10. If 2 women and 4 boys can hoe a field 1 a. 2 r. 20 p. in a day, how long will it take 2 men and 2 boys to hoe a field of 6 acres and a half? the rates of working of a man and woman being as 3 to 2 and of a woman and boy as 2 to I.

11. A combined with 3 other persons to import a chest of tea. These 3 were to take equal portions, but This he disposed

A agreed to take a double portion.

of again at cost price among 4 other persons equally, reserving as before a double portion for himself. What portion of the whole cost will fall upon A?

12. If a man earns twice as much as a woman and four times as much as a boy, when 7 men, 9 women, and 8 boys earn between them 47. Is. per diem, how much will 4 men, 3 women, and 5 boys earn in a week?

13. If 64 gals. of wine and 16 gals. of water are mixed, how much wine is there in 24 pints of the mixture?

14. If 2 lbs. 6 oz. of copper are mixed with 1 lb. 10 oz. of tin, what weight of each metal is there in a coin weighing 4 oz. ?

15. Two parcels of gunpowder contain nitre, sulphur, and charcoal in the proportion of 85, 10, '05 and '80, •12, 08 respectively: how much of each ingredient will there be in 2 lbs. of gunpowder made by taking lb. out of each parcel ?

16. A, B, C rent land; A puts 500 sheep on it for 4 months; B, 600 for 3 months; C, 1200 for 2 months: if the whole rent amounts to 116. 5s., how much has each to pay?

17. A, B, C contribute equal sums towards an enterprise; at the end of 6 months A buys of B's share and of C's: what share of the profits at the year's end will each be entitled to?

18. Four men working 15 hours, 3 men 12 hours, and

D

8 men 3 hours, jointly accomplish a work for which they are paid 67. 10s.: find the share of each man in each set, and also a man's wages per week of 6 days and 6 hours a day.

19. If a man and a boy earn 25s. in 5 days, and 2 meti and 3 boys earn 48s. in 4 days, how much would 3 men and 5 boys earn in a week?

2. Find correct to six figures the square root of

(17) 1958.

(18) 17.

3. Find to three places of decimals the square roots of

4. Extract the square roots, and where not exact to

three places of decimals, of

(1) 25, 2.5, '025, ‘00025.

(2) 16, 016, 16, 0016.

(3) 729, 729, 0729, 0000729.

5. The area of the floor of a square room is 35 square yards o ft. 9 in.: what is the length of each side?

6. A square fish-pond contains an acre; find the length of each side.

7. The surface of a square table contains 1387.5625 square inches; what is the length of a side?

9. Find the cube of '094, of '03, of, and of 2% of 18.

10. Find the 4th power of 8, of 9, of '09, and of 9.

11. Account for the use and position of dots set over certain figures in evolution, and shew that the number of decimal places in every square decimal is even.

XIX. MISCELLANEOUS.

1. If 15 cows are worth 37 sheep, find the value of a cow when 3 sheep are worth 22/. 10s.

2. If I lb. of tea is worth 50 oranges, and 70 oranges are worth 84 lemons, what does tea cost per lb. if a lemon costs a penny?

3. If A can walk 9 miles while B walks 14, and B can walk 7 miles while C walks 6, what start should C give A in a 10-mile match?

4. When a pound sterling is worth on the exchange 25.05 francs, a man sells 45 pieces of 20 francs at 16s. 2d. each; how much does he gain?

5. The centigrade thermometer in which water freezes at zero, and boils at 100°, stands at 25°; what will Fahrenheit's thermometer mark in which water freezes at 32° and boils at 212°?

6. A pays 217. 4s. income tax at the rate of 5 per cent. on his income; B pays 187. 5s. at the rate of 3 per cent.: what is the difference between their incomes?

7. A farmer makes 3 cheeses in 2 days during onehalf the year, and 2 cheeses in 3 days during the other half: how many does he make in 12 days on the average?

8. A person with an income of 500l., on which he has to pay 24d. in the pound every quarter as income-tax, finds that the payments have amounted to 261. os. 10d. in 12 months how many quarters are there in a year?

:

9. The gross receipts of a railway company are 462201.: after deducting 35 per cent. for working expenses, and paying a preference dividend of 6 per cent. on a capital of 500000l., what sum is available for division among the shareholders?

10. When the rates of exchange between England and France and England and America are 5s.=6 francs, and I dollar = 4s. 10d., how many francs will be = 290 dollars?

11. If the fare from London to Marseilles be 61. 5s. 3d., from Marseilles to Civita Vecchia 133 francs, and from Civita Vecchia to Rome I scudo 86 baiocchi, how many francs would a ticket to Rome cost, reckoning 1. = 25 francs and the scudo at 100 baiocchi of one halfpenny each?

EXAMINATION PAPERS.

ARITHMETICAL.

I.

1. A bankrupt's debts amount to 36257. 16s. 3d., and his assets to 1208/. 12s. Id.: how much can he pay in the £?

2. Reduce shilling, and

of a halfcrown to the fraction of a

of a cwt. to the fraction of a lb.

3. What will it cost to carpet a room 183 feet long and 171 feet wide with carpet 3 feet wide at 1. per yard?

4. Add together 290146, 3146'5, 2109, 62417, 14'16.

5. Divide 101 by 5, 05, 50, and 5000.

6. Reduce to vulgar fractions O1034 and 9′9.

7. Add together of 11, 11 of 15, 1 of 3%.

8. Divide of 19 by 33 of 111.

9. How many yards of canvas 18 inches wide would it take to cover a box 4 ft. long, 3 ft. high, and threequarters of a yard wide?

10. If 10257. are put out to simple interest for 13 years at 41 per cent., what will be the interest and amount? 11. Find the square root of 488601 and of 84-82410. 12. If 7 men can mow 6 acres in 12 hours, how many men will mow 15 acres in 14 hours?