8. Find the difference between 70323 of a pound, and 3.5646 of a shilling; and reduce 14 hrs. 15 min. to the decimal of 3 days.

9. What will a piece of plate cost, which weighs 3 lbs. 4 oz. 5 dwts., if the price of silver be £3 6s. per lb., and the charge for workmanship be 2s. 8d. per ounce?

10. How many hours a day must 42 boys work, to do in 45 days what 27 men can do in 28 days of 10 hours each, the work of a boy being half that of a man?

11. If 8 guineas be expended in purchasing Brussels carpet yd. wide, at 3s. 6d. per yard, for a room 20 ft. long and 16 ft. 9 in. broad; how much of the floor will remain uncovered?

12. At what rate per cent. will the interest on £375 amount to £48 2s. 6d. in 3 years 8 months?

XX.

1. How many acres, roods, poles, yards, feet, and inches are there in 40253798 square inches?

2. Simplify (1) 5−13+2+‡ of 21-2%.

45

(2) 819-815,37.

3. Find the value of £17 2s. 9d.÷11+£1 16s. 9d. +793.

83

What part of half-a-crown is 4 of 24 of 18 of 3 of

a guinea?

3

4. What is the value of of of a vessel, if a person who owns of it sells of of his share for £350?

5. Standard gold consists of 22 parts pure gold with two parts copper, and from a pound Troy of this metal are coined 4628 sovereigns. Find the quantity of pure gold in 100 sovereigns.

6. Divide 027 by 14·4; 1632 by 0008; and 7 by ‘091. 7. Reduce 7s. 81942 d. to the decimal of half a guinea; and express the difference between 2.778125 of 6s. 8d. and ⚫063 of £13 2s. 6d. as the decimal of 2s. 3d.

8. If an ounce of gold be worth £4.0099, what is the value of 561 of a lb. ?

9. If 12 men can dig a trench 40 yards long and 4 feet wide, in 10 days of 8 hours each, how many hours a day must 55 men work, in order to dig a trench of the same depth, 220 yards long and 5 feet wide, in 18 days?

10. When the three per cents. are at 925, what must be given for £533 6s. 8d. stock? What rate of interest will be obtained by purchasing three per cents. at 914?

11. Define simple and compound interest. Find the present value of £252 19s. 3d. due a year hence at 3 per cent.; and the amount of £850 in 3 years at 6 per cent. compound interest.

12. The content of a solid block of stone 12 ft. 6 in. broad, and 3 ft. 9 in. thick, is 27 cu. yds. 1 cu. ft. 810 cu. in. Required its length, and its price at 6d. per cubic foot.

XXI.

1. (1) Add together 369 tons 13 cwts. 1 qr. 14 lbs. ; 127 tons 1 cwt. 3 qrs. 17 lbs.; 258 tons 19 cwts. 2 qrs. 23 lbs.; and 1 ton 5 cwts. 3 qrs. 2 lbs. (2) Multiply £628 17s. 4 d. by 1407. (3) Divide 375 miles 2 fur. 7 po. 2 yds. 1 ft. by 39.

2. (1) How many seconds are there in a leap year ? (2) Divide £6 16s. 9d. between two persons so that one may have double the sum which the other receives. (3) How many times will a coach wheel of 18 ft. in circumference turn between London and York, being 197 miles ?

3. (1) If £4 15s. 74d. purchase 3 cwts. 17 lbs., what must be given for 16 cwts. 3 qrs. 12 lbs.? (2) A owes B £56 5s., but B consents to remit 15 per cent. for immediate payment; what sum does A pay B? (3) If 4 cwts. 1 qr. 7 lbs. cost £5 per cwt., what will be the cost per lb. when the cost of the whole is reduced by £5 9s. 3d.?

4. Divide 13 of 21 by 12 of 51.

5. Reduce 667 to its lowest terms.

6. Reduce of guinea to the fraction of £1.

7. Multiply 56 by 00457.

8. Divide 816 by 0004.

9. Reduce 7s. 41d. to the decimal of £1.

10. A man after doing of a piece of work in 30 days is assisted by another, with whom he completes it in 6 days; how long would each be about it separately?

11. What number is that from which if there be taken of, and to the remainder of be added, the sum will be 10?

12. How many 3-inch cubes can be cut from a 12-inch cube? (Royal Naval College.)

NAVAL CADETSHIP PAPERS.

