6. A coach goes from London to Liverpool, at the rate of 9 miles an hour, in 24 hrs.; in what time would the same distance be traversed by a train moving at the rate of 24 miles an hour?

7. A besieged town containing 22400 inhabitants has provisions for 3 weeks; how many must leave in order that the provisions may last 7 weeks?

8. If 5 men receive £18 15s. for 12 weeks' wages, what will be the wages of 16 men for 20 weeks?

9. If 6 iron bars 4 ft. long, 3 in. broad, and 2 in. thick, weigh 288 lbs., how much will 15 weigh each 6 ft. long, 4 in. broad, and 3 in. thick?

10. Find the value of 345 tuns 2 hhds. 42 gals. at £45 10s. per tun.

11. Reduce (1) ·00175 and (2) ∙1309 to fractions in their lowest terms.

12. 44 guineas used to be coined out of 1 lb. of standard gold, how many sovereigns are now coined out of this weight?

IX.

1. Reduce (1) 13 lbs. 7 oz. 16 grs. to grains; (2) 1847638 in. to miles &c., (3) 138297 cubic inches to yards.

2. Find, by Practice, the value of 3 lbs. 5 oz. 14 dwts. 12 grs. at 17s. 6d. an oz.

3. Find the value of (1) % ×

(2) L+ of £2 10s. 2d. +2

4

4. Reduce to decimals; and express 23·038125, 0006875 as vulgar fractions in their lowest terms.

5. Reduce of 1 cr. to the decimal of 21s.; and 63 cwt. to the dec. of 1 ton.

6. Reduce 135, 01236, to their equivalent vulgar fractions.

7. A bankrupt's effects amount to 2548 guineas, and his debts to £3057 12s., what will he pay in the £ ?

8. If 5 men can do a piece of work in 27 days, how long would 6 men be in doing double the quantity?

9. Find the interest on £260 10s. for 3 years, at 44 per

cent.

10. At what rate per cent. will £320 amount to £360 16s. in 3 years?

11. Find how many yards of paper yd. wide, will paper a room whose length is 26 ft. 4 in., breadth 18 ft. 8 in., height 12 ft. 3 in. ?

12. Extract the square root, (1) of 531441; (2) of 32§.

7312

X.

1. (1) Reduce $399 to its lowest terms; (2) divide the sum of %, 3, 1, 1 by 7; (3) find the value of ( of +of) of 1s.

18

2. (1) Multiply 305 by 25 and 32 by 231 (2) divide 721-41885 by 21.9, and 1·001 by ·2.

3. The price of consols is 883; how many railway shares, at £8 15s. each, can be purchased for £1000 stock?

4. The rates of the express and mail trains on a railway are 40 and 28 miles an hour respectively: what time is saved by taking the faster for a journey of 192 miles ?

5. If 21 men take days to dig 20 ac., how many acres will 16 men dig in 12 days?

6. Find, by Practice, the cost (1) of 11 mi. 3 fur. 55 yds. of railway at £32500 a mile; (2) of 716 ac. at £44 11s. 34d.

an acre.

7. Find the amount of £322 13s. for 10 years at 3 per cent. simple interest.

8. Find the discount on £1452, paid 2 months before it is due, at 5 per cent.

9. Find the amount of £240 in 4 years at 3 per cent., compound interest.

10. If 23 lbs. at 2s. are mixed with 27 lbs. at 3s., and the mixture is sold at 2s. 9d. per lb., what is the total gain; and what the gain per cent.?

11. Extract the square root of 106929; also of 803.7 to 3 places of decimals.

12. Explain the meaning of the term local value. Have Roman numerals any local value?

XI.

1. Multiply (1) 85001997 by 5, and (2) 73299863 by 497.

2. Divide 2975069895 by 35, and 628010082036 by 709. 3. From £19813 7s. 74d. take £2009 6s. 103d.

4. Multiply (1) £35087 17s. 71⁄2d. by 9, and (2) £9003 19s. 1 d. by 39.

5. How many yards of paper 1 yd. wide are required to paper a room 15 ft. long, 12 ft. wide, and 10 ft. high?

6. How often will a wheel 34 yds, in circumference turn in a distance of 208 miles?

7. If by paying down £70 17s. 6d. a person becomes entitled to £2 9s. 7d. a year, what income should he gain by paying down £2126 5s. ?

