end of 2 months withdraws $200; C furnishes $650, and at the end of 6 months $400 more. At the end of a year they realize a profit of $2516. How shall it be divided among them?

4. Two partners, A and B, begin business with capitals of $3500 and $8700, and A is to have .12 of the profits

for managing the business. How shall a profit of $1906.25 be divided between them?

?

5. A puts $2100 into a business, and B $1750. At the end of a year each puts in $700 more, and C joins them with $2500. At the end of 18 months from this time how shall a profit of $2166.50 be divided? 6. Three graziers hire a pasture, for which they pay $132.50. One puts in 10 oxen for 3 months, another 12 oxen for 4 months, and the third 14 oxen for 2 months. How much of the rent ought each to pay 7. A begins business, with a capital of $2400, on the 19th of March; and on the 17th of July admits B as a partner, with a capital of $1800. Dec. 31 the profits are $943. What is the share of each? 8. A and B join capitals in the ratio 7:11. At the end of 7 months A withdraws of his, and B of his; and, after 11 months more, they divide a profit of $5148.50. What is the share of each?

9. Divide £65 9s. among three persons, so that the first may have as many half-crowns as the second has shillings; and the second as many guineas as the third has pounds.

10. Two partners begin business each with a capital of

$2000. A adds $500 at the end of 2 months, and $500 more at the end of 7 months; B adds $800 at the end of 3 months. What is the share of each, at the year's end, of a profit of $3605.25?

CHAPTER XVI.

PERCENTAGE.

343. In considering the increase or decrease in quantities, it is usual to employ, as a common standard of reference, the number 100.

Thus, if the population of a town at one census were 1200, and at the next 1500, the increase would be 300 in 1200; that is, 25 in every 100; or, as it is generally expressed, 25 per cent.

344. The symbol % is used for the words per cent.

345. The representative number resulting after an increase has taken place will be 100+ increase per cent; and after a decrease has taken place will be 100 - decrease per cent.

346. The representative numbers in any particular case may be changed to quantities by applying them all to the same unit of quantity.

Thus, if gunpowder be said to contain 75% of saltpetre, the meaning is, that if the number 100 be taken as the representative of the whole weight, the number 75 will represent the weight of saltpetre in it; and if the numbers be applied to any unit of weight, as a pound, the meaning will be, that 100 lbs. of gunpowder will contain 75 lbs, of saltpetre.

(1) Ten years ago the population of a city was 26,275, and has increased 20%. What is its present population?

If 100 be taken to represent the population ten years ago, 100+20 will represent the present population.

Therefore, the present population will be 128 of 26,275 = 31,530.

Ans.

(2) Ten years ago the population of a city was 26,275; its present population is 31,530. Determine the increase per cent.

31,530 - 26,275-5255, actual increase.

Since the increase on 26,275 is 5255, the increase on 100 is 100 of 5255 = 20.

The increase, therefore, is 20%. Ans.

(3) A town, after decreasing 11%, has 4539 inhabitants. Find its number at first.

If 100 be taken to represent the population at first, 100–11 = 89, will represent the present population.

Therefore, the population at first was 100 of 45395100. Ans.

89

(4) In a certain school there are 200 girls, and the girls are 40% of the whole number of pupils. How many pupils in the school?

If 100 be taken to represent the whole number of pupils, 40 will represent the number of girls.

Therefore, the whole number of pupils is 100 of 200=500.

Ans.

(5) 50 lbs. is what per cent of 450 lbs. ?

40

If 100 be taken to represent the whole weight, the number required to represent 50 lbs. will be of 100 = 11}.

That is, 11% Ans.

50

450

347. In the process of computing by the hundred, it is generally more convenient to use 1 as the representative number, and to express the per cent as hundredths.

Thus, in example (1), if the number 1 be taken to represent 26,275 inhabitants, 1.20 will represent the number of inhabitants after an increase of 20%; and the present population will be 1.20 of 26,275 = 31,530. Ans.

In example (2), if the number 1 be taken to represent 26,275, the increase will be represented by 5255 ÷ 26,275=.20. Ans.

In example (3), if 1 be taken to represent the population at first, .89 will represent its present population. That is, 4539 is .89 of the former population. Therefore, the former population was 4539 ÷.89

-5100.

In example (4), if the number 1 be taken to represent the whole number of pupils, 200 will represent .40 of the whole number. Therefore, the whole number will be 200÷.40 500. Ans.

=

In example (5), if the number 1 be taken to represent 450 lbs., 50 lbs. will be represented by of 1= .11}. Ans.

EXERCISE LXVII.

1. The population of a town in 1870 was 12,275, and it increased 8% in the next ten years. Find its popu

lation in 1880.

2. How much metal will be obtained from 365 tons of ore, if the metal be 7% of the ore?

3. If gunpowder contains 75% of saltpetre, 10% of sulphur, 15% of charcoal, how much of each is there in a ton of powder?

4. A manufactory uses 24 tons of coal a day, and 20% of it is lost in smoke. How much coal would be needed if this waste could be prevented?

5. Air consists of 20.0265% (by measure) of oxygen gas and 79.9735% of nitrogen. How much oxygen in 1750 cu. ft. of air?

6. A town, after decreasing 25%, has 4539 inhabitants. Find its number at first.

7. 2% of a regiment of 750 men are killed in an engagement, 6% are wounded, and 4% are missing. What is the number still available for service?

8. If 3 tons of sulphur are required to make 311 tons of gunpowder, what is the per cent of sulphur in gunpowder?

9. In a school of 80 children, 17% are girls. Find the number of boys.

10. If goods are bought for $415, and sold for $500, what is the gain per cent?

11. If goods are bought for $415, and sold for $400, what is the loss per cent?

12. $500 is 4% of what number?

13. A farmer buys 24 head of cattle at $80 a head, and, after losing 6, sells the remainder at $105 a head. How much does he gain or lose per cent?

14. If a ton (2240 lbs.) of ore in a gold mine yields 5 oz. (troy) of gold, what is the yield per cent?

15. If the ore in a mine yields of 1% of pure gold, how many tons (2240 lbs.) of ore must be taken to obtain 7 lbs. (troy) of gold?

16. 12 tons of iron are obtained from 235 tons of ore. What per cent of the ore is iron?

17. Goods are sold, at a loss of 3%, for $2667.50. What was the cost?

18. Teas at 68 cents, 86 cents, and 96 cents a pound, are mixed in equal quantities, and sold at 90 cents a pound. Find the gain per cent.

19. By selling goods for $1173.92, a merchant gains $153.12. Find the gain per cent on the cost. 20. If to 25 gals. of alcohol 2 gals. of water are added, how much per cent of the mixture is water? how much per cent is alcohol?

21. What was the cost when 17% was gained by selling goods for $253.80?

22. A wine merchant mixes 24 gallons, at $7 a gallon, with 18 gallons, at $5 a gallon, and sells the whole at $7 a gallon. What does he gain per cent?

23. By selling a horse for $200, a dealer loses 121%. What would he have gained or lost per cent by selling at $250 ?