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42. My retail price of Axminster carpet is $3.50 per yard, by which I gain 25%. If I sell at wholesale, at a discount of 25% from the retail price, how much do I receive per yard. What is my per cent. of gain or loss, and how much is my actual gain or loss by selling 1000 yards at wholesale ?

43. If the loss equalled f of the selling price, what was the per cent. of loss ?

4. A grocer bought 200 quarts of berries, at 1114 per quart, and 150 quarts of cherries, at 614 per quart. Having sold the cherries at a loss of 30%, for how much per quart must he sell the berries, to gain 15% on the whole ?

45. A sells two horses to B at an advance of 103%, B sells them to C at an advance of 25%, and C sells them to D for $735, thereby making a profit of 20%. How much did A pay for the horses ?

46. Having bought 48 pounds of coffee, at the rate of 34 pounds for 914, and 84 pounds more at the rate of 7 pounds for $1.26, I sold the lot at the rate of 9 pounds for $1.53. What was my per cent. of gain or loss ?

47. By selling at a loss of 6$ per yard I get 87% of the cost of cloth. What per cent. of the cost would I have received had I lost 8¢ per yard ?

48. If 15% is lost by selling suits at $17 each, how much would be gained by selling them at 15% profit ?

49. The price of a suit of clothes having been marked down 20% or to $27, the dealer, in order to effect a sale, discounted again 15%, and still by the sale made a profit of 14%. What per cent. above cost was the suit originally marked

50. An Iowa farm passed through the hands of five owners, each of whom in succession gained 20% by its purchase and sale. If the average gain was $1488.32, what was its first cost, and what was its final selling price?

51. . By selling a stock of goods at 20% below cost, I received $150 less than I would have received had I sold the goods at 20% above cost. What should the goods have sold for to gain 20% ?

52. The first cost of Parisian goods purchased through an agent was increased 18% by the charges of the agent, the freight, and the import duties; I sold the goods at 25% advance on full cost, thereby gaining $1785. Find the first cost.

53. After using a carriage for two years, I sold it for 3% of its selling price less than it cost, thereby losing $5. How much would it have brought, had the amount received for it been 31% of the selling price more than it cost ?

54. An agent bought a reaper at 20% off from the wholesale price, and sold it at an advance of 30%, thereby gaining $37.50. If the wholesale price was 25% above the cost of manufacture, what was the cost to the manufacturer?

55. I sold a house at 25% profit, and invested the proceeds in dry goods, on which I lost 12%; I invested the proceeds from the sales of dry goods in stocks, on which I lost 10%. What was my net gain or loss per cent. ?

56. Having paid a retailer $138.60 for a set of furniture, I ascertain that by selling to me he gained 12%, that the wholesaler of whom he bought gained 10%, that the jobber by selling to the wholesaler gained 163%, and that the manufacturer sold to the jobber at 20% above its first cost. How much more than its first cost did I pay ?




57. I wish to line the carpet of a room 21 ft. long and 18 ft. wide with duck g of a yard in width, How many yards will be required, if it shrink 10% in width and 5% in length ? If the carpet be laid lengthwise of the room, and be furnished at $2.25 per yard, i of a yard wide, and the duck, before shrinking, at 20¢ per square yard, and a profit of 163% be realized on both, what will be the gain?

58. If I pay $3.20 for 20 gal. of vinegar, how many gallons of water must be added, that 40% profit may be realized by selling it at 15$ per gallon ?

59. A huckster sold a quantity of potatoes and onions, gaining 37% on the onions and 25% on the potatoes, 33}% of his profit being realized on the potatoes. At what price was each sold, if the total gain was $450 ?

What price each must be asked for cocoanuts, costing $4 per C, that an allowance of 16% for breakage, 20% for decay, and 113% for bad debts may be made, and still a profit of 331% be realized ?

61. A tree agent sold apple and pear trees for $2187.50; he gained 163% on the apple, and 374% on the pear trees, receiving for the pear 75% as much money as for the apple trees. Find the cost of each kind. .

