Tare is an allowance for the weight of the cask, and is generally at a certain rate per cwt. or per barrel, &c. Tret is an allowance for the waste by dust, and is generally at the rate of 4 lb. per &c. y 104 th an Cloff is an allowance made the buyer for the turn of the scale, and is generally at 2 lb. per 3 cwt. Gross is the whole weight of the goods, together with the weight of the cask, or box, &c. that contains them. Suttle is when part of the allowance is deducted. Neat is the remainder after all deductions are made. CASE I. When the tare is at a certain rate per hhd. C. RULE.-Multiply the tare per box, or hhd. by the number of boxes, &c. subtract the product from the gross weight, the remainder is the neat weight required. Examples. 1. What is the neat weight of 3 hhd. of tobacco, weighing in all 13 cwt. 2 qr. 27 lb.; tare at 1 cwt. 1 qr. per hhd.? cwt. gr. lb. cwt. qr.. cwt. gr. lb. 13 2 27-1 27 Ans. 2. What is the neat weight of 910 bags of India sugar, each weighing 1 cwt. 2 qr. 20 lb.; tare at the rate of 15 lb. per bag? Ans. 1405 cwt. 2 qr. 14 lb. CASE II. When the tare is at a certain rate per cwt. RULE.-If the rate per cwt. is an aliquot part, divide the gross by the aliquct part, or parts, and the quotient, or quotients will be the tare of the whole, which must be subtracted from the gross ; the remainder will be the neat weight required. Examples. 1. What is the neat weight of 19 cwt. 3 qr. 26 gross; tare at 2 qr. per cwt.? lb. 2. What is the neat weight of 347 bags of sugar, each weighing 2 cwt. 3 qr. 12 lb.; tare 21 lb. per Ans. 926 cwt. 1 qr. 13 lb. bag? CASE III, When the tare is at a certain rate per cwt, and is RULE. Say by single proportion as 112 lb. is to the rate per cwt. so is the number of lbs. gross to the tare required; which being subtracted from the gross, the remainder is neat. Examples. 1. What is the neat weight 38 cwt. O qr. 4 lb. of tobacco; tare at 11 lb. per 112 lb.? When tare and tret are allowed. RULE. Find and subtract the tare, as in the preceding cases; the remainder is suttle, divide the suttle by 26 (N. B..) The quotient is the tret, which subtract, and the remainder is the neat weight. lb. cwt. gr. lb. and 550-21528 neat 4 2 2424 Ans. 2. What is the neat weight of 21 cwt. 1 qr. 26 lb. of rice; tare 15 lb. per cwt.; and tret 4 lb. per 104? Ans. 17 cwt. 3 qr. 16† Ib. CASE V. When tare, tret and cloff are allowed. RULE. Find and subtract the tare and trét as in the preceding cases, and divide the remainder by 168 the quotient is cloff, which subtract, and the remainder is the neat weight sought. Examples. 1. What is the neat weight of 10 cwt.; tare 14 lb. per cwt.; tret 4 lb. per 104; and cloff 2 lb. per every 3 cwt.? 10 Cwt 1120 lbs. [1 qr. 14 lb. Ans. 2. What is the neat weight of 12 cwt. 2 qr.; tare 7 lb. per cwt. ; tret 4 lb. per 104; cloff 2 lb. per 3 Ans. 11 cwt. 0 qr. 24+ lb. cwt.? DISCOUNT. DEFINITION. Discount is a sum of money abated for the ready payment of money due at a future time. CASE I. RULE. As the amount of 100 dollars for the time given is to 100 dollars; so is the given sum, to its present worth subtract the present worth from the given sum, the remainder is the discount. Examples. 1. A. owes B. 1000 dollars payable in one year; A. offers to pay the ready money if B. will make discount, t 6 per cent.; I demand the discount to be made. As 106 100: 1000: 943-39% present worth. NOTE. It is thought by many, that the interest of the sum for the time, is the discount which ought to be nade; but this is an error. I shall here observe if B. ad discounted the interest of 1000 dollars for a year, the discount would have been 60 dollars; and he would have had but 940 dollars in ready money, which allow him to receive, and put at interest to a third person; and at the end of a year he would receive but $996.40 cents for the 1000 dollars; therefore he receives $3.60 less, than he would have received of A. had it remained in his hands; but allow B. to receive 943 39,66 cents of A. in ready money; and put it at interest to D. in one year it would amount to just 1000 dollars; Therefore by this rule neither party suffers any injury. 106 2. What discount must be made on 560 dollars due in 9 months; discount at 8 per cent. per annum? Ans. $31.69,86 cts. RULE II. As the amount of 100 dollars for the time and rate per cent. is to the interest of 100 dollars for the time and at the rate per cent so is the given sum to the discount to be made. Examples. 1. What is the discount upon 1000 dollars due in a year; at 6 per cent per annum ? : dols, cts. As 106 : 6 :: 1000 56-60,40 Ans. 2. What is the discount upon 560 dollars due 9 months hence; at 8 per cent. per annum ? 106 Ans. $31.69,86 3. What is the discount upon 75 dollars due in 3 years; at 3 per cent. per annum ? Ans. $6.19 29 109 EQUATION OF PAYMENTS. DEFINITION.-The use of this rule is to find a cer tain time to make a payment of several sums of money at once, due at several different times. RULE.-Multiply each separate payment by the time when it would become due; add the several products together for a dividend; add the several separate payments together for a divisor; divide, and the quotient is the equated time. Examples. 1. A. owes B. 100 dollars payable in 9 months: 72 dollars payable in 6 months: and 200 dollars pay able in 22 months in what time may A. pay all the notes at once, that neither party shall not be liable to suffer any harm? |