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Three graziers hired a piece of land for $60,50. A. put in 5 sbeep for 41 months, B. put in 8 for 5 months, and C. put in 9 for 6j months; how much must each pay of the rent ? Ans. A. $11,25, B. $20, ani C. $29,25.
LOSS AND GAIN.
Loss and Gain is a rule by which merchants estimate the profit or loss in buying and selling goods, and raise or lower the price of them so as to gain or lose so much
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 $100, so is the gain or loss to the gain or loss per cent.
If I buy corn for $0,75 per bushel, and sell it again for $0,80 per bushel, what do I gain per cent, or in laying out $100 ?
Sold at $0,80 per bushel,
$0,05 gain per bushel.
Then, as ,75 : 100,00 :: 05
,75)50000(6,664 = 1. Ans. $6,661%
If I buy cloth at $1,02 per yard, and sell it again at $0,90 per yard; what do I lose per cent, or in laying out $100 ?
If I buy 37 gallons of brandy at $1,10 per gallon, and sell it for $40, what do I gain or lose per
cent? Ans. $1,719 loss.
To know how a commodity must be sold, to gain or lose so much per cent ;-As $100 is to $100 with the profit added, or loss subtracted, so is the price which the commodity cost to the gaining or losing price.
If I buy corn for 80 cents per bushel, how must I sell it o as to lose 15
Ans. $0,68 per bushel.
If I buy cloth at $2,50 per yard; how must I sell it so as to lose 171 per cent?
Questions. What is fellowship? Of how many kinds is fellowship? What is single fellowship? What is the rule ? How does it appear that this will give a right answer? What is double fellowship? What is the rule for it? Why does this give the right answer? What is loss and gain ?.
How is the loss or gain found when the price of the commodity is given ?
Why should this give the answer?
How do you proceed when you wish to know how a commodity must be valued to gain or lose so much per cent? How does it appear that this will give the true answer?
Examples for Practice.
A. and B. have gained by trading, $182 into stock $300, and B. $400; what is each share of the profit ?
Aps A. $78, and 2. Three merchants, A. B. and C. freight a 340 tuns of wine ; 4. loaded 110 tuns, B. 97, a rest. In a storm the seamen were obliged to tups overboard ; how much must each sustain of
Ans. A. 271, B. 244, an 3. A bankrupt is indebted to A. $277,33 $305,17; to C. $152, and to D. $105. His worth only $677,50 ; how must it be divided ?
Ans. A. $223,814 185, B. $246,28791, C. $129 D. $84,739195
4. A and B. venturing equal sums of money, joint trade, $154. By agreement, A. was to ha cent, because he spent his time in the executio project, and B. was to have only 5 per A. allowed for his trouble ?
Ans. SE 5. A man died leaving 3 sons, to whom he b ed his estate in the following manner, viz. to th he gave $184, to the second $155, and to the th but when his debts were paid, there were but $1 what is each one's proportion of his estate?
40,606) 6. A. and B. companied ; A. put in $120, an of the gain ; what did B. put in ?
A 7. Four merchants traded in company ; A. $400 for 5 months ; B. $600 for 7 months ; C. $ 8 months ; and D. $1200 for 9 months; but by tunes at sea, they lost $750 ; What must each m tain of the loss
Ans. A. $94,93696, B. $142,40575, C. $227 D. $284,81049
8. Two merchants enter into partnership months ; A. put into stock at first $200, and at of 8 months, he put in $100 more; B. put in at firs
and at the end of 4 months took out $140. Now at the expiration of the time they find they have gained $526 ; what is each man's just share ?
Ans. A.'s, $192,9577.I, B.'s, $333,041194 9. A. with a capital of $1000, began trade January 1, 1820, and meeting with success in business, he took in B. a partner, with a capital of $1500, on the first of March following: Three months after that, they admit C. as a third partner, who brought into stock $2800, and after trading together till the first of the next year, they find the gain, since A. commenced business, to be $1776,50. How must this be divided among the partners ?
Ans. A's, $157,40,384 B's, 571,83317. C's, 747,19346.
10. A draper bought 60 yards of cloth at $4,50 per yard, 38 yards of cloth at $2,50 per yard, and sold them one with another, at $4,25 per yard; did he gain or lose, and what per cent ? Ans. gained $14,11 per cent.
11. If I buy an article at $1,20 per pound, and sell it at 90 cents per pound, what do I lose per cent ? Ans.$25.
12 If a barrel of potash cost $15, how must it be sold to lose 10 per cent?
Ans. $13,50 13. Bought 30 hogsheads of molasses at $600; paid in duties $20,66 ; for freight $40,78, for porterage $6,05, and for insurance $30,84 ; if I sell it at $26 per hogshead, how much shall I gain per cent ? Ans. $11,695.
DISCOUNT AND EQUATION OF PAYMENTS.
Tut. What is discount?
Pup. Discount, I believe, is an allowance made for the payment of a debt before it becomes due.
1. Tut. Discount is an allowance made by the creditor to the debtor, for the payment of a debt before it becomes due, and is the difference between that sum, due sometime hence, and its present worth. If A. owe B:
$500, payable in 6 months, with interest, after it becomes due, he would, by paying the debt before the 6 months were out, confer a favour on B. for which B. ought to make an allowance, and this allowance is the discount.
2. By the present worth, is meant such a sum, which, put at interest, would in the given time, and at the given rate, amount to the debt then due.
3. It is very evident that an allowance ought to be made for paying a debt before it is due; for if the debtor keep the money in his own hands, he can employ it to his own benefit, while it is of no benefit to the creditor; but if he pay the debt before it is due, he relinquishes this privilege to the creditor, hence the reason of making a discount.
4. Now the present worth is such a sum, which if put to interest, would, in the given time, and at the rate per cent. for which the discount is to be made, amount to the sum or debt then due. At first you might suppose the discount to be the interest on the sum or debt, from the time at which it is paid, to the time at which it is due. But this is not true, for if you cast the interest on the whole debt from the time it is paid to the time when it would become due, and subtract this interest from the whole debt, the remainder, put at interest for the same time and rate, will not amount to the debt, therefore the discount is not so much as the interest on the sum, for the time and rate for which the discount is to be made, but the discount is such a sum, which will be equal to the interest on the present worth for the given time and rate.
Hence the following rule for
As the amount of $100 for the given rate and time is to the given sum or debt, so is $100 to the present worth.
or, As the amount of $100 for the given rate and time is to the give en sum or debt, so is the interest of $100, for the same time, to the discount,