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 3 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 cistern 66' x 27' 6' x 10' will hold enough water to irrigate 2 A. of land to the depth of 2 inches. How many acres will a cistern 77' x 41' 3" x 12′ 6′′ irrigate to the depth of 3 inches?

9. If A pays of the cost of irrigation when the rate charged is $4 an acre to the depth of one inch, find his share of the cost.

P

PERCENTAGE

A per cent of a number implies a fraction of the number having 100 for denominator. Thus, 5 per cent, 5%, 156, and .05 are four ways of expressing the same fact. The per cent equivalents of the following fractions should be thoroughly fixed in mind:

3

5 1

1, 3, 3, 4, 4, 1, 4, 8, 4, 1, §, §, §, §, §, 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.

SOLUTION. $974,562,800 ×

75.35
100

= $9,745,628 × 75.35

= $734,333,069.80, value of imports through New York. As 75.35% is correct to four figures only, the result is not likely to be correct to more than four figures. To get four figures multiply 97.456 millions by 7.535 by the contracted process explained on page 191.

EXERCISE 112

1. Write the equivalent per cents of the following decimals:

.04, .08, .075, .0525, .1666.

2. Express as decimals the following per cents: 41%, 15%, 121%, 621 %, 61%, 3% %.

3. Find 5% of each of the following numbers: 2151, 366.7, 689.5, 7.188, 12.469.

4. Find 6% of each of the following numbers: 5262, 520.7, 2.66, 3.097, 6.41, .783.

5. Find 41% of each of the following numbers: 4150, 1418, 7120, 43.43, 53.17, 2.42.

6. The Engineer's Year Book for the year 1906 gives the cost of railway construction in England as $194,660 The per cents of cost were as follows:

per mile.

Find the cost of each of the above items of expense.

7. The value of the total imports to the United States for the year 1906 was $1,226,560,000. Of this value 79.45% came through the Atlantic ports, 4.42% through the Gulf ports, 1.38% through the Mexican border ports, 5.41% through the Pacific ports, 7.97% through the northern border ports, 1.37% through the interior ports. Find the value of the imports through each of these divisions.

8. The value of the total exports of the United States for the year ending June 30, 1906, was $1,743,860,000. The per cents of total value by principal customs districts were as follows:

Find the values of the exports through these cities.

Given a quantity, to find its value when decreased by a per cent of itself.

Example 1. In the year 1906 the state of Ohio produced 11,562,500 lb. of wool; this shrunk 50% from scouring. Find the number of pounds of scoured wool.

SOLUTION. 100%-50% 50% = 1.

=

11,562,500 × 1 = 5,781,250.

Ans. 5,781,250 lb.

EXERCISE 113

1. The wool production and per cent of shrinkage from scouring for the year 1906, as given by the Bulletin of National Association of Wool Manufacturers, for the states named are as follows:

Given a per cent of a number, to find the number.

Example 1. During the month of January the average daily attendance of a school was 414. This number was 92% of the school enrollment. Find the number enrolled. SOLUTION. 92% of enrollment is given.

100% of enrollment is sought.

... enrollment 414 x 100

414 x 100 = 450, or

=

Example 2. A dealer sells an article for $522 at a gain

of 16%. Find the cost price.

SOLUTION. 116% of cost price is given.

100% of cost price is sought.

1. Find the number of which 79 is 4%.

2. In a certain town 60% of the grown people are married. If there are 2394 married people, how many grown people are in the town?

3. A man spends $320 for board. This sum is 40% of his income. Find his income.

4. A man spends 83% of his salary and saves $170. What is his salary?

5. A lot is sold for $3380 at a gain of 121%. Find the cost of the lot.

6. After a discount of 163 % is given, a man pays $84 for a bill of goods. Find the amount of the bill.