(7) A wine merchant mixes together 20 gallons of wine at 12s. a gallon; 25 gallons at 14s. and 36 gallons at 16s. what will be the price of a gallon of the mixture? Answer: 14s. 4d.. (8) A mixture is made of 10 bushels of flour at 3s. 8d., 21 bushels at 3s. 10d., and 35 bushels at 4s.: what is the price of a bushel of it? Answer: 3s. 103d.. VII. THE DOCTRINE OF EXCHANGES. 149. DEF. 1. Exchange is the rule by means of which it is ascertained what sum of money of one country is equivalent to any given sum of another, according to some settled rate of commutation: and it is evident that the operations necessary to effect this, must, from the nature of the case, be merely applications of the Rule of Proportion. The Course of Exchange is used to express the sum of money of any place given in exchange for a fixed sum of that of another: and the Par of Exchange denotes the sum of money of any place, which is of the same intrinsic value as that fixed sum. Ex. How many pounds Flemish can I receive for £1050. sterling, the course of exchange being 35 shillings Flemish for £1. sterling? Here, from the nature of the question, we have 2,0)3675,0 shillings Flemish : £ 1837 10 the sum Flemish required; and it may be remarked that, in questions of this nature, all that is necessary to be known is the course of exchange, and the subdivisions of the monies to be commuted. 150. DEF. 2. The Arbitration, or Comparison of Exchanges, is the determining what rate of exchange called the Par of Arbitration, between any number of places corresponds with, or is equivalent to, any assigned rates between each of them and another place: and a competent knowledge of this subject will, of course, enable a person to judge how he may remit his money from one place to another, with the greatest possible advantage. Arbitration is styled simple or compound, according as three or more places are concerned. Ex. If the exchange between Amsterdam and Paris be 54d. for 1 crown, and between Amsterdam and London 33s. 9d. for £1.; what is the par of exchange, or the arbitrated price between Paris and London? = Here, 1 crown at Paris = 54 pence at Amsterdam: 240 pence in London: 405 pence at Amsterdam : thus, we obtain the equality of ratios, 1 crown at Paris 54 2 = : 2 whence, 1 crown at Paris = × 240 = 32 in London: 15 that is, 32d. per crown is the arbitrated price between London and Paris. If we arrange the equalities, so that the first term of one shall always be of the same kind as the second of that which immediately precedes it, as follows: 1 crown at Paris = 54 pence at Amsterdam; 405 pence at Amsterdam = 240 pence in London, and multiply together the corresponding terms, retaining the names only of the first and last countries and their denominations of money, we shall have 405 crowns at Paris = 54 x 240 pence in London; as before and a proceeding of this kind is sometimes distinguished by the name of the Chain Rule, from the connection of the first and last terms, thus ascertained through those which are intermediate. The reader, who may be desirous of extending his knowledge upon this subject, is referred to the last Edition of Dr KELLY'S Universal Cambist. VIII. MISCELLANEOUS QUESTIONS. 151. In this section are presented a few miscellaneous Questions, which could not with propriety be arranged under any of the preceding heads, and are still of too much importance to be passed over without notice, in a work like the present. Qu. 1. How many dozens of wine at £2. a dozen, must be given in exchange for 27 yards of broad cloth at 32s. a yard? = 864s.: The price of the cloth is 27 × 32 that is, 21 dozens of wine are of equal value with 27 yards of cloth. Questions of this kind are sometimes termed instances of Barter or Truck. Qu. 2. If a grocer by selling tea at 6s. 6d. a pound, clear one-sixth of the money: what will he clear per cent. by selling it at 7s. a pound? and therefore 5s. 5d. a pound is the price the tea cost him: whence, 5s. 5d. 7s. £100. £129. 4s. 71d.; and therefore, £129. 4s. 7 d., is the increased value of £100. at this rate: that is, the gain per cent. is £29. 4s. 7 d. 1. Questions of this description are generally classed under the heads, Profit and Loss, or Loss and Gain. Qu. 3. Required the neat weight of 27 cwt. 1qr. 14lbs., tare being allowed at the rate of 16 lbs. per cwt. Here, by the rules of Practice before given, we have Questions of this nature are usually inserted under a rule called Tare and Tret, which comprises all allowances made upon goods, on any ground whatever, whether by custom or by special agreement. Qu. 4. If two men A and B together can finish a piece of work in 10 days, and A by himself can do it in 18 days: what time will it take B to do the whole? Assuming 1 to represent the piece of work, we have 4 9 B in 10 days: wherefore, 1 10days: 22 days; or, B can do the whole work in 221 days. Qu. 5. Three agents A, B, C, can produce a given effect in 12 hours; also, A and B can produce it in 16 hours, and A and C in 18 hours: in what time can each of them produce it separately? Here, reasoning as before, we shall have the time in which C alone can produce it: effect produced by A and C in 1 hour: again, 12 18 = 1 213 1 2/82/8 and 1 -- 3 = 3 the time in which B alone can produce it: -effect produced by A, B & C in 1 hour: = B and C in 1 hour: 1 5 whence, 5 144 1: 1hr. 28 hrs., the time in which A can produce the effect proposed. Qu. 6. Distribute £200. among A, B, C and D, so that B may receive as much as A; C as much as A and B together; and D as much as A, B and C together. If the share of A be represented by 1; then will the share of B be represented by 1: the share of C by 1+1=2: and the share of D by 1+1+2=4: whence, the question is merely to divide £200. into four parts having the same proportions as the numbers 1, 1, 2, 4: also, 1+1+2+4=8, and the Rule of Fellowship gives the following proportions: The same mode of reasoning will be applicable, what ever be the number of persons concerned. |