3. How many days will 21 men require to dig a ditch 80 ft. long, 3 ft. wide, and 8 ft. deep, if 7 men can dig a ditch 60 ft. long, 8 ft. wide, and 6 ft. deep, in 12 days?

ANALYSIS.-In this example the causes and the effects each form a compound ratio. The required term is an element of the second cause and a mean. Hence divide the product of the extremes by the product of the given means, and the quotient is the required factor or term, 23 da. (763, 2).

4. If 4 horses consume 48 bushels of oats in 12 days, how many bushels will 20 horses consume in 8 weeks?

RULE.-I. Of the given numbers, select those which constitute the causes, and those which constitute the effects, and arrange them in couplets as in simple cause and effect, putting x in the place of the required term.

II. If the required term, x, be an extreme, divide the product of the means by the product of the given extremes ; if x be a mean, divide the product of the extremes by the product of the given means; the quotient will be the required term.

Solve the following by either of the foregoing methods: 5. What sum of money will produce $300 in 8 mo., if $800 produce $70 in 15 months?

6. If 20 reams of paper are required to print 800 copies of a book containing 230 pages each, 40 lines on a page, how many reams are required to print 3000 copies of 400 pages each, 35 lines on a page?

7. If 10 men can cut 46 cords of wood in 18 da., working 10 hr. a day, how many cords can 40 men cut in 24 da., working 9 hr. a day?

8. What is the cost 36 yards of cloth 1 yd. wide, if 2 yards 18 yd. wide, cost $3.37?

9. A contractor employs 45 men to complete a work in 3 months; what additional number of men must he employ, to complete the work in 2 months?

10. If a vat 16 ft. long, 7 ft. wide, and 15 ft. deep holds 384 barrels, how many barrels will a vat 174 ft. long, 10 ft. wide, and 13 ft. deep hold?

11. What is the weight of a block of granite 8 ft. long, 4 ft. wide, and 10 in. thick, if a similar block 10 ft. long, 5 ft. wide, and 16 in. thick, weigh 5200 pounds?

12. If it cost $15 to carry 20 tons 1 miles, what will it cost to carry 400 tons of a mile?

13. If it take 13500 bricks to build a wall 200 ft. long, 20 ft. high, and 16 in. thick, each brick being 8 in. long, 4 in. wide, and 2 in. thick, how many bricks 10 in. long, 5 in. wide, 3 in. thick, will be required to build a wall 600 ft. long, 24 ft. high, and 20 ft. thick?

14. What will 15 hogsheads of molasses cost, if 28 gallons cost $71 ?

15. At 61d. for 12 yards of cotton cloth, how many yards can be bought for £10 6s. 8d.?

16. If $750 gain $202.50 in 4

gain $155:52 in 1 yr. 6 mo. ?

yr.

6 mo.,

what sum will

17. In what time can 60 men do a piece of work that 15 men can do in 20 days?

18. If 24 yd. of cloth 6 quarters wide can be made from 1 lb. 12 oz. of wool, how many yards of cloth 4 quarters wide can be made from 70 lb. of wool?

19. If the use of $300 for 1 yr. 8 mo. is worth $30, how long, at the same rate, may $210.25 be retained to be worth $42.891 ?

20. A farmer has hay worth $18 a ton, and a merchant has flour worth $10 a barrel. If the farmer ask $21 for his hay, what should the merchant ask for his flour?

21. How many men will be required to dig a cellar 45 ft. long, 34.6 ft. wide, and 12.3 ft. deep, in 12 da. of 8.2 hr. each, if 6 men can dig a similar one 22.5 ft. long, 17.3 ft. wide, and 10.25 ft. deep, in 3 da. of 10.25 hr. each?

22. If a bin 8 ft. long, 4 ft. wide, and 2 ft. deep, hold 67 bu., how deep must another bin be made, that is 18 ft. long and 3 ft. wide, to hold 450 bu. ?

23. What will 120 lb. of coffee cost, if 10 lb. of sugar cost $1.25, and 16 lb. of sugar are worth 5 lb. of coffee?

24. Two men have each a farm. A's farm is worth $48.75, and B's $431; but in trading A values his at $60 an acre. What value should B put upon his?

25. If 6 men in 4 mo., working 26 da. for a month, and 12 hr. a day, can set the type for 24 books of 300 pp. each, 60 lines to the page, 12 words to the line, and an average of 6 letters to the word, in how many months of 24 da. each, and 10 hr. a day, can 8 men and 4 boys set the type for 10 books of 240 pp. each, 52 lines to the page, 16 words to the line, and 8 letters to the word, 2 boys doing as much as 1 man?

PARTNERSHIP

ORAL EXERCISES.

775. 1. If John has 10 marbles, William 15 marbles, and Charles 25 marbles, what part of the whole has each ?

2. Two men bought a barrel of flour for $9, the first paying $4 and the second $5. What part of the flour belongs to each?

3. Three men bought 108 sheep, and as often as the first paid $3, the second paid $4, and the third $5. How many sheep should each receive?

4. If $45 be divided between two persons, so that of every $5, one receives $2, and the other $3, how many dollars does each receive?

5. Two men hired a pasture for $36; one put in 2 horses for 3 weeks, the other 3 horses for 4 weeks. What should each pay?

DEFINITIONS.

776. Partnership is the association of two or more persons under a certain name, for the transaction of business with an agreement to share the gains and losses.

gy. A Firm, Company or House is any particular partnership association.

778. The Capital is the money or property invested by the partners, called also Investment, or Joint-Stock.

779. The Resources of a firm are the amounts due it, together with the property of all kinds belonging to it; called also Assets, or Effects.

780. The Liabilities of a firm are its debts.

781. The Net Capital is the excess of resources over liabilities.

WRITTEN EXERCISES.

782. To apportion gains or losses according to capital invested.

1. A and B engage in trade; A furnishes $400 capital, B $600. They gain $250; what is the profit of each ? 1ST OPERATION. (By Fractions.)

2D OPERATION. (By Proportion.)

$1000 (whole cap.): $400 (A.'s inv.): : $250 (whole gain) : A.'s share. $1000 (whole cap.): $600 (B.'s inv.): : $250 (whole gain): B.'s share. 3D OPERATION. (By Percentage.)

1000

=

25% of the whole capital.

$250 gain is 250 $400 × .25 $100, A.'s gain; $600 × .25 $150, B.'s gain.

=

1000

ANALYSIS. (1st Method.) Since $400, A.'s investment, is 400 or, of the whole capital, he is entitled to of the gain, or $100; and B is entitled to g of the gain, or $150.

2d Method. The ratio of $1000, the whole capital, to $400, A.'s investment, is equal to the ratio of $250, the whole gain, to A.'s share of the gain. Hence the proportions, etc.

3d Method. Since the gain is 25% of the whole capital, each partner is entitled to 25% of his investment as his share of the gain.

The third method (by dividend) is that generally adopted by joint. stock companies having numerous shareholders.