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8. A merchant purchasing a bill of goods was allowed discounts from the list price of 15%, 10%, 10%, and 6%. If the total discount allowed was $352.81, what must have been the asking price of the goods ?
578. To find a Single Equivalent Per Cent. of Discount, a Discount Series being given.
EXAMPLE.- What single rate of discount is equal to the series 25%, 20%, 10%, and 5%?
OPERATION. $1000 = assumed list price or base.
250 = 1st discount. $750 = 1st rem. or 2d base. 150 = 2d discount.
EXPLANATION. — Assume $1000 as the list
price, and successively deduct the discounts as $600 = 2d rem. or 3d base.
by the series, and compare the result with the 60 = 3d discount.
base assumed, $540 = 3d rem. or 4th base.
27 = 4th discount. $513 = 4th or last rem. or net price.
$1000 = list price, or base.
513 = net price. $487 = total discount on $1000, which, divided by 1000, gives 4876, the per
cent. of discount equivalent to the given series.
Rule.- From $1000 as a list price, or base, take the discounts in order; subtract the final remainder from the base taken, and the result will be the total discount; then point off from its right three places for decimals, and the expression thus obtained will be the equivalent per cent. of discount required.
REMARK.—This is the usual method, and it is more convenient for business men than to compute the net price for each sale through a series of discounts.
EXAMPLES FOR PRACTICE.
579. 1. Find a single discount equivalent to a series of 10% and 10%. 2. Find a single discount equivalent to a series of 25%, 15%, and 5%. 3. Find a single discount equivalent to a series of 30%, 20%, 10%, and 3%.
4. Goods were sold 25%, 35%, 20%, and 15% off ; what single discount would have insured the same net price ?
5. What is the difference between a single discount of 50% and a series of 20%, 20%, and 10% ?
6. What per cent of the list price will be obtained for goods sold at a discount of 35%, 20%, 15%, 10%, and 5%?
7. From a list price, I discounted 30%, 25%, 20%, 15%, 12%, 10%, and 5%. What per cent. better for the purchaser would a single discount of 75% have been ?
580. Storage is a provision made for keeping goods in a warehouse for a time agreed upon, or for an indefinite time, subject to accepted conditions.
581. The term storage is used also to designate the charges for keeping the goods stored.
582. Rates of storage may be fixed by agreement of the parties to the contract, but are often regulated by Boards of Trade, Chambers of Commerce, Associations of Warehousemen, and by legislative enactment.
583. Storage Charges may be made at a fixed price per package or bushel, or at a fixed sum for a term or terms; they may be made for a term of days or months; but usually, if the goods stored are taken out before the storage time expires, the charge made is for the full time.
584. The rates of storage often vary for grains, or goods of different grades or values, and also on account of different modes of shipment.
REMARKS. - Storage Receipts, especially of grains, are frequently bought and sold under the name of “Warehouse Receipts” or “Elevator Receipts,” as representing so much value by current market reports.
585. Cash Storage is a term applied to cases in which the payment of charges is made on each withdrawal or shipment, at the time of such withdrawal or shipment, notwithstanding the fact that the owner may still have goods of the same kind in store at the warehouse.
586. Credit Storage is a term applied to cases in which sundry deposits or consignments are received, from which sundry withdrawals or shipments are made, and all charges adjusted at the time of final withdrawal.
REMARKS.—1. When deposits or consignments, and withdrawals or shipments, are made at different times, credit is to be given for the amount of each deposit or consignment, from the date to its final withdrawal or shipment, and credit given to the owner or consignor for each withdrawal or shipment, from date up to the time of settlement,
2. In the private bonded warehouses of the United States, goods may be taken out at any time, in quantities not less than an entire package, or, if in bulk of not less than 1 ton, by the payment of duties, storage, and labor arges. The storage are computed for periods of one month each, a fractional part of a month being counted the same as a full month.
3. Drovers sometimes hire cattle fed on account, entering and withdrawing them as circumstances require; such accounts are closed in the same manner as are those for storage.
