169. A speculator sold a quantity of teas, coffees and spices. His gain on the teas was equal to his gain on the coffees and spices together; his gain on spices was 75% of his gain on coffees, plus 50% of his gain on teas; and his gain on coffees was $40. What was the total profit? 170. A man ordered a quantity of Brussels carpet to cover the floor of a room. The dimensions of the room as given to the carpet dealer were 193 feet in length and 9 in width. The dealer found that by true measurement the dimensions given were 14% less than the actual length of the room, and 55% more than its width. The dealer charged $1.80 per yard for the carpeting, which was of a yard wide and at 20% above cost. What did he gain by the transaction, the proper quantity of carpet being furnished?

171. If a man lose 25% of a lot of apples, what must be his % of gain on the remainder to net a gain of 25% on the cost of the whole?

172. A fruit dealer bought 530 crates of peaches at 95 cents per crate, and sold 150 crates at a gain of 20%, 75 crates at a gain of 12%, 50 crates at cost, 200 crates at a loss of 5%, 25 crates at a loss of 50%, and threw away the remainder as worthless. What was his net gain or loss?

173. A grain dealer purchased 3500 bushels of wheat at $1.30 per bushel, 25% more oats than wheat at 53 cents per bushel, and 40% less rye than oats at 95 cents per bushel. He sold the wheat at 10% advance, the oats at 121%, and the rye at 15%. What was the total gain?

TRADE DISCOUNTS.

INDUCTIVE EXERCISE.

1. If a merchant's prices are based upon sales of less than $100 and on 60 days' credit, with a discount of 10% on all sales over $100 and less than $200, what is the net price of a bill amounting to $150? If a further discount of 2% be allowed upon this net price for payment in cash, what will be the net cash price?

2. What is the net price of a bill of goods amounting to $400 if subject to a discount of 10% and 10%? Of 25% and 20% ? Of 20% and 10%?

[a] The invoice price, gross price, or marked price, is the base.

[b] The discount and net price are percentages, of which the rate of discount and of net price are the respective rates.

[c] Gross price × rate of discount or of net price = discount or net price.

7. What is the net cost of hardware invoiced at $460, and subject to

a discount of 20%, 10%, and 5%?

8. The gross amount of a bill of goods is $750.35, and the rates of discount are 10%, 10%, and 5%. What is the net cost?

9. An invoice of crockery amounting to $1575.50 was sold Jan. 18, 1883, payable in 90 days, and subject to a discount of 20% and 10%, with an additional discount of 1% if paid in 60 days, 2% if paid in 30 days, or 3% if paid within 10 days of date of purchase. How much will pay the bill on Feb. 20, 1883 ?

10. A and B offer the same quality of hats at the same list price, but A offers a discount of 10% and 5%, and B a single discount of 15%. Of whom will it be more advantageous to buy, and how much will be saved in an order the gross amount of which is $185.50 ?

11. A's list price of a certain quality of pocket-knives is $9 per dozen, 20% and 5% off; and B's list price of the same quality of knives is $9.50 per dozen, 25% and 10% off. How much will be saved by ordering 15 dozen knives from B?

12. The gross amount of a bill of tinware is $275.30, of which $75 is sold at a discount of 25% and 10%; $150 at 20% and 5%; and the remainder at 10% and 5%. What is the net amount of the bill?

Reduce the following discount series to equivalent single discounts: 13. 10% and 5%. 17. 30%, 10%, and 5%.

21. What is the difference between a discount series of 10%, 5%, and 2%, and a direct discount of 17% ?

22. What is the difference between a discount series of 30% and 10%, and a single discount of 40%?

23. What is the difference between a discount series of 30%, 10%, and 5%, and a single discount of 55% ?

24. What single discount is equivalent to the series 25%, 20%, and 10%?

[d] Net price rate of net price = marked price.

Find the marked price.

Find the marked price.

27. $2.88 per gross,

20%, 10%.

32. $30 per case,

28. $14.58 per doz., 40%, 29. $12 per bbl.,

10%, 10%.

33. $3.60 per pair,

10%, 10%.

[e] Discount ÷ marked price = rate per cent. of discount.

