RULE. First find the selling price by Problem 3; then find the marking price by Problem 6, (a.) 3. Bought a piece of broadcloth at $5 per yard, but it being damaged, I am willing to lose 20 per cent. on the cost; how shall I mark it so that I may fall 25 per cent. from the marked price? $5 cost. .20 $1.00 loss. 100 × $4=$5.333, marked price. 4. Paid $4 a pair for a case of boots; how shall I mark the same so that I may fall 10 per cent. from the marked price and yet make 12 per cent. on the cost? 5. Paid $8 each for a case of bonnets; how shall I mark the same so that I may fall 16 per cent. from the marked price and yet make 5 per cent. on the cost? MISCELLANEOUS EXAMPLES IN PROFIT AND Loss. 1. Bought 75 pounds of tea for $37.50 ad sold of it at 48 cents per pound and the remainder at 56 cen's; did I gain or lose? How much? 2. What per cent. do I gain if I buy boots at $3 per pair and sell them at $3.371? 3. Sold flour at $7.50 per barrel and lost 64 per cent. on the cast; for what should it be sold to gain 12 per cent.? 4. Paid $3 per yard for a piece of lace; how shall I mark the same to enable me to fall 10 per cent. from the marked price and yet gain 20 per cent. on the cost? 5. Bought hats at $3 per hat and sold them at $2.50; what per cent. on the cost was lost? 6. Sold a watch for $42 and lost 12 per cent. on the cost what was the cost? 7. Sold cloth at $2 per yard and lost 10 per cent.; should I have gained or lost, and how much per cent., if I had received $2.12 ? 8. Bought a horse for $87.50 and sold him so as to gain 12 per cent.; what did I receive for him? PARTNERSHIP. 310. PARTNERSHIP is the association of two or more persons in business. The company thus formed is called a firm or house. The money or other property invested is called the capital c stock of the company. The profits and losses of the firm are divided among the partners in accordance with their interest in the business. 1200 311. PROBLEM 1. To find each partner's share of gain or loss when their capital is employed equal times. Ex. 1 A and B trade in company; A furnishes $400 and B $800. They gain $300; how shall they share the gain? A furnishes 400 of the stock, .. he is entitled to of the gain, viz. $100. For a like reason B's gain is of $300= = $200. Or we may solve the question as follows: $300 stock; . A's s are of profits == $400 .25 B's hare of profits == $800 X .25 = $200 Entire profits, $1200.25; i. e. the profits = 25 per cent. of the $100 $300 Hence, RULE 1. Multiply the total gain or loss by each partner's fractional part of the stock, and the products will be the respective shares of gain or loss; or, RULE 2. Find what per cent. the total gain or loss is of the whole stock, and then multiply each partner's stock by this per cent. written decimally. 312. PROof. The sum of the shares of gain or loss must equal the total gain or loss. 2. A, B, and C form a partnership; A furnishes $4000, B $5000, and C $6000. They gain $3000; how shall the gain be divided? Ans. A's, $800; B's, $1000; C's, $1200. 310. What is Partnership? What is the company called? What is the capital or stock? How are the profits and losses divided among the partners? 311. Rule for finding the shares of gain or loss? Second rule? 312. Proof? 3. Had the firm in Ex. 2 lost $750, what part of the loss should each partner sustain? How many dollars? 1st Ans. A,; B, }; C, f. 4. A, B, and C engage in trade. A puts in $6000, B $10000, and C $8000. They gain $4000; what is each partner's share? NOTE. These rules are equally applicable to distributing the property of a bankrupt, and many other similar problems. 5. A bankrupt whose property is worth $5000 owes A $3000. B $1500, and C $3500; to what fractional part of the property is each creditor entitled? To how many dollars? 6. Divide $1500 between A, B, and C so that A shall receive $2 as often as B receives $3 and C $5. 7. A, B, and C hire a pasture, for which they pay $90; A pastures 3 cows, B 5, and C 7; what part of the rent shall each pay? How many dollars? 