Percentage

See Book II, pages 168, 176, 195, 212.

1. What is 5 per cent of 100? of 200? of 500? 2. What is 8% of 100? of 50? of 25?

163% of 48?

331% of 45?

3. What is 1% of 3200? 4% of 3200? 4. What.common fraction equals 121 %? 5. What common fraction equals 25%? 6. What is 121% of 48? 7. What is 25% of 36? 8. Of what number is 12 1%? 9. Of what number is 60 20%? 10. 7 is 121% of what number? 11. 9 is 20% of what number? 12. What is 1% of $1250? 13. What is 1% of $240?

14. What is 1% of 416?

15. What is the profit on

at a gain of 30%?

10% of 3200 ?

16%? 20%? 331%? 621%?

20% of 60? 621% of 16?

2%? 4%?

30%? 50%? 163% of what number? 25% of what number? 10% of $1250?

% of $240? 11% of 416?

goods costing $225, and sold

16. What is the loss on a car load of potatoes bought for $180 and sold at a loss of 121%?

17. By gaining 20% on goods I gained $35. What was the cost?

18. By losing 4% on goods I lost $32. What was the cost?

19. An agent charges 15% for collecting bills. He has collected $160. How much will his commission be?

20. An agent's commission amounts to $40. His rate is 5%. Upon what sum is the commission reckoned? 21. How much will it cost to insure a house for $2600 at 1%?

Drill Work

Add both vertically and horizontally the following statements of cash receipts for the successive weeks:

2d

1st $2561.45 $ 1562.73 $4830.26 $ 2056.42 $1852.07 $675.25

584.32 1082.36 873.41 456.90 748.92 1742.80

1st $3287.40 $923.75 $1432.87

2d

3d

7th

$834.54 $6378.23 $925.00 832.00 1254.76 823.45 2410.34 823.78 3267.40 234.75 96.43 84.54 125.67 4th 2873.52 973.82 823.46 925.25 775.24 1402.40 5th 1205.34 2467.89 1345.23 1623.86 1243.80 989.75 6th 765.34 970.75 972.04 1328.75 2234.37 1734.52 3875.43 1325.43 876.43 634.52

89.70 236.84

863.00

2007.26

8th 990.70 750.25 1450.80 2123.88 9th 1450.50 865.32 784.35 988.78 10th 2132.45

1123.12

890.85

878.87 1334.54 1540.42 2110.40 1654.42 2457.67 2004.45

Total

Problems from Geography

1. The earth is 25,000 miles in circumference. It is now possible to make a trip around the world in 40 days. What is the average possible rate per day for the journey?

2. When the railroad is completed from Cairo to Cape Town, connecting northern and southern Africa, the length of the road will be about 5500 miles. How many days will it take to make the trip, at the rate of 30 miles an hour, if we allow for 20 stops of 10 minutes each?

3. There are now about 170,000 miles of telegraphic cable in the world. How many times would all this cable reach continuously around the world?

4. When the canal is completed across the isthmus between North America and South America, more than 10,000 miles will be saved in the trip from New York to San Francisco. If we reckon 12 miles an hour as an average rate for a vessel, about how many days will the voyage be shortened?

5. It is estimated that this canal will cost $125,000,000. How much would have to be collected each month from the ships that pass through to pay 5% annually on this sum?

6. If the tunnel which is now being built through the Alps will be 123 miles long, and will cost $14,000,000, what will be the average cost for each foot in length?

7. The great tunnel under the city of New York will cost about $35,000,000. When the population of the city is 3,500,000, how much must this tunnel be worth upon the average, each year, to every inhabitant, in order that the total advantage may equal an income of 6% on the investment?

Interest

Interest is a sum paid or allowed for the use of money. It is reckoned in per cent for each year.

The principal is the money for the use of which interest is paid.

The amount is the sum of the principal and the interest.

At 4% the interest of $1 for one year is 4 cents, for 2 years, 8 cents, for 2 years, 10 cents, etc. At 5% the interest of $1 for 1 year is 5 cents, the interest of $2 for 1 year is 10 cents, etc.

1. What is the interest of $3 for 1 year at 5%?

2. What is the interest of $3 for 3 years at 5%?

3. What part of a year are 2 months? 3 months? 4 months? 6 months? 9 months?

4. What is the interest of $1 at 6% for 6 months? 4 months? 8 months?

Since the interest for 1 year is 69, for 8 months or year, it is of 6% or 44.

5. What is the interest of $1 at 4% for 3 months? For 6 months? For 9 months?

6. What is the interest of $1 for 2 years and 3 months at 8%?

Give the interest of the following:

14.

$12 for 5 yr. 6 mo. at 5%.

15.

$8 for 3 yr. 3 mo. at 7%.

16.

9. $6 for 3 yr. at 4%. 10. $5 for 4 yr. at 5%. 11. $8 for 6 yr. at 6%. $15 for 4 yr. 2 mo. at 6%. 17. How much interest will $5 gain in 31 yr. at 8%? 18. What will be the amount of $10 for 3 yr. at 4%?

The interest of $10 for 3 yr. at 4% is 12% of $10 or $1.20. The amount is $10 + $1.20 or $11.20.

19. What will be the amount of $15 for 2 yr. at 6%? 20. Find the amount of $12 for 3 yr. at 3%.

Longitude and Time

1. In which of two places is the time earlier, a place farther east or one farther west? Why?

15

Since the earth, in its daily revolution, turns through 360° in 24 hours, it turns through 15° in one hour, and through 1o in of an hour, or 4 minutes. Since it turns through 1o or 60' of longitude in 4 minutes of time, it turns through 15' of longitude in 1 minute of time, and through 15" of longitude in one second of time.

The number of degrees, minutes, and seconds of longitude is fifteen times the number of hours, minutes, and seconds of time.

2. At noon, what time of day is it at a place 15° farther west? At a place 15° farther east? At a place 30° farther west? At a place 45° farther east?

3. At 8 o'clock, what time is it at a place which is 60° farther west? At a place 90° farther east?

How many degrees of longitude farther west or east has a place where the time is:

4. 2 hours earlier?

5. 4 hours later?

6. 11⁄2 hours earlier?

7. 11 hours later?

8. 13 hours earlier ?

9. 5 hours later?

10. What is the difference in longitude between two places whose difference in time is 4 hr. 30 min.?

15 x 460, the number of degrees of longitude; 15 × 30 = 450, the number of minutes of longitude, which equal 7° 30′; 60° + 7° 30′ = 67° 30'.

11. What is the difference in time, if the difference in longitude is 20° ?

12. What is the difference in longitude, if the difference in time is 2 hr. 40 min. ?