587. To find the Simple Average Cash Storage.
EXAMPLE. — There was received at a storage warehouse : Oct. 11, 300 bar. apples; Oct. 30, 250 bar. potatoes; Nov. 13, 200 bar. apples; Nov. 20, 60 bar. quinces ; Nov. 28, 280 bar. apples. The merchandise was all delivered Dec. 2.
If the contract specified that the rate of storage was 5% per barrel for a period of 30 days average storage, what was the storage bill ?
The storage of 300 bar. for 52 da. = the storage of 1 bar. for 15600 da. The storage of 250 bar. for 33 da. = the storage of 1 bar. for 8250 da. The storage of 200 bar. for 19 da. = the storage of 1 bar. for 3800 da. The storage of 60 bar. for 12 da. = the storage of 1 bar, for 720 da. The storage of 280 bar. for 4 da. = the storage of 1 bar. for 1120 da. The total storage
= the storage of 1 bar, for 29490 da. Or, 983 periods of 30 days each; $.05 X 983 = $49.15, storage bill.
EXPLANATION.—The 300 barrels constituting the first deposit or delivery were stored from Oct. 11 to Dec. 2, or for 52 days; the storage of 300 bar. for 52 days equals the storage of 1 barrel for 15600 days; the storage of 250 barrels for 33 days equals the storage of 1 barrel for 8250 days; that of 200 barrels for 19 days equals 1 barrel for 3500 days; that of 60 barrels for 12 days equals 1 barrel for 720 days; that of 230 barrels for 4 days cquals 1 barrel for 1120 days. The total storage was equal to that of 1 barrel for 29490 days, or for 993 storage terms or periods of 30 days each. Since the storage charge was 5¢ per barrel for each average period of 30 days, the charge would amount to $.05 X 983, or $49.15.
Rule.-Multiply the number of articles of each receipt by the number of days between the time of their deposit and withdrawal; divide the sum of these products by the number of days in the storage period, and multiply the quotient by the charge per period.
EXAMPLES FOR PRACTICE.
588. 1. There was received at a warehouse: May 30, 4000 bu. wheat; June 5, 2600 bu. oats; June 24, 3500 bu. barley; July 18, 5000 bu. corn. If all of this was shipped July 20, what was the storage bill, the charge being 1}4 per bushel per term of 30 days average storage ?
2. A farmer received for pasture: April 30, 12 head of cattle; May 15, 14 head of cattle; May 23, 27 hcad of cattle; June 9, 5 head of cattle; June 30, 8 head of cattle; July 16, 40 head of cattle. All were delivered July 25, and the charges were 75% per head for each week of 7 days average pasturage. How much was his bill ?
589. To find the Charge for Storage with Credits.
EXAMPLE.-The storage charges being 24 per barrel for a month of 30 days average, what will be the bill in the following transaction ? Received.
Delivered. July 19, 100 bar.; July 31, 240 bar.; Aug. 15, 300 bar.; Sept. 12, 200 bar.; Sept. 8, 360 bar.
Oct. 1, 200 bar.
OPERATION. From July 19 to July 31 = 12 da.; 100 bar, stored for 12 da. = 1 bar, stored for 1200 da. July 31
240 bar, received. From July 31 to Aug. 15 = 15 da.; 340 bar. stored for 15 da. = 1 bar, stored for 5100 da. Aug. 15
300 bar. delivered. From Aug. 15 to Sept. 8 24 da.; 40 bar. remaining for 24 da. 1 bar. stored for 960 da. Sept. 8
360 bar, received. From Sept. 8 to Sept. 12 = 4 da.; 400 bar. stored for 4 da. = 1 bar, stored for 1600 da. Sept. 12
200 bar. delivered. From Sept. 12 to Oct. 1 = 19 da.; 200 bar. remaining for 19 da. = 1 bar, stored for 3800 da. Oct. 1
200 bar. delivered.
Total = 1 bar, stored for 12660 da., Or, 422 terms of 30 da. each; $.02 X 422 = $8.44, total storage bill.
