CASE IV.

ART. 73. A number being given which is a given per cent. more or less than another number, to find the required number. Ex. 1. Sold broadcloth at $5 per yard and made 25 per cent.; what did the cloth cost per yard?

1.00

.25

1.25)5.00

$4. Ans.

Explanation.-Since I gain 25 per cent., I receive 125 cents for every 100 cents the cloth cost; hence the cloth cost as many times 100 cents as I receive times 125 cents, which is 4, and 4 times 100 cents is $4.

Or thus:

Since I gain 25 per cent., the sum received is 125 per cent. of the cost; hence, $5 is 12% of the cost, which is found by dividing by 1.25.

When the given per cent. is a convenient part of 100, it may be solved by using the common fraction; thus,

+1=; hence, $5 is Ex. 2. A drover lost ease, and then had 2200;

100

12

88)2200 25

25 × 100-2500 Ans. X

Or,

• 2200 × 100 88

=2500 Ans.

of the cost.

12 per cent. of a flock of sheep by dishow many sheep in the flock at first?

Explanation.-Since he lost 12 per cent. of his sheep, for every 100 sheep at first there remained but 88; hence, the flock at first contained as many times 100 sheep as there remained times 88, or 25 times 100 sheep=2500 sheep. Or thus:

Since he lost 12 per cent, of his flock, there remained 88 per cent.; hence, 2200 sheep must be of his original flock, which is 2500 sheep.

100

RULE.

Divide the given number by 100, increased or diminished by the rate per cent., and multiply the quotient by 100. Or, Divide the given number by 1, increased or diminished by the rate per cent. expressed decimally.

Examples.

3. 168 is 20 per cent. more than what number? Ans. 140. 4. $63.75 is 15 per cent. less than what? Ans. $75. 5. The population of a certain city is 25000, which is 25 per cent. more than it was in 1850; what was the population in 1850 ? Ans. 20000.

6. A grocer sells flour as follows:

Extra Family, $5.50 per bbl.

and makes a profit of 12 per cent. ; what was the cost of each brand? Ans. to last, $3.777.

7. A cargo of corn being injured, the owner was obliged to sell the same for $28000, which was at a loss of 30 per cent.; what was the cost of the cargo ? Ans. $40000.

at

8. The sales of a dry goods firm amount to $90000 per year; of the sales were made at a profit of 25 per cent.; a profit of 35 per cent.; and the remainder at a profit of 20 per cent.; what was the cost of goods?

Ans. $71300.

APPLICATIONS OF PERCENTAGE.

ART. 74. The four preceding cases underlie the whole subfect of Percentage in all its numerous and important applications. The importance of fully understanding them can not be urged too strongly upon one who wishes to become a competent accountant. It is not enough to be able to solve the examples in accordance with the directions of the rules. Rule accountants are always liable to make serious errors. Do I see clearly why such a process gives the required result? To this question the student should be able to give an affirmative answer.

There is such a thing as common sense, and the use of it in solving practical business problems is a sine qua non. The answer of almost any question may be anticipated, at least approximately, previous to its solution. The common-sense

student sees from the conditions of the question about what answer he may expect. In solving a problem in discount, for example, he knows whether the present worth will be nearest $3, $30, or $3000. I have often known rule students" to hand in the most ridiculous answers to the simplest practical problems.

PROFIT AND LOSS.

ART. 75. The price paid for an article, or the total expense of producing it, is its cost; the amount received for an article by the vender is its selling price. It is evident, from this, that the selling price of the vender, or salesman, may be the cost of an article to the purchaser.

When an article is sold for more than its cost, there is a profit, or gain; when it is sold for less than its cost, there is a loss. The actual gain or loss is the amount of this increase or decrease.

Profit or loss is generally computed as a given amount upon every hundred, or at a given rate per cent. The rate per cent. is the number of hundredths of the cost gained or lost.

Profit and Loss, though usually, are not always limited to transactions in money. When any quantity, whether it is money, or goods, or time, distance, or any thing else, undergoes an increase or decrease, there is gain or loss, and it may be computed at a rate per cent.

