product will be the answer required. 1. How many different arrangements may be made in seating a class of 14 pupils. Ans. 87,178,291,200. (21.) 2. How many days can 7 persons be placed in different positions at dinner? Ans. 5040 days. 3. In what length of time may the greatest possible number of changes be rung upon 12 bells, allowing 3 seconds to every change. Ans. In 45 years, 195 days, 18 hours. 4. What time will it require for 8 persons to seat themselves in the greatest possible number of different ways at dinner? Ans. 110 years, 142 days. COMBINATION. Combination consists in taking a less number of things out of a greater without any regard to the order in which they stand. Thus, out of the letters a, b, and c, three different combinations may be made, viz. ab, ac, bc; no two combinations having the same letters. This number of combinations may be expressed Take for a dividend a series of numbers, the first term of which is equal to the number of things out of which the combinations are to be made, and decreasing by 1 till the number of terms is equal to the number of things to be taken. Then take for a divisor the natural series, 1, 2, 3, 4, &c. up to the number of things to be taken at a time, and the quotient will give the answer required. 1. How many combinations can be made of 7 letters out of 10, the letters all being different? 110 Ans. 120 2. How many combinations can be made of 6 letters out of 12? Ans. 924. 3. What is the value of as many different dozens as may be chosen out of 24, at 1d. per dozen? Ans. £11,267 6s. 4d. MISCELLANEOUS QUESTIONS. 1. The sum of two numbers is 4638; one of the numbers is 2469, what is the other? Ans. 2169. 2. The difference of two numbers is 468; one of the numbers is 376, what is the other? Ans. 844. 3. The product of two factors is 19,475; one of the factors is 1025, what is the other? Ans. 19. 4. If the quotient be 4298 and the divisor 437, what is the dividend? Ans. 1878226. 5. 468 is of what number? 14 Ans. 6. What number is that which being divided by 231, the quotient will be of 3 of 9} ? = Ans. 110. 7. What is the difference between six dozen dozen, and half a dozen dozen? Ans. 792. 8. If the fourth of 20 be 3, what will be the ninth of 63 ? Ans. 41. 9. What number is that to which if its and its added the sum will be 792? 10. What number is that to which if its more be added, the sum will be 19,887 ? Ans. 432. be , its, and 89 Ans. 12,504. 11. What number is that which being divided by 4, the quotient will be 48? |