of 10 hr., and the number of men can be found from the proportion: 30: 1824 : x. But it would require more men working 8 hr. a day than it would working 10 hr. a day to complete the house in the same length of time; and the number can be found from the proportion : The compound proportion obtained from these two proportions is: 1. If 12 horses plow 84 A. in 6 da., how many acres will 16 horses plow in 4 da.? 2. If 14 men pave a street 200 ft. long in 8 da., how many feet will 12 men pave in 7 da.? 3. If a man earns $117 in 3 mo. working 6 hr. a day, how much will he earn in 5 mo. working 8 hr. a day? 4. A garrison of 3650 men consumed in 30 da. 82.3 T. of food. How much food would be required for 7500 men for 1 yr. at the same rate? 5. If 8 masons build in 2 da. a wall 40 ft. long and 6 ft. high, what height of wall 30 ft. long can they build in 5 da. ? 6. If 21 men complete a piece of work in 8 da. of 71 hr. each, in how many days of 10 hr. each can 18 men do the same work? 7. A wall is to be built in 10 da. by 30 men. After 2 da. 10 men are dismissed. In what time will the remaining 20 men finish the work? 8. If 4 men or 6 boys dig a trench in 12 da., in what time can 2 men and 9 boys dig it? 9. If 12 men mow 30 A. in 3 da. of 8 hr. each, how many hours a day must 16 men work to mow 48 A. in 4 da.? 10. If the interest on $100 for 1 yr. is $6, find the interest on $840 for 2 yr. 3 mo. 11. If 12 men working 7 hr. a day earn $227.50 in 20 da., how much will 15 men earn in 20 da., working 9 hr. each? 12. If 6 men mow of a meadow in 41 da., how long will it take 8 men to mow the remainder? 13. In 10 da. of 8 hr. each 9 horses can plow of a field. In how many days of 9 hr. each can the remainder of the field be plowed by 15 horses? 14. A marble block 3 ft. by 4 ft. by 5 ft. weighs 5.1 T. Find the weight of a marble block 7 ft. by 3 ft. by 10 ft. 15. A mason can build 3 yd. of a wall in 15 hr. How long will it take 9 masons to build 24 yd. of a wall which is one third higher than the other wall? 16. If a trough of water 12 in. × 24 in. × 36 in. weighs 10,368 oz. how long must a trough 12 in. by 24 in. be if the water weighs 3456 oz.? PARTNERSHIP Example 1. A, B, and C enter into partnership. A puts in $840, B puts in $350, and C puts in $ 2000. A withdraws from the concern in 5 mo., C in 7 mo., and at the end of 8 mo. the profits are divided. If the entire profit is $450, how shall this be divided among A, B, and C? SOLUTION. Each partner's share in the business depends upon the amount of his investment, and the length of time for which the investment is made. In order to make comparison more easy, the investments are computed which could be invested for one month and produce the same results as the given investments. A's investment of $840 for 5 mo. equals an investment of 5 x $840, or $4200 for 1 mo. B's investment of $350 for 8 mo. equals an investment of 8 x $350, or $2800 for 1 mo. C's investment of $2000 for 7 mo. equals an investment of 7 x $2000, or $14,000 for 1 mo. The total investment is equal in effect to an investment of $4200+ $2800 +$14,000 = $21,000 for 1 mo. C's share of the profits of $450= $300. = Example 2. A and B are partners, A having $4 to B's $5. A gets 15% of the entire profits for managing the business, and the remainder is divided proportionally to their capitals. B receives as his share $1700. How much does A receive? SOLUTION. AS A invests as much as B, his share of the profits is of B's share; but B's share is $1700. Therefore, A's share is of $1700 = $1360. The total profit is $1700 +$1360 = $3060. But this is 85% of amount upon which A's 15% for managing the business was reckoned. If $3060 is 85%, one per cent is of $3060, and 100 per cent equals 100 × $3060 = $3600. 85 Of this $3600, B received $1700. Therefore A received $3600 $1700 = $1900. EXERCISE 114 1. A, B, and C enter into partnership with capitals of $3000, $3750, and $4500 respectively. At the end of the year they divide among themselves a profit of $3000. Find each person's share. 2. Two partners, A and B, invest $600 and $1125. A's money remains in the business 6 mo., and B's 8 mo. If they make a profit of $2100, find each person's share. 3. Two men rent a pasture for $171; one puts in the pasture 30 cattle for 30 da., and the other 45 cattle for 18 da. How much rent should each pay? 4. A and B enter into partnership. A's capital is $200 more than B's. Out of a profit of $640, B gets $280. Find A's and B's capital. 5. A and B enter into a partnership, A contributing $6400 and B $7200. At the end of three mo. A withdraws $1600, and at the end of 5 mo. B withdraws $1440. C then enters into the partnership with a capital of $4800. Seven months later a gain of $2154 is divided among them. Find each person's share. 6. A, B, and C enter into partnership. A puts in $1000, B $1200, and C $1800. At the end of 3 mo. C withdraws, and at the end of 10 mo. B withdraws.. At the end of a year the profits are divided. If C gets $135, how much do A and B receive? 7. Two men form a partnership. Their capitals are in the ratio 2:3. After 6 mo. the first man increases his capital by of itself, and the second man diminishes his capital by of itself. After 6 mo. more they divide their profits, amounting to $1450. Find each partner's share. 8. A, B, and C form a partnership, each contributing $3000. At the end of 6 mo. A adds $1000 and B $2500, but at the end of 7 mo. C withdraws $2000 of his capital. If A gets from the year's profits $2100, what ought B and C to get? PERCENTAGE What is percentage? How is it reckoned? What does per cent mean? What symbol is used for per cent? How is per cent usually written? The per cent equivalent of the following fractions should be thoroughly fixed in mind : 1, 1, 3, 1, 4, 1, 2, †, †, ž, §, 1, 8, §, 7, 12. Example 1. The total value of imports into this country through the Atlantic ports for the year 1906 was $974,562,800; of this 75.35% came through New York City. Find the value of the imports through this city. = $9,745,628 × 75.35 = SOLUTION. $974,562,800 × 75.35 $734,333,069.80, value of imports through New York. |