6. Find the values of 159375 of a £, and 6875 of a shilling, and express their difference as the decimal of a guinea.

7. A room is 12 ft. broad and 22 ft. long; what will it cost covering with carpet of a yard wide at 4s. 6d. a running yard?

8. If the cost of 750 soldiers for 12 days be £900, how long can 2000 soldiers be maintained for £3000 at the same rate?

9. A gold and a silver coin are respectively worth 2s. 6d. and 1s. 11d. each; an amount of 100 guineas has to be paid with these coins, so that there shall be twice as many gold as silver coins employed; how many will be required of each?

3. Reduce £3 11s. 9ąd. to the decimal of £1; and find value of •1825 of £2 6s. 8d.

5. Find square root of 250080-0064.

6. Three merchants invest respectively in a cargo the sums £5200, £3600, £2000; when sold, there is a profit of £1647. Find what each should receive, and at what rate per cent. the profit is.

7. If after deducting 12 per cent. from my money I have £525 10s. left, what had I at first?

8. What sum of money at 44 per cent. will produce the same income that £2700 does at 5 per cent.? Find the income, and how much must be given for the stock in the 3 per Cents at 90, necessary to produce the same yearly amount.

9. A is 2640 yards in advance of B; A runs 5 miles an hour, and B 6; in what time will B overtake A ?

10. If 16.125 yards of cloth 1.375 yards wide cost 2.2 £, what would 45 yards, 875 yards wide, at the same price per square yard, cost?

EXERCISE CCCXXVIII.

1. A candidate having been examined in 15 subjects, gained the following numbers of marks: 95, 80, 66, 71, 74, 87, 92, 93, 125, 47, 65, 43, 115, 75, 76, 80. How many marks did he get altogether, and how many more must he have gained to have the full number of 1500 marks?

2. A mass of wet clay weighed 76 tons 11 cwts. 2 qrs. 12 lbs., but when dried it weighed only 69 tons 15 cwts. 3 qrs. 16 lbs.; what weight of water was in the wet clay?

3. If a railway carriage wheel turns 1689 times in going a league how many turns will it have made after it has travelled 3574 leagues?

4. The average extent of each of 439 fields is 13 a. 2 rds. 15 pls.; what is the extent of all of them together?

5. Certain persons had to subscribe £5 17s. 44d. each to make up a total of £223 Os. 3d.; how many persons subscribed?

6. An estate is left among three heirs; the first receives £5000, the second three-fourths of the share of the first, and the third fivesixths of the share of the second. What is the whole value of the estate?

7. If 264 men can earn £480 12s. in a certain time, how many at the same rate could earn £229 4s. 6d. in the same time?

8. If 31404 gallons of water can be raised to the height of 321 feet for a certain sum, how many gallons could be raised to the height of 428 feet for half the sum, reckoning the expense of raising the water at the same rate per foot per gallon in both cases?

9. Add together 17, 33, 3, and 2; and find the value of 17 of 33 of of 2 of 10s. 8d.

10. Towards a charitable purpose two persons each contributed £27 5s. 11⁄2d., and a third contributed £42 16s. 73d.; what fraction of the total was formed by each contribution? (Express the answers in their lowest terms.)

EXERCISE CCCXXIX.

1. The value of land bought for some railways was £442165 5s. 10 d., being an average of £97 13s. 54d. per acre; find the number of acres.

2. The valued rents of a parish are £5070 16s. 8d., and on this a rate of £405 13s. 4d. is to be paid; what will the rate be on a rent of £68 8s. 9d. ?

3. If 24 sappers in 2 days can dig 139 yards of a trench, how many yards can 90 men dig in 13 days?

4. Find, by practice, the value of 43781 square yards of work estimated at 11s. 8d. per square yard; also the value of 2705 oz. 13 dwts. 13 grs. of gold, valued at £3 17s. 104d. per oz.

5. In what time will £712 10s. amount to £1136 8s. 9d. at 3 per cent. per annum, simple interest?

7092

6. Reduce the fraction 2595 to its lowest terms. Find the G. C. M. of 238, 374, 442; also find the L. C. M. of 7, 14, 28, 42, 35.

7. Reduce 43 + 33 + 24 + 1§ to a mixed number in its lowest terms, and to a decimal. Also reduce the product 43 × 3 × 2 × 18 to a mixed number in lowest terms, and to a circulating decimal.

