5. A and B together take 3 days to do a piece of work; B alone takes 8 days to do it: how long would A take working alone?

6. In 1871 the population of a town was 21456, and in 1881

it was 20115; find the percentage rate of decrease.

5 12

7. If 13 yards of cloth are worth of a bushel of corn, and

12 yards of cloth cost 44 dollars, what is the value of 5 quarters of corn, a dollar being equal to 4s. 2d.?

8. The Scotch express runs from London to Edinburgh, a distance of 393% miles, in 9 hours, making one stoppage of 30 minutes, three of 5 minutes each, and one of 3 minutes: what is its average speed when in motion?

EXERCISE XLVII.

1. Reduce 875 of 17s. 6d. +16 of £1. 88. 14d. to the decimal of £7.

2. Add together 5618, 2.418, 1136.

3. Find to the nearest penny the amount of £8751. 15s. 3 years at 33 per cent. compound interest.

4. If a cubic foot of lead weighs 720 lbs., find the thickness of a sheet 18 ft. long and 6 ft. wide, weighing 1 cwt. 2 qrs. 12 lbs.

1

5. Of a regiment of soldiersth are killed or disabled in

the first battle,

3

7 29

30

ths of the remainder in the second battle, and

ths of the remainder in the third, and 512 men are left. How 11 many were there at first?

6. What sum will amount to £470. 8s. 103d. in 4 years at 2 per cent. simple interest?

7. A square field is bordered by a path three yards wide, the field and path together occupying 2 acres; find the cost of covering the path with gravel at 1s. 6d. per square yard.

8. By weight distilled water contains 88.9 per cent. of oxygen, the rest being hydrogen: find the weight of hydrogen contained in 40 gallons of water, a gallon of water weighing 10 lbs.

H. AR. E.

3

2. Divide 7.0175 by 17·5 and 17·5 by 7·0175 correct to two places of decimals.

3. Find the smallest sum of which 14s. 7d., £1. 11s. 6d., and £3. 15s. are exact parts.

4. Find the value of a field 231 yards long, and 125 yards broad; an acre of land being worth £8. 16s.

5. In what time will £244. 1s. 8d. amount to £253. 4s. 83d. at 3 per cent. simple interest?

6. A cistern has two pipes one of which can fill it in 2 hrs., the other in 3 hrs.; a third pipe can empty it in 5 hrs.: if while the cistern is empty all these are opened, in what time will it be one-quarter filled?

7. Find to the nearest farthing the compound interest on £450. 6s. 8d. for 2 years at 2 per cent., interest being payable half-yearly.

8. A river 30 feet deep, and 200 yards wide flows 4 miles an hour; find the number of tons of water that falls into the sea in a minute: a cubic foot of water weighing 1000 oz.

EXERCISE XLIX.

1. Find the least common multiple of 1701, 972 and 756, and add together

4 5 1701' 972

and

11 756'

2. Divide 37 by 1:17; multiply the result by the quotient of 052 divided by 18, and give the result in the form of a fraction.

3. If a cubic foot of air weighs 14 oz., find the weight in cwt. of the air contained in a room 15 yds. long, and 211 ft. broad, and 10 ft. 8 in. high.

4. At what rate per cent. simple interest will £276. 7s. 1d. amount to £309. 10s. 4d. in 3 years?

5. Find the mean proportional between 1692 and 2303; and the fourth proportional to 2401, 2058, 1764.

6. If 40 men can dig a trench in 4 days of 9 hours each, how many men must be employed to dig a trench twice as long as the former, half as wide again, and three-quarters of the depth, in 5 days of 8 hours?

7. Two clocks point to 2 o'clock at the same instant on the afternoon of Christmas day; one loses 8 seconds, and the other gains 7 seconds in 24 hours; when will one be half an hour before the other, and what time will each clock then shew?

8. The present worth of £159. 7s. 6d. due in a certain time is £150: if interest is allowed at the rate of 2 per cent. find the time.

EXERCISE L,

1. Subtract the square of 036 from the square root of '0036.

1 17

2. Express of £1. Os. 24d. +875 of 1s. 8d. as a decimal of 1s. 2d.

3. Find the present value of £2674. 6s. due at the end of 3 years at 43 per cent.

4. Find, by Practice, the wages of a man working for 30 weeks 2 days 3 hours at 25s. a week, reckoning 6 days to a week and 12 hours to a day.

5. What length must be cut off a board 16 inches wide and 4 feet long so that the area of the part remaining may be 5 square feet?

5

6. A prize of £2770 was divided amongst three persons in 3 14 the proportion of and : find their respective shares. 4' 15

7. A level tract of land, 21 miles long and of a mile broad, is flooded to a depth of 5 feet: given that a cubic foot of water weighs 62 lbs., find in tons the weight of water on the land.

8. The annual consumption of brandy in a country is 4500000 gallons, and the duty is 98. 2d. per gallon; the duty is reduced 6 per cent., and the consumption then increases 8 per cent.; how is the revenue affected?

PART V.

Including Profit and Loss and Stocks.

EXERCISE LI.

1. Subtract 7.3125 of a furlong from 103125 of a mile, giving the result in yards and the decimal of a yard.

2. Find the amount of £1485 in 3 years at 5 per cent. compound interest, neglecting fractions of a penny.

3. A bankrupt owes A, B, C respectively £65, £75. 3s. 4d., £108. 8s. 4d.; his assets are £136. 14s. 5d.; what will each creditor receive?

4. If a publisher gains £2000 in selling 120000 shilling copies of a book, what is his gain per cent.?

6. A roll of carpet 70 yards long and 30 in. wide weighs 23 cwt.: how many rooms measuring 18 ft. by 17 ft. could be carpeted with a roll weighing 11 tons?

7. At what rate per cent. per annum will £1885. 15s. amount to £2569. 6s. 81d. in 7 years and 3 months simple interest?

8. Find the prime factors of 111540, 42336, and 67392, and thence find the quotients obtained by dividing their least common multiple by each of the numbers in turn.

2. By selling 10 acres of land for £4699. 8s. 3d. a person gained 51 per cent.; how much did he give per acre?

3. Find the true discount of £619. 19s. 11d. due in 6 months, allowing interest at 3 per cent. per annum.

4. Multiply 3142857 by 63, and express the quotient of 03 by 285714 as a decimal.

5. A bankrupt's debts amount to £4875. 5s., and his assets to £3250. 38. 4d.: what will a creditor receive in payment of a debt of £574. 10s.?

6. Subtract 2.00751 quarts from 0865 of a bushel, and give the answer in pints and the decimal of a pint.

7. Brussels carpet is 2 ft. wide, costs 7s. 6d. a yard, and will last 5 years; Kidderminster carpet is 2 ft. wide, costs 5s. a yard, and will last 3 years: find the ratio of their cost, not reckoning interest on the outlay.

8. A person received £525 as the interest on two sums of money, one of which was double of the other; he received 5 per cent. on the larger sum and 4 per cent, on the smaller : how much were the sums?

2. If 5 cwt. 3 qrs. 8 lbs. of tea cost as much as 55 cwt. 1 qr. 6lbs. of sugar, what quantity of sugar should be given in exchange for 15 lbs. of tea?

3. Extract the square root of 3263-8369; also of 65 to four decimal places,