7. LOSS AND GAIN. "Loss and Gain is a rule which enables merchants to estimate the profit or loss in buying and selling goods; also to raise or fall the price of them, so as to gain or lose so much per cent.' CASE I. To know what is gained or lost per cent. First, find what the gain or loss is by subtraction, then as the price it cost is to the gain or loss, so is $100 (or £100) to the gain or loss per cent. CASE II. To know how a commodity must be sold to gain or lose so much per cent; As 100 dollars (or £100) is to the price; so is 100 dollars (or £100) with the profit added or the loss subtracted to the gaining or losing price. 3. If 120lb. of steel cost £7, how must I sell it per lb. to gain 15 per cent? Ans. 1s. 4d. per lb. SUPPLEMENT TO LOSS AND GAIN. QUESTIONS. 1. What is Loss and Gain ? 2. Having the price at which goods are bought and sold, how is the loss or gain estimated ? 3. To know how much a commodity must be valued at to gain or lose so much per cent, what is the method of procedure? 4. How may questions in Loss and Gain be proved? EXERCISES. 1. A draper bought 100 yards of broadcloth for £56. I demand how he must sell it per vard to gain £15 in laying out £100? Ans. 12s. 10d. 2g. 2. Bought 30 hogshads of for freight $40,78; for portera sell it at $26 per hog, how asses at $600; paid in duties $20,66; $6,05, and for insure, $30,84; If I much shall I gain per gent? Ans. $11,695. § 8. DUODECIMALS; OR, CROSS MULTIPLICATION. This rule is particularly useful to Workmen and Artificers in casting up the contents of their work. Dimensions are taken in feet, inches and parts. Inches and parts are sometimes called primes (') seconds (") thirds (") and fourths ("") TABLE. By this rule also may be calcula ted the solid contents of bodies, naving the measures of their different sides, and is very useful therefore in measuring wood. RULE. 1. Under the multiplicand write the corresponding denominations of the multiplier. 2 Multiply each term in the multiplicand, beginning at the lowest, by the feet in the multiplier, and write the result of each under its respective term, observing to carry an unit for every 12, from each lower denomination to its superior. 3. In the same manner multiply the multiplicand, by the inches in the multiplier, and write the result of each term in the multiplicand, thus multiplied, one place to the right hand in the product. 4. Proceed in the same manner with the other parts in the multiplier, which if seconds, write the result two places to the right hand; if thirds, three places, &c. and their sum will be the answer required. The more easily to comprehend the rule-NOTE. Feet multiplied by feet EXAMPLES. 1. Multiply 7 feet, 3 inches, 2 seconds, by 1 foot, 7 inches and 3 seconds. OPERATION. F. I. 732 173 732 m 4 2 10 2 1996 Prod. 11 7 9 116 give feet-Feet multiplied by inches give inches-Feet multiplied by seconds give seconds-Inches multiplied by inches give seconds-Inches multiplied by seconds give thirds-Seconds multiplied by seconds give fourths. Here I multiply the 7f. 3in. 2" by the 1f. in the multiplier, which gives seconds, inches and feet. Next I multiply the same 7f. 3in. 2" by the 7in. saying 7 times 2 is 14 which is once 12 and 2 over, which (2) I set down one place to the right hand that is in the place of thirds and carry one to the next place and proceed in the same manner with the other terms. Lastly, I multiply the multiplicand by the 3" saying 3 times 2 are 6, which I set down two places to the right hand and so proceed with the other terms of the multiplicand. The "m of all the products is the answer. |