6. At 4s. 6d. in the pound profit: How much per cent. ? £ £ s. d. 7. If I buy candles at 1s. 6d. per £ s. 22 10 Ans. and sell them again at 2s. per What do I gain per cent.? Mo. £ Mo. £ s. As 18: 24: 100: 133 6 8; then by discount, As 12: 6 :: 3 : 1 10 £ S. £ s. £ s. d. £ s. d. Then, as 101 10:1 10 :: 133 6 3:1 19 43, which taken from £133 6s. 8d. leaves £131 7s. 31d. therefore, Ans. £31 7s. 3d. 8. If I buy cloth at 13s. per yard, on 8 months credit, and sell it again at 12s. ready money, do I gain, or lose, and what per cent.? Ans. lost £4 per cent. or 6d. in the yard. 9. if I buy gloves at $1 25c. per pair: How long credit must I have, to gain $13 per cent. when I sell them at $1 36c. per pair? $ c. C. $ $ c. $ c. Sold at 1.36 As 1.25: 11: 100: 8.80 gain per cent. rdy. mo. Prime cost 1.25 $ $ c. $ c. Then, 13-8.80 4.20 Now, $ Mo. c. Mo. days. In casting up the amount of goods bought, imported or exported: to the prime cost of such goods we must add all the charges upon them, in order to fix the price they stand us in. 10. Suppose I import from France, 12 bales of cloth, containing 10 pieces each, which, with the charges there, amounted to $360: I pay duty here 92c. per piece, for freight $12 and portage $1 25c.; What does it stand me in per piece, and how must I sell it per piece to gain $10 per cent.? Ans. $4 43 3 the price at which it must be sold per piece. CASE II. 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. Or, In federal money, multiply 100 dollars added to the gain, or less by the loss per cent. by the cost; and pointing off the two right band figures of the product gives the auswer. EXAMPLES. 1. If I buy a quantity of serge at 90c. per yard: How must I sell it per yard to gain 13 per cent.? Or, 113 334×90=102; and pointing off two right hand places, $1 02, Ans. as before. 2. If a barrel of powder cost £4, how must it be sold to lose £10 per cent. ? £ Or thus: £ £ As 100: 4 :: 90 4 100)360(3 300 60 20 90 £360 20 s.12 00 100)1200(12 Ans. £3 12s. 3. Bought cloth, at $2 50c. per yard, which not proving so good as I expected, I am content to lose 17 per cent. by it: How must I sell it per yard? Ans. $2 6c. 21m. 4. If 120 of steel cost £7, how must I sell it per tb to gain £153 per cent. ? Ans. 1s. 4d. per . 5. A gentleman bought 10 tons of iron for £200, the freight and duties came to £25, and his own charges to £8 6s. 8d.; How must he sell it per b to gain £20 per cent. by it? £ £ £ s. d. £ s. d. £ s. d. £ s. d. £ As 100 20: 233 6 8:46 13 4 Then, 233 6 8+46 13 4280. As 10 280 :: 1: 3 per cent. Ans. 6. If a bag of cotton, weighing Scwt. Oqrs. 20 cost $45 55c. how must it be sold per cwt. to lose $8 per cent.? Áns. $5 12c. 3m. 7. Bought fish in Newburyport, at 10s. per quintal, and sold it at Philadelphia, at 17s. 6d. per quintal; now, allowing the charges at an average, or one with another, to be 2s. 6d. per quintal, and considering I must lose £20 per cent. by remitting my money home; what do I gain per cent.? Selling price 17 6 Philadelphia currency, per quintal. As 10 2: 100: 20 per cent. gained, Ans. 8. Bought 50 gallons of brandy, at 75c. per gallon, but, by accident, 10 gallons leaked out: At what rate must I sell the remainder per gallon, to gain upon the whole prime cost, at the rate of 10 per cent.? Ans. $1 3c. 14m. CASE III. When there is gain or loss 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. Or, In federal money, divide the price with two cyphers annexed by $100 added to the gain, or less by the loss, per cent. for the answer. EXAMPLES. 1. If 1 yard of cloth be sold, at $1 2c. and there is gained 131 per cent. what did the yard cost? As 100+131:1 2: 100: 90 prime cost, Ans.. 113-333 2. If 12 yards of cloth are sold at 15s. per yard, and there is £7 10s. loss per cent in the sale: What is the prime cost of the whole. Yds. S. Yds. £ As 1 15: 12: 9 : 3. If 40 of chocolate be sold at 25c. per and I gain 9 per cent. what did the whole cost me? Ans. $9 17c. 4m.+ 4. If 19cwt. sugar be sold at $14 50c. per cwt. and I gain $15 per cent.: What did it cost per cwt.? £ s. £ £ £ s. d. As 92 10: 9: 100: 9 14 7 Ans. CASE IV. Ans. $12 60c. Sm. If by wares sold at such a rate, there is so much gained or lost per cent. to know what would be gained or lost per cent. if sold at another rate. RULE. As the first price is to £100 with the profit per cent, added, or loss per cent. subtracted; so is the other price to the gain or loss per cent. at the other rate. N. B. If your answer exceed 100, the excess is your gain per cent. but if it be less than 100, the deficiency is your loss per cent. EXAMPLES. 