Value of the ship, Contributary Articles. Do. of R. S. Davis's goods thrown overboard, Do. of J. Smith's goods at Mobile, deducting freight, do. Do. of two thirds the ship's freight, do. $9272 1728 2000 7000 5000 $25,000 A Statement of what each Contributary Article pays in the General Average. A Statement of what each Party receives. Davis receives $1728 x .80 = $1382.40 By this rule merchants estimate their profit and loss in buying and selling goods. The questions are to be performed by Proportion and the other preceding rules. The pupil should give an analysis of each question. One of four things is generally required by this rule: 1. To know what per cent. is gained or lost, either in purchasing or selling goods. 2. To ascertain at what price to sell an article to gain or lose a certain per cent. 3. To ascertain the price of an article, when we know what per cent. is gained or lost. 4. If goods be sold at a certain price, and there be gained or lost a certain per cent., to ascertain what would be gained or lost at some other price. The eight following examples will illustrate the above problems. EXAMPLES. 1. If I buy cloth at $4 per yard, and sell it at $5 per yard, what per cent. do I gain? Ans. 25 per cent. OPERATION BY PROPORTION. $5-$4=$1; $4 : $1 : : $100: $ 25, that is, 25 per cent. By analysis. If $4 gain $1, it is evident that $1 will gain of $1 = $0.25; and $100 will gain 100 times $0.25 = $25, that is, 25 per cent., answer as before. 2. When cloth is purchased at $5 per yard, and sold at $4 per yard, what per cent. is lost? Ans. 20 per cent. OPERATION BY PROPORTION. $5-$4 $1. $5: 81: $100 $20, that is, 20 per cent. By analysis. If $1 be lost on $5, it is certain that on $1 there will be lost of $1 = $ 0.20; and if on $1 there be lost $0.20, on $100 there will be lost 100 times $0.20 $20, that is, 20 per cent., answer as before; therefore, when we wish to know what per cent. is gained or lost, either in purchasing or disposing of goods, we adopt the following RULE. - As the price of the goods is to the gain or loss, so is $100 to the per cent. gained or lost. 3. If I buy cloth at $4 per yard, for how much must I sell it to gain 25 per cent. ? Ans. $5. OPERATION BY PROPORTION. $100+$25 $125; $100: $125 :: $4: $5 Ans. By analysis. If for $100 I receive. $125, it is evident that for $1 I shall receive only of $125: = $1.25, and for $4 I shall have 4 times $1.25 = $ 5, answer as before. 4. If I buy cloth at $5 per yard, for what must I dispose of it per yard to lose 20 per cent. ? OPERATION BY PROPORTION. $100 $20 = Ans. $4. = $80; $100: $80::$5: $4 Ans. By analysis. If $80 are to be received for $100, it is certain that for $1 there will be paid only of a dollar = 80 100 $0.80, and for $5 I can receive only 5 times $0.80 = = $4, answer as before; therefore, to ascertain at what price to sell an article to gain or lose a certain per cent. we adopt the following RULE. As $100 is to $100 with the profit added or loss subtracted, so is the price given to the price required. 5. If I sell cloth at $5 per yard, and thereby make 25 per cent., what was the prime cost of the goods? $100+$25 OPERATION BY PROPORTION. = $125; $125 : $100 :: $5: $4 Ans. By analysis. As $125 are received for $ 100, it is evident that for $1 there will be received only 129 = of a dollar = $0.80; and for $5, 5 times $0.80= $4.00 Ans. 6. If I dispose of cloth at $ 4 per yard, and by so doing lose 20 per cent., required the prime cost of the goods. Ans. $5. OPERATION BY PROPORTION. $100-$20 = $80; $ 80: 100 :: $4: $5 Ans. By analysis. As $100 are received for $80, it is certair. that for 100 = of a dollar $1.25 there would be received only $1; therefore, for $4 which I receive I should have had 4 times $1.25 = $5, answer as before; therefore, when we wish to ascertain the price of an article, when we know wha per cent. is gained or lost, we adopt the following RULE. As $100 with the gain per cent. added or loss per cent. sub tracted is to $100, so is the price to the prime cost. 7. If I sell cloth at $5 per yard, and thereby gain 25 per cent., what would be my gain if I were to obtain $7 per yard? Ans. 75 per cent. OPERATION BY PROPORTION. $100 + $25 = $125; $5 : $7 :: $125: $175; $175 $100 $75, that is, 75 = per cent. By analysis. As $5 amounts to $125, it is evident that $7 will amount to of $125 = $175; and if $7 amount to $175 it is certain that $175 - $100 = $75 are gained on $100, that is, 75 per cent. 8. If I purchase cloth at $7 per yard, and thereby gain 75 per cent., do I gain or lose if I sell the same at $3 per yard? Ans. lose 25 per cent. OPERATION BY PROPORTION. $100 + $75= $175; $7 : $3 :: $175 : $75. $100- $75 $25; the loss is therefore 25 = per cent. By analysis. If $7 give $ 175, $3 will give of $175 = $75. Therefore, for $100 there are received only $75; therefore there is $100 – $ 75 = $25, or 25 per cent. loss, answer. If, therefore, goods be sold at a certain price, and there be gained or lost a certain per cent., and we wish to ascertain what would be gained or lost per cent. at some other price, we deduce the following RULE. As the first price is to the proposed price, so is $100 with the profit per cent. added or the loss per cent. subtracted to the gain or loss per cent. at the assumed price. -- NOTE. - If the answer exceeds $100, the excess is the gain per cent.; but if it be less than $100, the deficiency is the loss per cent. EXAMPLES TO EXERCISE THE PRECEDING RULES. 9. Sold broadcloth at $ 6.124 per yard, and by so doing lost 121 per cent. What was the original cost per yard? Ans. $7.00. 87 By analysis. If 124 per cent. be lost, 87 per cent. will remain. It is now required to find of what number $6.12 is This is done by multiplying $6.12 by 100, and dividing by 871, and it produces the answer, $7.00. 10. Bought cloth at $7.00 per yard, and sold it at $6.124. What per cent. did I lose? Ans. 12 per cent. 11. Bought cloth at $7.00 per yard, and sold it for 12 per What did I receive? cent. less than what it cost. 12. Bought cloth at $3.60 per yard. I sell it to gain 12 per cent. ? 13. Sold cloth at $ 4.05 per yard, and 121 per cent. What did it cost? by so doing I gained Ans. $3.60. For how much Ans. $9.35 per cwt. and gained 10 per cent. Ans. $8.50 per cwt. 14. Bargained for cheese at $8.50 per cwt. must I sell it to gain 10 per cent.? 15. Sold cheese at $9.35 per cwt. What did I give for it? cent. 16. Sold cloth at $1.25 per yard, and by so doing lost 15 per For what should I have sold it to gain 12 per cent. ? Ans. $1.64,7 per yard. 17. Sold cloth at $1.25 per yard, and lost 15 per cent. What per per cent. should I have gained had I sold it for $1.64,7 yard? Ans. 12 per cent. 18. Sold cloth for $1.64,7 per yard, and gained 12 per cent. For what should I have sold it to lose 15 per cent. ? Ans. $1.25 per yard. 19. Sold cloth for $1.64,7 per yard, and gained 12 per cent. What should I have lost had I sold it for $1.25 per yard? Ans. 15 per cent. 20. A buys corn for $0.90 per bushel, and sells it for $1.20. B buys for $1.12, and sells for $1.50. Who gains the most per cent. ? Ans. both gain alike. 21. If I buy cotton cloth at 13 cents per yard, on 8 months' credit, and sell it again at 12 cents cash, do I gain or lose, and how much per cent. ? Ans. lose 4 per cent. 22. If 24 yards of cloth are sold at $2.50 per yard, and there is 7 per cent. loss in the sale, what is the prime cost of the whole ? Ans. $64.86,437. 23. Bought 24 yards of cloth for $64.86,433. For what must I sell it per yard to lost 7 per cent.? Ans. $2.50. 24. Bought a certain quantity of cloth for $ 64.86,432, and by selling it at $2.50 per yard, I lost 7 per cent. How many yards were bought? Ans. 24 yards. 25. Bought 24 yards of cloth for $ 64.86,434, and sold it at $2.50 per yard; what per cent. is lost? Ans. 7 per cent. 26. If 27 cwt. of sugar be sold at $12.50 per cwt., and there is gained 17 per cent., what was the first cost? Ans. $10.68,397. 27. Sold a horse for $75, and by so doing I lost 25 per cent.; whereas, I ought to have gained 30 per cent. How much was he sold under his real value ? Ans. $55.00. 28. Bought a horse which was worth 30 per cent. more than I gave for him; but having been injured, I sold him for 25 per cent. less than what he cost, and thereby lost $ 55 on his original value. What was received for the horse? Ans. $75.00. 29. Bought molasses at 42 cents per gallon, but not proving so good as I expected, I am willing to lose 5 per cent. For what must I sell it per gallon? Ans. $0.39,9. 30. Bought a hogshead of molasses for $112, but 15 gallons having leaked out, I am willing to lose 5 per cent. on the cost. For how much per gallon must I sell it? Ans. $2.21,63. 31. Bought a hogshead of molasses for $112, but a number of gallons having leaked out, I sell the remainder for $2.21,63 |