8. Multiply 052375 by 88; also divide 0042003 by 1·17. Then subtract the latter result from the former, and reduce the difference to a vulgar fraction in its lowest terms.

9. By selling goods for £773 10s. 34d. a gain is made of 34 per cent. on their prime cost; find the prime cost.

EXERCISE CCCXXX.

1. A number of subscribers contributed in equal shares a sum of £14525 towards an enterprise which was afterwards abandoned. The money was returned to the subscribers after the expenses, amounting to £523 10s. 3d., had been paid out of the fund, and each of them received £538 10s. 44d. How many subscribers were there?

2. Find the value of 3061 cwts. 2 qrs. 15 lbs. at £7 10s. 9d. per cwt. 3. A sum of £3362 12s. yields an annual income of £157 12s. 54d. ; what would £5310 17s. 4d. yield at the same rate?

4. If three engines, each of 520 horse-power, can lift 60 million

gallons of water to the average height of 260 feet by working for 57 days of 8 hours each, how many days of 11 hours each would be required to lift 49 million gallons of water to the average height of 104 feet by means of 2 engines, each of 832 horse-power ? 5. A sum of money has for three years been accumulating at compound interest at the rate of 4 per cent. per annum, and now amounts to £24283 17s. 1d. Determine the sum, and calculate what its amount would have been at the same rate but at simple interest.

6. Three partners, A, B, and C, contribute £868, £700, and £672 to a speculation, and at the end of six months found their profits amount to £225 10s. Out of this they agree to take each of them a dividend of 6 per cent. on his capital, and to divide the remainder in proportion to their actual second-class railway travelling expenses. Now, for a certain number of days in each month, A has travelled 20 miles a day for 4 months, B 30 miles a day for 5 months, C 35 miles a day for 4 months. Determine what share of the £225 103. each is to receive, and also what fraction his share is of the whole profits.

121%

7. Reduce 12-2} + 1412 - 1+34 of 21 to the simplest form as a vulgar fraction in its lowest terms, and also as a recurring decimal.

8. Extract the square root of 30801, and the cube root of 9.528128. 9. The proceeds of the sale of 3 per Cents stock at 934 amounted to £6844 13s. 9d.; find the amount of the stock, and the clear annual income derived from it, deducting income-tax at 5d. in the £.

EXERCISE CCCXXXI.

1. Find the value of 13 yds. 3 qrs. 37 nails, at 10s. 6d. per yd.

3. Express as a vulgar and as a decimal fraction of acre,

4. Convert

sq. po. + sq. yd. + 5 sq. ft.

into a recurring decimal, and find its square

correctly to the fourth place of decimals.

5. Find the first two significant figures (not more) of the quotient of 660375 divided by 23.54, and prove their correctness.

6. How many rods (2724 sq. ft.) of brickwork, 1 bricks thick (14 inches), will a million bricks, measuring 9 × 4 × 3 inches, suffice for? 7. If by selling at £26 17s. 6d. I gain 25 per cent., how much shall I gain per cent. by selling at £28 13s. 4d.?

8. What is the value of the gold in an ornament weighing 13 dwts., of which are pure gold, if 11 oz. of pure gold is worth

£3 17s. 10 d. ?

9. A person transfers his money from the Three per Cents at 917 to the Four per Cents. at 98; find the ratio of the new to the former income.

10. What annual payment will be sufficient to discharge a debt of £100, due in 10 years, with simple interest at 5 per cent. ?

11. One cubic foot of water weighs 1000 ounces avoir., and 1 gallon contains 277.274 cubic inches; what must be the length of the side of a square tank capable of holding 2000 gallons, if the depth be 5 feet? and what is the weight (in pounds) of water in the full tank? (N.B., two decimals only required.)

EXERCISE CCCXXXII.

1. Explain the common system of notation by which ten symbols are sufficient to represent all numbers.

What decimal of £1 is 4ths of 21th of 6s. 6d.?

2. Simplify the expression

89 × (£28 19s. 3d.) – 143 (£6 3s. 2d.) + 57 (£45 6s. 8d.)

and find out what is the least sum that should be added to the numerator in order to make the answer an integral number of sixpences.

3. A tradesman buys a hundredweight of coffee for £5, and sells it for £6 7s. 6d; what is his gain per cent. ?

4. Find, by practice, the value of 448 articles at £1 12s. 74d. each. 5. Find the sum, difference, product, and quotient of 78962 and 3.

R