EXPLANATION.—100 barrels were stored for 12 days, when 240 barrels were added; these 340 barrels were stored 15 days, when 300 barrels were withdrawn; the 40 remaining barrels were stored 24 days, when 360 barrels were added; these 400 barrels were stored 4 days, when 200 barrels were withdrawn; the remaining 200 barrels were stored 19 days and then withdrawn. The total storage thus equalled that of 1 barrel for 12660 days, or for 422 terms of 30 days each; and since the charge for 1 term is $.02, for 422 terms it would be 422 times $.02, or $8.44, the total amount of the bill.
Rule.-I. Multiply the number of articles first received by the number of days between the date of their receipt and the date of the next. receipt or delivery; add the number of articles of such next receipt, or subtract the number of such delivery, as the case may be, and so proceed to the time of final delivery.
II. - Divide the aggregate storage by the number of days in the storage term, and multiply the quotient by the storage charge per term.
EXAMPLES FOR PRACTICE.
590. 1. What will be the storage charge, at 4° per barrel, for a term of thirty days average, in the following transaction ? Received.
Mar. 1, 100 bar. apples.
Mar. 28, 190 bar. flour.
60 bar. potatoes. Mar. 13, 300 bar. flour.
60 bar. flour.
Apr. 29, 230 bar, flour. 2. A drover hired pasture of a farmer, agreeing to pay $4.20 per head of stock pastured for each average term of 30 days. What was the amount of the bill, the receipts and deliveries being as follows ? Received.
Delivered. June 15, 21 head of cattle.
July 1, 30 head of cattle. June 27, 20 head of cattle.
July 20, 15 head of cattle. July 5, 15 head of cattle.
July 30, 15 head of cattle. July 29, 40 head of cattle.
Aug. 21, the remainder. July 31, 40 head of cattle.
591. To find the Storage where Charges Vary.
Jan. 23, 250 bar.
Mar. 1, 400 bar. 300 bar. The storage charge on the above was, 5% per barrel for the first 10 days or part thereof, and 34 per barrel for each subsequent period of 10 days or part thereof. What sum must be paid in settlement?
OPERATION. Date. Receipts and Deliveries.
Rate. Storage. Jan. 3, received 150 bar.
1 term, 5¢ 5.00 100 remainder. Feb. 1, received 300
in store. Mar. 1, delivered 400 100 bar. stored 40 days, or 4 terms, 14¢ = $14.00
11¢ = 33.00
= $64.00 EXPLANATION.-Of the 250 barrels delivered Jan. 23, 150 barrels had been in store since Jan. 3, 20 days or 2 terms, and the charge was 5 cents plus 3 cents, or 8 cents per barrel, which equals $12 storage. The remaining 100 barrels of the delivery of Jan. 23, had been in store only since Jan. 20, 3 days or 1 term, at 5 cents per barrel, equal to $5 storage. Of the 400 barrels delivered Mar. 1, 100 barrels had been in store since Jan. 20, 40 days or 4 terms, at 5 cents plus 3 cents plus 3 cents plus 3 cents, or 14 cents per barrel, equal to $14 storage; while the remaining 300 barrels had been in store since Feb. 1, 28 days or 3 terms, at 5 cents plus 3 cents plus 3 cents, or 11 cents per barrel, equal to $33 storage. By addition, the total storage is found to be $64.
Rule.-Multiply the number of articles of each delivery by the charge for the term or terms stored, and add the products so obtained.
EXAMPLE FOR PRACTICE.
592. 1. The receipts and deliveries of goods at a storage warehouse were as follows: Received.
Sept. 20, 100 bar.
Sept. 30, 100 bar.
Oct. 10, 100 bar.
Oct. 20, 100 bar.
Oct. 30, 100 bar.
Nov. 20, the remainder. The contract required the payment of 64 per barrel for the present term of 30 days or fraction thereof, and 3¢ per barrel for each subsequent term of 30 days or fraction thereof. Find the storage bill.