20. How many rix-dollars are equal to £2420. 10s. 6d. sterling, drawn on Hamburgh; exchange at 250 marcs banco per 100 rix-dollars Danish? ARBITRATION OF EXCHANGE. 314. Instead of carrying on the business of exchange directly between two given places, merchants find it often more advantageous to exchange with some intermediate place, we shall, therefore, determine the course of exchange between the first place and the last corresponding to these courses; and also the value of any sum of money of the first place in that of the last : this is called Arbitration of Exchange. Ex. 1. Suppose the exchange between London and Amsterdam be 35 florins per £1 sterling, and the exchange between Amsterdam and Paris 4 florins per 3 francs; required the par of arbitration between London and Paris, and also the value of £720 in Paris. Here 4 florins=3 francs, ..1 florin=2 franc; And .. £1, or 351⁄2 florins=. 35x3 frs. or 26.62 francs= arbitrated value of £1 sterling. 4 .*.£720=720 × 26.621, or 19170 francs. It follows that if a merchant in London wishes to remit a sum of money to Paris, and the course between London and Paris be below 26.62, the indirect exchange should be preferred; if the exchange between London and Paris were at 26.624, both courses offer the same advantages; but if the course between London and Paris were above, then a direct remittance should be adopted: the reasons are obvious. Ex. 2. The exchange between Amsterdam and London is 56 florins for £5; between Amsterdam and Hamburgh 351⁄2 florins for 40 marks; and between Hamburgh and Petersburgh 9 schillings per bank ruble. Find how many pounds sterling are equal to 3400 rubles, and also how many rubles make £280. The following proof is as simple as it is satisfactory :— *.*563 florins=£5, 5 ..1 florin= ; To convert £280 into rubles we have the following solution :...9 schillings=1 ruble, The last answer could have been found by dividing the value of 1 ruble, viz., 9×35×5 into £280, as may be easily ascertained. 640 × 563 In practice, the following method is usually employed, called the chain rule: In the arrangement of the quantities we must take care to begin each line with the term which is of the same kind as the last term of the preceding line. Ex. 3. A French merchant desires to remit £1200 to London, and he applies to his banker for that purpose, who charges 1 per cent. that How many francs must the banker receive, supposing £20=125 rubles, 60 rubles= 144 marks of Hamburgh, 11 dollars=41 francs? Solution by fractions: £20=125 rubles, it follows that £1 =125 rubles; similarly,. 624 rubles 144 marks, it follows that 20 144 marks, and .. £1 = 1,25 of marks; but. 95 624 20 marks 46 dollars, it follows that 1 mark=g dollar, and .. £1 = 125 of 20 144 624 of dollars; but 11 dollars=41 francs it follows that 1 dollar = francs; and therefore that £1= .. the banker receives 31186.68+312 31498.68 francs, By the chain-rule method, we have: The principle of arbitration of exchange may be extended to a variety of questions, which an example will illustrate. Ex. 4. 14 Welshmen perform a piece of work in 8 days. 6 Irishmen in 2 days do as much as 5 Englishmen in 3 days. 3 Englishmen in 4 days 4 Scotchmen in 5 days 2 Scotchmen in 6 days. 7 Welshmen in 21 days. How long will 10 Irishmen, 12 Englishmen, and 16 Scotchmen be doing the same work respectively? ...6 I. in 2 d., or 12 I. in 1 d.=5 E. in 3 d., or 15 E. in 1 d. 3 E. in 4 d., or 12 E. in 1 d.=2 S. in 6 d., or 12 S. in 1 d. 4 S. in 5 d., or 20 S. in 1 d. 7 W. in 24 d., or 171⁄2 W. in 1 d. ...1 I. in 1 d. 3×12×17 W. in 1 day, or W. in 1 day. _ X3 3 XXXX2×29 4 25 32×8 ... 10 I. in or 10, d. 14 W. in 8 days. 1st answer. 25 ..16 S. in 8 d. 14 W. in 8 days. 3rd answer. 315. EXERCISES. 1. If London exchanges with Russia, at £24 for 150 rubles; between Russia and Hamburgh, at 275 rubles for 600 marks; between Hamburgh and Venice, at 112 marks for 42 piastres; and between Venice and Paris, at 12 piastres for 65 francs. Find how many francs there are in £600. 2. Of four different kinds of cloth, 4 yards of the 1st kind are worth 7 yards of the 2nd kind, 10 yards of the 2nd are worth 8 yards of the 3rd, and 3 yards of the 3rd are worth 5 yards of the 4th. Required, how many yards of the 4th kind are worth 51 yards of the 1st. 3. If the course of exchange be £8 for 1124 florins Amsterdam, 56 florins for 64 marks of Hamburgh, and 19 schillings of Hamburgh for 2 rubles of Russia. Determine how many pounds sterling are equivalent to 4000 rubles, and also how many rubles to £4000. 4. The rates of exchange are at £1 for every 25.15 francs, at 30 francs for 16 marks of Hamburgh; also at £ for 1 thaler of Berlin, and at 51 thalers for 100 marks of Hamburgh; also at £7 for 100 marks. Which is the most advantageous way to exchange 1500 marks in pounds sterling, through Paris, Berlin, or direct from Hamburgh to London? 5. If 12 lbs. at London = 10 lbs. at Amsterdam. 100 lbs. at Amsterdam = 120 lbs. at Toulouse. 18 lbs. at Toulouse-24 lbs. at Leghorn. 36 lbs. at Leghorn 31 lbs. at Antwerp. 49 lbs. at Antwerp 58 lbs. at Dantzick. many lbs. at Dantzick=540 lbs. at London? How 6. Admit that 48 Russians perform a piece of work in 17 days, and 27 Poles in 14 days=38 Russians in 13 days, 11 Prussians in 8 days=16 Austrians in 6 days, |