ART. 76. All the problems in Profit and Loss come under one or more of the four following cases, which correspond to the four cases of Percentage, already explained.

1. The cost and the per cent. of gain or loss being given, to find the selling price.

RULE.-Multiply the cost by the rate per cent. of gain or loss expressed decimally; the product will be the gain or loss. The cost increased by the gain or diminished by the loss will be the selling price.

2. The cost and the selling price being given, to find the per cent. of gain or loss.

RULE.-Divide the gain or loss by the cost, and express the quotient decimally.

3. The actual gain or loss, and the per cent. of gain or loss being given, to find the cost.

RULE.-Divide the gain or loss by the per cent. of gain or loss, and multiply the quotient by 100.

4. The selling price and the per cent. of gain or loss being given, to find the cost.

RULE. Divide the selling price by $1 increased or diminished by the rate per cent. expressed decimally.

Note.-Keep in mind that gain or loss is computed upon the COST.

Examples.

1. For how much per bbl. must I sell flour costing $4.50 per bbl., to gain 163 per cent. ?

Explanation. It must be sold for the cost plus 163 per cent. of the cost (found according to Case I., Percentage); or, since 163 per cent., it must be sold for the cost plus of the cost.

Remark. When the given per cent. is a convenient part of 100, it is best to use the common fraction, instead of the given per cent.

2. A man offers a farm, for which he gave $3450, for 20 per cent, less than its cost. What is his price?

Explanation. He offers it for the cost minus 20 per cent. of the cost; or, since 20 per cent., he offers it for the cost minus of the cost, or $2760.

3. How must I sell sugars that cost $7, $8.25, and $10.50 per cwt. to gain 12 per cent. ? Ans. to last, $11.81}.

4. Bought linen cloth for 45 cents, 50 cents, and 62 cents. per yard; for what per yard must I sell it (being damaged) to lose 18 per cent. ? Ans. to last, 51 cts. cost $3.75 per yard for Ans. 330.

5. A merchant is selling cloth that $5; what per cent. is his profit ?

=

Explanation. He gains $5.00-$3.75 $1.25 on each yard, or on $3.75, which (Case II. Percentage) is 33 per cent.;

or, since he gains $1.25 on $3.75, his gain is or of the cost, or 331 per cent.

6. A grocer sells coffee that cost 15 cents per lb. for 12 cents per lb.; what is his loss per cent. ? Ans. 200. Remark. The simple question in this problem is, what per cent. of 15 is 3?

7. A grocer sells tea costing 62 cents per lb. for 75 cents; sugar costing 9 cents for 12 cents; flour costing $5.20 for $5.75. What does he gain per cent. on each article? Ans. to last, 101%.

8. Bought a horse for $130, paid for its keeping, two months, $6, and then sold it for $124; what per cent. was my loss ? Ans. 8140%. 9. A merchant made a profit of $156 by selling a quantity of silks at a gain of 12 per cent. What was the cost of the silks, and for how much were they sold? Ans. $1300 cost. Explanation.-Since he gained 12 per cent., or of the cost, $156 must be of the cost, which (Case III. Percentage), is $1300; $1300+$156=$1456, selling price.

12

100

10. A grocer bought a lot of apples, and sold them at 30 per cent. profit, by which he gained $36.60. How much did. they cost him, and for how much did he sell them?

Ans. Cost $122; sold for $158.60.

11. Sold a cargo of wheat for $16000, at a profit of 25 per cent. What was the cost of cargo ?

Explanation.-$16000 is 25 per cent.

Ans. $12800. more than what

number? (Case IV. Percentage). Or thus:

25

25 per cent. or =, I must have sold it for

100

54

Since I gained

of the cost. 12. Gould & Brown sold a lot of goods for $16500, at a profit of 331 per cent. What did the goods cost them? Ans. $12375.

13. Sold tea at 90 cents per lb., and gained 20 per cent. What per cent. should I have gained had I sold it for $1.00 per lb. ? Ans. 331

Note. This example involves Case IV. and Case II. of Percentage. First find the cost and then the gain per cent. on the cost by selling for $1.00 per lb.