1. If cloth, sold at $1 2c. per yard, be 13 profit per cent. what gain or loss per cent. shall I have, if I sell the same at 90c. per yard? $ c. $ C. As 1 2: 113 :: 90: 100 And, 100-100=0, Ans. I neither gain, nor lose. 2. If cloth, sold at 4s. per yard, be £10 per cent. profit: What shall I gain or lose per cent. if sold at 3s. Ed. per yard? 48)4620(96 Ans. I lost £33 per cent. by the last sale. 432 300 12 3. If I sell a galion of wine for $1 50c. and thereby lose 12 per cent. What shall I gain or lose per cent. if I sell 4 gallons of the same wine for $6 75c.? Ans. 1 per cent. loss. 4. I sold a watch for 501. and by so doing, lost 171. per cent. whereas in trading I ought to have cleared 201. per cent. How much was it sold under its real value ? Ans. 221. 5s. 91d. EQUATION OF PAYMENTS IS the finding a time to pay, at once, several debts, due at different times, so that no loss shall be sustained by either party. RULE 1.* Multiply each payment by the time at which it is due; then divide the sum of the products by the sum of the payments, and the quotient will be the equated time, or that required. This rule is founded upon a supposition that the sum of the interests of the several debts, which are payable before the equated time, from their terms to that time, ought to be equal to the sum of the interests of the debts payable after the equated time, from that time to their terms. Some, who defend this principle, have endeavoured to prove it to be right by this argument; that what is gained by keeping some of the debts after they are due, is lost by paying others before they are due; but this cannot be the case; for though, by keeping a debt after it is due, there is gained the interest of it for that time; yet, by paying a debt before it is due, the payer does not lose the interest for that time, but the discount only, which is less than the interest, and therefore the rule is not accurately true; however, in most questions, which occur in business, the errour is so trifling, that it will always be made use of as the most elligible method. From the principle assumed in this rule, the rule may be derived in the following manner. Thus in Example 1, where 8 months is found to be the equated time, let the interest be supposed at any rate, as 6 per cent. Then the first payment is to be at interest for 8-6 or 2 months, and by the rule for interest, 100×6×8-6 100 its interest. The second sum is to be on interest 8-7 or 1 month, and N n EXAMPLES. 1. A owes B $380 to be paid as follows, viz. $100 in 6 months. $120 in 7 months, and $160 in 10 months: What is the equated time for the payment of the whole debt? 100x 6 600 120X 7 840 100+120+160=380)3040(8 months, Ans. 3040 What is the 2. A owes B 1041. 15s. to be paid in 4 months, 1611. to be paid in 3 months, and 1521. 58. to be paid in 5 months: equated time for the payment of the whole? Ans. 4 months and 8 days. 3. There is owing to a merchant 9931. to be paid, 1781. ready money, 2001. at 3 months, and 3201. in 8 months; I demand the indifferent time for the payment of the whole ? Ans. 4 months. 4. The sum of $164 16c. 6m. is to be paid, in 6 months, in 2 months, and in 12 months: what is the mean time for the payment of the whole? Ans. 73 months. RULE II. 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 his money, as the case may require, and the sum, or remainder, will be the true time of the second's payment. EXAMPLES. 1. P is indebted to Q $150 to be paid, $50 at 4 months, and $100 at 8 months: Q owes P $250 to be paid at 10 months: It is agreed 120×6×8-7 its interest to the equated time. The sum of the interest of 100 these two payments is, by the assumed principle, to be equal to the interest of 160×6×10-8. the third payment, or £160 for 10-8 or 2 months, which is 100 cent. and 100 will be factors common to every term in every case, they may be expunged from every term, and then we have, 100×8-6+120×8-7=160 × 10−8. From this equivalent expression, it is easy to find the equated time; for, 100×8-100×6+120×8-120×7=160 X10-160×8, or 100x84-120 × 84-160×8=100×6+120x7+160x10, or, 8×100+1204-160100×6+120×7+160×10, and 8=100×64120×74-160×10 100-4-120-4-160 which is the rule. The same may be shown in every similar case, and the general rule inferred. This rule is manifestly incorrect. The true rule will be given in Equation of Payments by Decimals. |