8. Find the value of; (1) 9 tons 4 cwts. 3 qrs. 21 lbs. at £14 5s. 9d. a ton; (2) of 2174 yards of lace at £2 17s. 71⁄2d. a yard.

9. Find the interest on £194, at 5 per cent. per annum, from the 3rd of March to the 20th of December following. 10. When the 3 per cents. are at £85 17s. 6d., what is the rate of interest?

11. Find the sum of (1) £33, 93s. and 24d.: (2) of •130055, 900, 57·1, 13.34 and 00000397.

12. Divide the quotient of 16 ÷ 2 by ·0002.

XII.

1. (1) Multiply £3467 5s. 71⁄2d. by 346; (2) divide 2665 miles 2 furl. 31 poles yard by 58.

2. A train is travelling at the rate of 32 miles per hour; over how many feet does it pass per second?

3. If 84 men can do a piece of work in two months, how long will it take 12 men to do the same?

4. If the carriage of 18 tons 13 cwts. 3 qrs. 14 lbs. cost 18s. 7 d., what will be the cost of carriage of 255 tons,

6. Find, by Practice, the value of 1389 tons of coal at £1 13s. 8d. per ton.

7. What decimal of a pound troy is 16 dwts.?

8. What are the values of 346 of a pound sterling, and of •058 of a year?

9. (1) Multiply 32.47 by 0033; (2) divide 1·0226816 by

⚫0436.

10. What sum placed out at interest at 4 per cent. would amount to £560 in 3 years, allowing simple interest.

11. Divide £350496 among 4 persons in the proportion of 3, 7, 9, and 11.

12. A sum of £250 17s. 6d. is transmitted through Paris to New York. One sovereign English is worth 24 francs 79 cent. at Paris, and 6 francs 20 cent. French are worth 2 dollars 25 cents American. What is the value of the sum at New York in American currency?

COLLEGE OF PRECEPTORS.

XIII.

1. What sum added to £43 14s. 32d. will make 48000 farthings?

2. Multiply 3 tons 14 cwts. 2 qrs. 14 lbs. 12 oz. by 38, and prove the result.

3. A person bought 240 yards of cloth at 14s. 9d. a yard, and sold it at 15s. 7d. a yard; how much did he gain?

4. How long a time would it take a column of men, extending half a mile in length, to pass by, at the rate of 75 steps a minute, reckoning each step as 2 feet 8 inches?

5. Explain clearly the meaning of a vulgar fraction. State the rule for the addition of vulgar fractions, and prove it by an example.

6. (1) Add together
(2) From 23 of 4
(3) Divide 5+ 3

7. How often is of £1

+ + 11 + 13.

take 2 + 419•

by (3÷14).

11s. 8d. contained in 19 guineas? 8. If 5 yards make one pole, show that there are 301 square yards in a square pole.

9. A man working 10 hours a day completes a piece of work in 12 days; in how many days could he do it, working 8 hours a day?

10. If a garrison of 1500 men, having provisions for 5 weeks, be reinforced with 500 men, how long will the provisions last?

11. Find, by Practice, the rent of 209 acres, at £2 17s. 6d. per acre.

12. Find the area of a path 6 feet wide, which surrounds a court 30 yards long and 24 yards broad.

XIV.

1. Multiply 591863 by 907; and divide 10546279 by 84 by short division, (two factors).

2. What will be the cost of relieving 165000 poor persons at 1s. 3 d. per head ?

3. If £1279 13s. 83d. be divided into sums of £55 12s. 9 d. each, how many such sums will there be?

4. A building society purchases three estates containing 35 a. 2 r. 23 p. 124 square yds., 9 a. 2 r. 36 p. 274 sq. yds., and 40 a. 0 r. 35 p. 203 sq. yds. respectively. If the property be divided into 128 equal parts, of how much does each part consist?