so, to raise or fall the price of them, so as to gain or lose so much per cent. CASE I. To know what is gained or lost per cent., first find what the gain or loss is by subtraction; then, as the price it cost is to the gain or loss, so is 100 to the gain or loss, per cent. EXAMPLES. 1. A merchant bought 436 yards of broad cloth, at 8s. 6d. per yd. which he sold at 10s. 4d. per yard. How much did he gain on the whole? Find both the buying and selling price by the most concise method, and their difference is the gain. Or, find the gain per yard, by subtracting the buying rate from the selling rate; and then find the gain on 436 yards, by the most concise method. Or, decimally, as lyd.: £0916 :: 436 : £39 19s. 4d. 2. A draper bought 124 yards of Holland for £31: how must he sell it per yard to gain £10 6s. 8d. on the whole? yds. £ S. d. yd. S. d. As 124 41 6 8 1 6 8 Ans. O buying price 8 gain. 6 8 selling price. Or decimally. As 124 41, 3:1 : 6 8 3. If 2d. in the shilling be trader's profit, what does he gain per cent? Because 2 pence is of a shilling, take of £100, as follows: 6) £100 Ans. £16 13 4 or 163 per cent. Hence it is obvious that whatever part of a shilling the profit or loss is, the same part of 100 will be the gain or loss per cent. Tous 3d. of profit or loss on the shilling is 25 per cent. And in like maŋner, from the gain or loss per cent given, may the profit or loss per shilling be found. 4. A chapman has goods to the value of £415 12s. 6d. but coming to a bad market, was obliged to sell them at 12 per cent loss: what were they sold for? From 100 Take 12 Or thus: As 1.0.0 8.8 :: 415 12 6 5)249 7 6 Loss 49 17 6 Prime cost, 415 12 6 Ans. £365 15 To know how a commodity must be sold, to gain or lose so much per cent. RULE. As £100 is to the price, so is £100, with the profit added or loss subtracted, to the gaining or losing price. EXAMPLES. 1. If I buy a quantity of serge, at 5s. per yard, how must I sell it per yard to gain £13 6s. 8d. per cent? £ s. £ s. d. As 1.0.0: 5 :: 113 6 8 Or thus: £ 400 20 S. d. 113 6 8 2. If 120 of any thing cost £7, how must I sell it per pound to gain £15 per cent? 3. The prime cost of a parcel of goods sent to Jamaica is £37 & 14; and being sold at 75 per cent. advance on the invoice, what does that amount to? Ans. £65 9s. 21d. £ As 1.0.0 CASE 3d. When there is gained or lost per cent. to know what the commodity cost. RULE. As £100 with the gain per cent. added, or loss per cent subtracted, is to the price, so is £100 to the prime cost. EXAMPLES. 1. If 1 yard of cloth be sold at 5s. 8d. and there is gained £13 68. 8d. per cent. what did the yard cost? As £113 6s. 8d. : 5s. 8d. :: £100: 5s. Answer. Prime cost. 2. If a merchant, in selling goods at 8d. per b. gain 12 per cent. what will he gain per cent. in selling the same goods at 9d. per b? As 8d. 1.1·2d.:: 9d.: 126-100-26 Answer, per cwt. : 14 3. A merchant sells 8 tuns of wine for £440 and loses 12 per cent: how much did it cost per tun, and how does he sell it per gallon ? Ans. It cost £62 10s. per tun; and he sells it 4s. 4d: 11qrs. per gallon. Tuns. £Tun. £ As : 440 :: 1 : 55, then As 88: 100 :: 55: £62 10s. per tun. Tun. £ s. gall. s. d. qr. As 1 62 10 :: 1: 4 4 111 per gallon. 4. A merchant in Boston, sends to Ostend 20 hhds. of tallow, wt. neat 10 Ton 17cwt. 3qrs. at £30 10s. 9d. the ton; pays for duty and other charges, £25 10s. and for prem. of insurance, £55 10s. the tallow at Ostend weighed 24388. and the merchant there sells it at 18 guilders the 100, pays for freight, duty and other charges, 595 guilders, 10 stivers, and 4 ponnings, and reckons for his commission 2 per cent, and remits the neat proceeds to London, at 333. 9d. Flemish, per £ sterling, and the American merchant draws it from London, at 4 per cent advance. To know whether he gains or loses ? He loses £32 15s. 1,3429 d. 1350000 * EQUATION OF PAYMENTS, Ans: Is the finding of a time to pay, at once, several debts due at different times, so that no loss shall be sustained by either party. RULE. Multiply the several debts into their respective times, divide the sum of the products by the sum of the debts, and the quotient will be the equated time, or that required. EXAMPLES. 1. A. owes B. £600, to pay at 40 days; £200, at 60 days, aud £200 at 120 days when may these debts be paid at once, without injury to either party? Debts. Days. Prod. 600 X 40=24000 200 X 60=12000 200 X 120 24000 60,000(60 days. Ans. 1,000 in 2. A. owes B. a certain sum, whereof is present payment, 6, and the remainder in 8 months; required the equated time for paying the whole ? Ans. 4 months. The above method is easy, and on that account commonly practised, but is not accurate; for a person, by keeping money unpaid after it becomes due, gains the interest thereof for that time; but by paying money before it becomes due, the interest is not lost as the rule supposes, but the discount thereof only for that time, which is always less than the interest. METHOD 2, RULE. Find the present worth of each debt, and then find in what time the sum of the present worths will amount to the sum of the debts. EXAMPLES. A. owes B. £50, whereof £20 is payable in 2 years hence, and £30 in 5yrs. hence: what is the equated time for paying both debts at once, discounting interest at 5 per cent.? [Carried up The present worth of £20 for 2 years is £18.18 See by rule 1st at what time the first man mentioned ought to pay in his whole money; then, as his money is to his time, so is the other's money to his time, inversely; which, when found must be added to or subtracted from the time at which the second ought to have paid in bis money, as the case may require, and the sum or remainder will be the true time of the second's payment. EXAMPLES. 1. A. is indebted to B. £150, to be paid, £59 at 4 months, and £100 at 8 months: B. owes A. £250 to be paid at 10 months: it is agreed between them that A. shall make present payment of his whole debt, and that B. shall pay his so much the sooner as to balance that favour: I demand the time at which B. must pay the £250, reckoning Simple Interest? £ M. As 150 £ 6 months-A's equated time. Then 10mo.-4mo.-6mo. time of B's payment. 2. A merchant has £1200 due to him, to be paid at 2 months, at 3 months, and the rest at 6 months; but the debtor agrees to pay down how long may the debtor detain the other half, so that neither party may sustain loss? mo. mo. x2=01 X6=3 Equated time 4 Now, as was paid 4 months before it be came due, it is reasonable that he should detain the other 4 months after it became due, which, added together, gives 8 months, the true time for the second payment. N. B. Some complain that the foregoing rules are not absolutely perfect; and argue that the rule for finding the mean or equated time ought to be such as will make the debts paid after they are due, exactly equal to the discount of the debts paid before they are due. |