2. Bought a horse for $150, but it being injured, I am willing to lose 6 per cent.; for what shall I sell him?

$150
.0 6

$9.00 loss.

$150-$9=$141, Ans.

This is the same as finding the present worth of a sum due a year hence, discounting interest (Art. 253, Note 2). Hence,

RULE. Multiply the purchase price by the per cent. to be gained or lost, written decimally, and add the product to, or subtract it from, the purchase price.

3. Bought a farm for $4848; for what shall I sell the same to gain 5 per cent.?

Ans. $5090.40. 4. Bought 3cwt. of sugar at 12c.; how shall the same be sold per lb. so as to gain 10 per cent.?

5. Bought a house for $3500, expended $750 in repairing it, and then sold it so as to lose 15 per cent. on the whole cost; what did I receive for it?

307. PROBLEM 4. To find the first cost of an article, the selling price and gain or loss per cent. being given. Ex. 1. Sold wheat at $1.50 per bushel, and thereby gained 25 per cent. on the cost; what was the purchase price?

2. Sold apples at $1.80 per barrel, and thereby lost 10 per cent. on the cost; what was the cost?

of $1.80 $2, Ans.

The cost was = of the selling price, .. the cost was of $1.80 $2. Hence, =

RULE. Make a fraction by writing 100 for a numerator, and 100+ the gain per cent., or 100— the loss per cent., for a denominator; then multiply the selling price by this fraction.

306. Rule for finding the selling price, the cost and gain or loss per cent. being given? 307. Rule for finding the first cost, the selling price and gain or loss per cent. being given?

3. Sold 6 yards of cloth for $26.88, and gained 12 per cent. on the cost; what was the purchase price per yard? Ans. $4.

4. Sold 10 shares of the Fitchburg R. R. Stock for $1090, gaining 9 per cent. on the cost; what did I pay per share?

5. By selling 25 lb. of sugar for $2, I lose 20 per cent. on the cost; what was the cost per lb. ?

308. PROBLEM 5. The selling price of goods, and the gain or loss per cent. being given, to find what would be gained or lost per cent. if sold at some other price.

Ex. 1. Sold a pair of oxen for $175 and gained 5 per cent. ;

what per cent. should I have gained if I had sold them for $200?

2. Sold a farm for $5000, and thereby made 25 per cent.; should I have gained or lost, and how much per cent., if I had sold it for $3500 ?

5000

3888=35=7o; fo of 12587; 100-871=121= loss per cent., Ans.

The proposed price is found to be 87 per cent. of the cost, ..there would be a loss of 12 per cent. if the farm were sold for $3500. Hence,

RULE. Make a fraction by writing the proposed price for the numerator, and the actual price for the denominator, then multiply the per cent. at which the article is sold by this fraction, and the product will be the per cent. at the proposed price. The difference between the product and 100 is the gain or loss per cent. at the proposed price.

308. Rule for finding gain or loss per cent. when goods are sold at a proposed price?

3. Sold flour at $7 per bbl. and thereby gained 12 per cent.; what per cent. should I have gained if I had sold it at $7.25? Ans. 16 per cent.

4. Sold beef at $6 per cwt., and thereby lost 4 per cent.; should I have gained or lost, and how much per cent., had I sold it at $6.50?

5. Sold a watch for $21, and gained 5 per cent. on the cost; had I sold it for $18 should I have gained or lost, and how much per cent. ?

309. PROBLEM 6. To mark goods so that the merchant may fall a certain per cent. on the marked price and yet sell the goods at cost, or at a certain per cent. above or below cost.

(a) To sell at cost.

Ex. 1. How shall I mark a coat that cost me $18 so that I may fall 10 per cent. from the marked price and yet sell the coat at cost? 100 =1o; 1o of $18

=

$20, Ans. Since I am to fall 10 per cent., it follows that the cost, $18, is only of the marked price, and if $18 is then

will be of $18=$2, and 18 will be 10 times $2= $20; i. e. the marked price will be 0 of $18 = $20, Ans.

PROOF. 10 per cent. of $20.

leaves $18, the cost. Hence,

= $2, which taken from $20

RULE. Make a fraction by writing 100 for the numerator, and 100 diminished by the per cent. to be abated for the denomi nator; multiply the cost by this fraction, and the product will be the marked price.

2. Bought a case of watches at $23.50; at what price shall I mark them to enable me to abate 6 per cent., and yet sell them at cost? Ans. $25.

(b) To sell at a certain per cent. above or below

cost:

309. Rule for marking goods so as to fall a certain per cent. and yet sell at cost? To sell at a given per cent. above or below cost?

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?

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 and sold of it at 48 cents per pound and the remainder at 56 cents; 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 $3.371⁄2?

3. Sold flour at $7.50 per barrel and lost 64 per cent. on the cost; 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 $2.121?

8. Bought a horse for $87.50 and sold him so as to gain 12 per cent.; what did I receive for him?

310.

PARTNERSHIP.

PARTNERSHIP is the association of two or more per

sons in business.

The company thus formed is called a firm or house.

The money or other property invested is called the capital or stock of the company.

The profits and losses of the firm are divided among the partners in accordance with their interest in the business.

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 1200 = of the stock,.. he is entitled to 3 of the gain, viz. $100. For a like reason B's gain is of $300=$200. 景 Or we may solve the question as follows:

$300

$1200.25; i. e. the profits 25 per cent. of the stock; A's share of profits

B's share of profits

$400 × .25 = : $100 = $800 X .25 = $200 Entire profits,

$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?