8. A and B hire a pasture for $12; A's horse was in the pasture 43 weeks and B's 73 weeks; what rent shall each pay? 9. A, B, C, and D freight a ship to Canton; A furnishes $3000 worth of the cargo, B $5000, C $7000, and D $11000. They gain $5200; what is each one's share of the gain? 10. A and B form a partnership with a joint capital of $1200, of which A furnishes in cash, and B, for his share, furnishes 160 yards of broadcloth. They lose $300; how shall the loss be divided? What is the price of B's cloth per yard? 313. PROBLEM 2. To find each partner's share of gain or loss when their capital is employed unequal times. Ex. 1. A and B trade in company; A puts in $300 for 8 months, and B $400 for 9 months. They gain $800; what part of the gain belongs to each? How many dollars? A's $300 for 8m.—$2400 for 1m. $6000 for 1m. It is,.., as though the joint stock were $6000 for 1 month, 312. What is the Note? 313. Explain Ex. 1. = of which A put in $2400, and B $3600; hence A is entitled to 3488 = of the gain, and B to 688 ; i. e. A is entitled to } of $800= $320, and B to % of $800 = $480, Ans. Hence, RULE. Multiply each man's stock by the time it is continued in trade, and, regarding the products as the respective shares of stock, and the sum of the products as the total stock, proceed as in Problem 1. 2. A and B engage in trade; A furnishes $4000 for 12 months, and B $6000 for 11 months. They lose $570; what is the loss of each? Ans. A's loss, $240; B's, $330. 3. A, B, and C engage in partnership; A furnishing $600 for 9m., B $800 for 8m., and C $1000 for 12m. They gain $1071; what is each one's share of the gain? 4. A, B, and C hire a pasture for $48. A pastures 3 horses for 8 weeks, B 5 horses for 6 weeks, and C 6 horses for 7 weeks what part of the rent shall each pay? 5. B, T, and C enter into partnership, doing business in the name and signature of B, T, and C. Jan. 1, B puts in $3000, T $4000, and C $2000. May 1, B puts in $2000 more, C $1000, and T takes out $1000. Sept. 1, B takes out $3000, T puts in $2000, and C $2000. At the end of the year they settle, having gained $6400; what is each partner's share of the gain? Ans. B's $2000, T's $2400, C's $2000. 6. Jan. 1, 1860, B commenced business with a capital of $3000. Sept. 1, 1860, wishing to enlarge his business, he took in H as a partner, with a capital of $4000. July 1, 1861, they admit L into the partnership, with a capital of $2500. On the 1st of Jan. 1862, they dissolve partnership, having gained $7550; what is each one's share of the gain? 7. A, B, and C hire a pasture for $92. A pastures 6 horses for 8 weeks, B 12 oxen for 10 weeks, and C 50 cows for 12 weeks. Now if 5 cows are reckoned as 3 oxen, and 3 oxen as 2 horses, what part of the rent shall each pay? How many dollars? 313. Rule for finding the shares of gain or loss when the capital is in for unequal times? 8. A, B, and C hire a pasture for $300. A puts in 10 oxen for 20 weeks, 15 cows for 14 weeks, and 99 sheep for 26 weeks; B puts in 7 oxen for 24 weeks, 12 cows for 20 weeks, and 66 sheep for 25 weeks; C puts in 25 oxen for 8 weeks, 12 cows for 12 weeks, and 33 sheep for 15 weeks. Now, if 11 sheep are reckoned as 1 cow, and 3 cows as 2 oxen, what is the cost per week for a sheep? a cow? an ox? How many dollars does each man pay for sheep? cows? oxen? What part of the rent does each man pay ? How many dollars? Ans. Cost per week for a sheep, 1c; a cow, 16c.; an ox, 24c. A pays for sheep, $37.44; for cows, $33.60; for oxen, $48. B pays for sheep, $24; for cows, $38.40; for oxen, $40.32. C pays for sheep, $7.20; for cows, $23.04; for oxen; $48. A pays $119.04; B, 1= $102.72; C, 83 $78.24. 9. J. Fox and S. Low enter into partnership. January 1, Fox puts in $5000, but Low puts in nothing until May 1; what shall he then put in that the partners may be entitled to equal shares of the profits at the close of the year? = 10. Jan. 1, 1853, A, B, and C form a partnership for 1 year, and each furnishes $3000; Mar. 1, A furnishes $1000 more; June 1, B withdraws $500, and C adds $500; Sept. 1, A withdraws $2000 and C $500, and B adds $1500. Having gained $1000, at the close of the year the partnership is dissolved. What is each partner's share of the gain? 11. A, B, and C traded in company. A at first put in $1000, B $1200, and C $1800; in three months A put in $500 more and B $300, and C took out $400; in 7 months from the commencement of business, A withdrew all his stock out $700, B put in as much as he at first put in, and C withdrew as much as A at any time had in the firm. At the end of a year they found they had gained 10 per cent. on the largest total stock at any one time in trade. What is the total gain? What fractional part shall each have? How many dollars? |