62. A dry goods house bought a stock of goods, and sold of it at 25% profit, ☆ of it at 20% profit, of it at 16% loss, } of it at 12% gain, and the remainder, which cost $4549.25, at 15% gain. What was the net gain or loss, and the per cent. of gain or loss, on the entire stock ?

63. A butcher paid equal amounts of money for calves, pigs, and sheep; he cleared 14% on the calves, 10% on the pigs, and lost 30% on the sheep. How many dollars were paid for each kind of stock, the total amount received having been $1336.50 ?

64. I sold my house to B and lost 10% of its cost; B expended $375 for repairs and sold it to C at 120% of its full cost to him; C expended $525 in enlarging the house, and then sold it for $6354, thereby making a profit of 20% of its full cost. How much did I pay for the property ?

65. A speculator, investing equal sums in corn and wheat, gained $2713.50 more on the corn than on the wheat. If he gained 102% on the wheat and 15% on the corn, how many bushels of each must have been purchased, the corn having been bought at 60¢ per bushel and the wheat at 804 per bushel ?

66. A drover bought 50 horses, cows, and sheep for $870; the number of cows was 600% of the number of horses, and the number of sheep was 300% of the number of cows; the horses cost 200%, and the sheep 20%, as much as the cows. If the entire purchase was sold at a profit of 20%, how much was received per head for each kind ?


570. Discount is the allowance made for the payment of a debt before it becomes due.

571. Trade Discount is the allowance made by manufacturers and mer. chants upon their fixed or list prices.

REMARKS.-1. It is customary in many branches of business for merchants and manu. facturers to have fixed price lists of their goods, and when the market varies, instead of changing the price list, to change the raie of discount,

2. Business houses usually announce their terms upon their “bill-heads;" as, “ Terms, 3 months, or 5% off for cash;” “ Terms, 60 days, or 3% discount in 10 days,” etc. When bills are paid before maturity, legal interest for the remainder of the time is usually deducted.

572. There may be more than one Trade Discount, and they are then known as a Discount Series.

573. Trade Discount is computed by the rules of percentage, on the marked price as a base. When a series of discounts is allowed, the first only is so computed, and in every subsequent discount the remainder, after each preceding discount, is regarded as the base.

574. To find the Selling Price, the List Price and Discount Series being given.

EXAMPLE (first illustration).—The list price of a sewing machine is $60. What is the net selling price, if a discount of 40% is allowed ?

OPERATION. $ 60 = list price. .40 = % of discount. .

EXPLANATION.-Since the discount is 40 per cent., and $ 24 = discount.

the list price, or base, is $60, the discount to be deducted

will be 40 per cent. of $60, or $24; and the net price will $ 60 = cost.

be $60 minus $24, which equals $36. 24 = discount. $ 36 = net selling price.

EXAMPLE (second illustration).—The list price of a threshing machine is $900. What is the net price, if a discount series of 25%, 20%, and 10% is allowed ?

OPERATION. $900 = list price. 225 25%, or 1 = 1st discount.

EXPLANATION.-- From the list price take the $675 = rem, after 1st discount. first discount, and make each remainder the base 135 = 20%, or = 2d discount.

for the succeeding discount. The last remainder

will be the net price. $540 = rem. after 2d discount.

54 10%, or 10 3d discount. $486 = rem, after 3d discount, or net price. REMARK.-In like manner treat any series of discounts.

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Rule.-Deduct the first discount from the list price, and each subsequent discount from each successive remainder.


575. 1. What is the selling price per dozen of hats, listed at $36, and discounted 20% and 15% ?

2. Find the net price of a ton of fence wire, listed at 94 per pound, and sold at 70% and 5% off.

3. Find the net cost to the purchaser of a bill of goods invoiced at $1100, from which discounts of 20% and 25% were allowed.

4. An invoice of silk amounting to $12000 was sold Sept. 21, 1888, at a discount of 25%, 20%, and 12%, with a further discount of 10% to be allowed if paid within 30 days. How much cash will pay the bill Oct. 15, 1888 ?

5. Having bought merchandise at 25% and 15% discount from the list price of $1500, I sell it at 15%, 15%, and 10% from the same list price. Do I gain or lose, and how much ?