XXII.

1. The moon's distance from the earth is 240,000 miles, and the sun's is 95,000,000 miles; how much farther is the sun from the earth than the moon is?

2. (1) Reduce 540,697 inches to miles, furlongs, &c.

(2) Multiply 15 lbs. 9 oz. 17 dwts. 18 grs. by 23. 3. If 4 cwt. 1 qr. 26 lbs. of tobacco cost £43 18s. 6d. what quantity can be purchased for £4 19s. 9d.?

4. What quantity of silver can be bought for £36, when 14 lbs. 6 oz. 15 dwts. cost £45 ?

5. A person's income is £598 10s., his weekly expenses are £7 10s., and he gives away £20 annually in charity; how much will he have remaining?

6. When coals cost 11s. 6d. a ton, what will be the annual expense of fuel for an engine whose daily consumption averages 2 tons ?

7. How many days of 15 hrs. each would 60 men take to perform a piece of work, if 45 men can do it in 30 days of 12 hrs. each?

8. If 1 lb. troy of gold be coined into £46 14s. 6d. what

is the weight of a sovereign?

9. (1) Reduce 998 to its lowest terms.

739

(2) From 10 take 714.

(3) Multiply together, and 23.

10. (1) Multiply 7.51 by 0016.

(2) Divide 201·4095 by 703.

(3) Reduce 100 to a decimal.

125

11. How many square ft. of glass are required to glaze 5 windows, each containing 14 panes of glass, each measuring 18 in. by 6 in. ?

12. A man mixes 20 gal. of ale which cost him 16d. a gallon, with 65 gal. of beer which cost him 9d. a gallon ; at what price must he sell the mixture to gain 20 per cent. ?

XXIII.

1. Express in figures five hundred and nine millions six thousand and one.

2. Divide 7,890,567 by 42, first, by long division, and secondly, by its factors 6 and 7.

3. If a land mile consists of 1,760 yds., and a knot, or sea mile, of 6,080 feet, how many knots correspond to 1,400 land miles?

4. (1) Divide 121,260 c. yds. 22 c. ft. 392 c. in. by 584. (2) Find the value of 17 pieces of cloth each 41 yds. 1 qr. long, at £1 8s. Od. for 2 yds. 3 qrs.

5. A coach-wheel 7 ft. 8 in. in circumference revolves 3,762 times in performing a certain journey; what would be the circumference of a wheel which made 3,496 revolutions in the same distance ?

ac. in 3 days

6. Standard gold being worth £3 17s. 101d. per oz. troy, what will be the price of 2 lbs. 9 oz. 6 dwts. 16 grs.? 7. If 11 men can reap a field of corn of 7 of 12 hrs. each, how long will it take 8 men working 16 hrs. a day?

to reap 9 ac.

8. A can perform a piece of work in 4 days, which B can perform in 5 days; in what time can they perform it together?

9. (1) From 1× take.

T

(2) Divide 53 of 41 by 73.

(3) Reduce 14s. 10d. to the fraction of a pound.

10. (1) Multiply ·1 by ⚫1, and divide the product by '00625. (2) Reduce 2 to a decimal.

(3) Find the sum of 125 of 30s. and 375 of 13s. 4d. 11. How much water must be added to a cask containing 80 gal. of spirits at 14s. a gal. to reduce the price to 10s. 6d. a gallon?

12. If by selling a chronometer for £40, I lose 20 per cent., what ought I to sell it for to gain 10 per cent. ?

1. What number divided by 48,762 will give 6,285 for a quotient and 26,108 for a remainder?

2. How many dollars are there in £289 17s. at 4s. 3d. per dollar?

3. A stationer buys 36 reams of paper at 16s. 6d. per ream, and 84 reams at 17s. 9d. per ream; find his entire outlay.

4. If 2 cwt. 1 lb. cost £116 19s. Oąd. what is the cost of 1 lb.?

5. An equal number of men, women, and boys, earned £8 5s. in 6 days; each man earned 1s. 4d., each woman 10d., and each boy 4d., a day; how many were there of each?

6. If the duty on hops at 1d. per lb. amounts to £26,357 9s. 10 d., on what quantity is it paid?

7. (1) What will 1 ton 11 cwt. 2 qrs. 14 lbs. cost at £1 13s. 7d. per cwt. ?

(2) Extract the square root of 22,071,204.