Find the rate % of discount from marked price to net cost.

51. What must be a jobber's list price of axes costing $7.50 per dozen, that a discount of 20%, 10%, and 5% may be offered on the list price, and net a profit to the jobber of 10% ?

52. In a closing out sale, a jobber desires to sell dishes costing $5 per dozen at 10% loss, and offers a discount series of 30% and 20% on the marked price. At what price per dozen should the dishes be marked?

53. The net cost of 240 yards of dress goods is $126.36. What was the gross charge per yard, if purchased subject to a discount of 10%, 10%, and 21%?

54. The marked price of a set of furniture costing $120 was $150. What per cent. of discount can be offered to have the furniture net its cost?

55. The cost of manufacturing a certain kind of cooking stoves is $15 each. What must be the manufacturer's list price that he may offer a discount thereon of 20% and 5%, and still realize a profit of 10%? 56. What must be the marking price of clothing which cost $18 per suit, that a discount of 10% may be offered on the marked price, and yet net cost to the seller?

57. The net cost of 500 yards of dress goods is $243. What was the gross price per yard, if purchased at a discount of 10% and 10%?

58. A merchant bought 240 yards of linen at 30 cents per yard, and 640 yards of calico at 6 cents per yard. He marked the linen 25% above cost and the calico 60% above cost. He sold 200 yards of linen at 10% gain, and 500 yards of calico at 20% gain. How much less than the marked price did he obtain for the goods sold; and what rate per cent. of discount did he allow upon the marked price of each article?

59. A cabinet-maker directed his salesman to mark a set of furniture so that, by allowing 20% on the marked price, he would realize a gain of 25%. The salesman marked the set by mistake $200, or at a loss to the dealer of 20% of the sale. At how much less than the required marking price were the goods marked by mistake?

60. If I buy augers at $2.50 per dozen and mark them at 60% above cost, what rate of discount can I allow on the marked price and net cost?

61. A retail dealer in notions marked a lot of handkerchiefs at 30 cents each, or at a profit of 20%. 6 of them becoming soiled, he offered them at a discount of 20% on the marked price, expecting thereby to net cost. What was his loss?

62. A merchant bought a quantity of goods at a certain gross price with 20% and 10% off, and sold them at the same gross price with 10% and 5% off. What per cent. of profit did he make?

63. If I buy goods at a given list price with 10%, 10%, and 5% off, and sell them at the same list price with 10% and 10% off, what per cent. of profit do I make?

64. If I wish to net 644% of my catalogue price, what third rate % of discount must I add to 20% and 10%?

65. What third rate % of discount should be combined with 25% and 20% that the series may equal a single discount of 43% ?

66. Goods which cost $2.38 per yard were marked $2.80 per yard. What rate % of discount on the marked price will enable the seller to realize cost?

67. If goods are marked at a profit of 25%, what per cent. of discount should be allowed on the marked price to net cost?

68. A merchant bought a bill of goods upon which the total discount was $318, the discount series being 20%, 20%, and 10%. What was the net price of the goods?

69. If goods are sold at their marked price, the rate of profit will be 20%. What will be the rate of profit if the same goods are sold at 10% discount on their marked price?

70. If a jobber's prices are based upon sales on 60 days' credit and amounting to less than $100 gross, with a discount of 10% on all sales from $100 to $500, a second discount of 10% on all sales from $500 to $1000, a third discount of 5% on all sales over $1000, and a further discount of 2% for cash payment, what is the net cash price of a bill of goods amounting to $1865 gross? Amounting to $400 gross? What is the net price of a bill amounting to $800 gross and sold on 60 days' credit?

71. If the retail price of sewing machines be $30 each, subject to a discount of 20% in favor of the local agent, a second discount of 10% in favor of the State agent, and a third discount of 5% in favor of the general agent, what will be the general agent's compensation on each machine sold to the State agent? The State agent's compensation on 8 machines sold to the local agent?

72. A dealer bought merchandise at a fixed price with 20% and 10% off, and sold them at the same fixed price with 10% off, netting a total gain of $66.60. What did the dealer pay for the goods sold?

73. Considering each of the following columns as a separate question, if the terms marked are given how may the term marked ? be found;