6. A wholesale dealer offers cloth at $2.40 per yard, subject to a discount of 25%, 20%, 10%, and 5%. How many yards can be bought for $246.24 ?

7. What is the net cost of a bill of goods invoiced at $2150, and sold at a discount of 15%, 10%, 5%, and 3% ?

8. Three drummers, A, B and C, offer me the same grade of goods at the same list price. A offers to discount 25% and 15%; B 20% and 20%; and C 15%, 15%, and 10%. With which will it be most advantageous for me to deal, and how much would I save from a list price of $200 ?

REMARKS.-1. It is often convenient in finding the net price to multiply the list price by 1 minus the first discount, the remainder by 1 minus the next, and so on.

2. The order in which the discounts of any series are considered is not material, a series of 25, 15, and 10 being the same as one of 15, 10, and 25, or of 10, 25, and 15.

576. To find the Price at which Goods must be Marked to Insure a Given Per Cent. of Profit or Loss, the cost and Discount Series being given,

EXAMPLE (first illustration).—Having bought goods for $105, at what price must they be marked to allow a discount of 25%, and still make a profit of 10% ?

EXPLANATION.—The cost, $105, is 100 per OPERATION

cent. of itself ; the rate of discount to be al$105 = the cost.

lowed is 25 per cent.; 100 per cent. minus 25

per cent., or 75 per cent., is the per cent. which .10 = % to be gained.

the price to be insured is of the price to be $10.50 = gain to be insured.

asked. And if 10 per cent. must be insured, 105.00 = cost.

the goods must actually bring 10 per cent., or

$10.50 more than cost, or $115.50. And since $115.50 selling price to be insured.

a deduction of 25 per cent. is to be made from .75 ) $115.50

the asking price, the selling price, $115.50, will

be only 75 per cent. of the asking price. $154 asking price.

Therefore, divide $115.50 by .75, and the quotient, $154, will be the asking price,

EXAMPLE (second illustration).-A seal sacque cost a manufacturer $240. what price must it be marked, that a discount series of 25%, 20%, and 20% may be allowed, and he still make a profit of 30% ?

OPERATION. $240 = cost or base.

$1.00 = % of price realized. .30 = % to be gained.

% of 1st discount. 72 = gain to be insured.

.75 =

% of price to be received in 240 = cost.

order to gain 30% and allow

1st discount. $312 = price to be received.

.25 =

.75 ) $312.00
$416 = asking price in order

to pay $240, gain
30%, and allow a dis-
count of 25%.

$1.00 = % of price.

.20 = % of 2d discount.
.80 = % of price to be received in

order to gain 30% and dis-
count 25% and 20%.

.80 ) $416.00

$1.00 = % of price.
.20 =

% of 3d discount.
$520 = asking price in order to

pay $240, gain 30%, and .80 = % of price to be received in discount 25% and 20%.

order to gain 30% and dis

count 25%, 20%, and 20%. .80 ) $520.00 $650 = asking price in order to gain 30% and

allow the full discount series.

Rule.-Add to the cost the gain required, and divide consecutively by 1 minus each of the rates in the discount series.


577. 1. What must be the asking price of a watch, costing $18, that 331% may be gained, after allowing the purchaser a discount of 20% ?

2. Having bought an invoice of lawn mowers at $15 each, I desire to so mark them that I may gain 20%, and still discount 25% and 20% to my customers. At what price must each be marked ?

3. Having paid $8800 for a stock of goods, what price must be asked for it, in order to gain $1100 and allow 12% and 10% discount?

4. After buying velvet at $5 per yard, I so marked it as to allow discounts of 25%, 20%, and 163% from the marked price, and yet so sell it as to lose but 10% on my purchase. At what price per yard was the velvet marked ?

5. The cost of manufacturing silk hats being $36 per dozen, how must they be marked, that a gain of 163% may be realized by the manufacturer, after allowing discounts to the trade of 20% and 12%?

If a carriage be marked 33% above cost, what per cent. of discount can be allowed from the marked price and realize cost?

7. If the list price of an article is 25% advance on the cost, what other per cent. of discount than 10% must be allowed, to net 10% gain by sale ?

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