10. If the wholesale dealer sell to a retailer at 10 per cent. profit, and the retailer sell to the consumer at 50 per cent. profit, what proportion of the price paid by the consumer is profit?

11. A is twice, and B is just one and a half times as good a workman as C. The three work together for two days, and then A works on alone for half a day and B for one day. How long would it have taken A and C together to complete as much as the three will have thus performed?

12. A London merchant owes a sum of money in Paris: which method of payment will be most advantageous to him, a direct exchange, or a circuitous remittance from London to Venice, from Venice to Hamburg, and from Hamburg to Paris; the exchanges being as follows: £124.6 French francs, 19 francs 10 Hamburg marks, a mark=4 lire of Venice, 55 lire = £1?

=

IX.

1. IF 118 yds. of cloth that is of the width of 1 yd. cost £332. 5s. 24d., find how much cloth of the same quality, but of the width of 18 in., can be purchased for £59. 14s. 2d.?

2. If 10 francs be worth 6 florins, and 15 florins be equivalent to 4 moidores, how many francs must be given for 16 moidores?

(a)

()()()

= 0.

(-)

(a−b) (a−c) (a–d) + (b−a) (b−c) (b−d)+(c-a) (c-b) (e−d)+(d-a) (d-b)(d–c)

1

(3) 1 − (a2 + b2 — c2)2 = (a+b+c) (a+c−b) (a+b−c)(b+c−a) ̧

2ab

=

(7) Find the square root of

4a2b2

- 12a1b1+96*+ 16a3c*—246*c*+16c3.

4. Riding a journey of 27 miles into town, I meet the coach which left town at the same moment that I started from home (being at 7 o'clock) at the 18th milestone from town. Supposing that it travels 10 miles an hour, determine the hour when we meet, and the time when (proceeding at the same rate as before) I shall arrive in London.

5. A rectangular parish, which is mile long, and mile wide, is enclosed; a belt of plantation 200 feet wide being carried the whole way round, a main road 60 feet wide traversing the land parallel to its length, and a cross road 40 feet wide perpendicular to this; how many acres of field are there?

6. (a) In a cricket-match a certain number of the players make 147 runs among them, in another match this number increased by 2 make 234 runs, th

average of each being 5 more in the second case than in the first, find the averages, and the number of players who made these runs in each match.

(3) A clock which goes correctly indicates 12 o'clock when a watch indicates a quarter past 12. The watch loses 20 minutes in 12 hours. Find after what interval the clock and watch indicate the same time.

7. If 60 guns firing five rounds in 8 minutes kill 350 men in 11 hours, how many guns firing 7 rounds in 9 minutes will kill 980 men in 25 minutes at the same rate?

8. If the income-tax be 7d. in the pound in the first half of the year, and 3d. in the second, what is the net income of a gentleman whose gross annual receipts are £1542, 10s. 6d. ?

9. A man invests £15561 in shares which are at 114, and which pay 6 per cent. After 5 years he sells out, when the shares are at 102, and invests his money and the interest he has received in the 3 per cents. which are at 91. Find the income which he will receive.

11. If the coal-field of Great Britian, consisting of 8139 square miles be represented by a sq. in., what is the length of a side of the square which will represent on the same scale the coal-field of the United States, which comprises 133132 square miles?

12. The gold coin in England contains th alloy, and in Franceth alloy. In England the alloyed gold is so coined that 1 oz. is equivalent to £3. 17s. 10§d. in France, 1 kilogramme (31·15 oz.) of the alloyed gold forms 155 Napoleons. What is the real value of a sovereign in French gold money, neglecting the value of the alloy in both cases?

X.

1. (a) How would 356d 6h 9m 9.65. be expressed were a day divided into 10 oras, 100 primas, 1000 secondas, 10000 terzas?

(B) Find (1) the interest on £578. 6s. 3d. and (2) that on £578. 3f. 2c. 23m. where £110f. = 100 c. = 1000 m., each for 24 years at 2 per cent. per annum.

2. Assuming only the definition of a vulgar fraction, prove that the numerator and denominator of any vulgar fraction may be multiplied or divided by the same integer without altering its value.

What fraction of a sovereign is 4-1044 +9 - 5 of a penny?

3. Obtain the continued product of a+b+c+d, a + b - c - d, a — a-b-c+d, -b+cd: also of a+b+c+d, a- ·b+c+d, a + b − c + d, a + b + c −d; and the sum of these products.

a

4. Find the L. C. M. of (1) 12, 20, 30, 70, 74. (2) 1036, 987. (3) 1·36652 and 246-8642. (4) 15x3- 23x2+9x − 1, 1513 +7x2 - 7x + 1, 15x3 — 17x2 + x + 1.

5. Define Course of Exchange, and Par of Exchange. When £170 will purchase 4233 French francs, what is the course of exchange between London and Paris? And, if 503 gold pieces of 20 francs contain as much pure gold as 400 sovereigns, what is the par of exchange between London and Paris?

6. Prove the rule for the solution of an adfected quadratic equation.

Solve the following equations:

(a) 5x-{8x-3 (16 – 6x − 4 – 5x) } = 6.

7. Supposing the supply from California to become so great that the market price of gold decreases in the ratio of 7:5, what would be the absolute loss sustained by a fundholder upon every £100 which was paid off at par, if he had bought in before the depreciation took place, when the price of stock was at 89}?

8. With a gallon of rum which cost 15s. a man mixes a quart of water, and then sells it for 16s. a gallon: with a gallon of gin at 11s., he mixes 23 pints of water and sells it at 12s. a gallon: and with a gallon of brandy which cost 22s. he mixes 3 pints of water, and then sells it for 23s. a gallon; how much does he gain per cent. supposing him to sell twice as much rum as gin, and twice as much gin as brandy?

9. The Squire of a Parish bequeaths a sum equal to one hundredth part of his estate towards the restoration of the Church; £200 less than this towards the endowment of the School; and £200 less than the latter sum to the County Hospital. After deducting these legacies of the estate remains to the heir. What was its value?

10. A field of 7 acres is sown with turnips, beet, and cabbages; the areas of the crops being respectively as 13 1: 14. If the values of an acre of

:

be also respectively in the same ratios, and an acre of turnips be worth £7; what is the worth of the whole crop?

11. A person purchases a hundred shares in a company at £3500; and ultimately sells at a profit of £43 per cent., after having received four dividends of 15s. 4d., 20s. 10d., 30s. 4d., and 38s. 9d. a share; by how much do his receipts exceed his outlay?

12. There was a run on two bankers A and B; after 3 days B stopped payment when the daily demand on A was trebled, so that he failed after two days more. If A and B had joined their capitals they might have stood the run as it was at first for 7 days when B would have owed £4000 to A; find the daily call on A at first.

1. Forty-three; sixty; eighty-eight; ninety-seven; fifty-nine; twelve; twentyone; nineteen.

2. Two hundred and fifty-six; four hundred and one; five hundred; nine hundred and ninety-nine; three hundred and sixty-five; five hundred and seventyeight; eight hundred and thirty-seven.

3. Two thousand; one thousand, seven hundred and twenty-four; three thousand and three; seven thousand, five hundred and eighty-four; one thousand and seventy-five; four thousand, five hundred and forty-one.

4. Thirty-seven thousand and three; forty-seven thousand and forty-nine; sixty-three thousand and ninety; eighty thousand and eight; three hundred and forty-one thousand, three hundred and twenty-three.

5. Six millions, eight hundred and fifty thousand, four hundred and six; eight millions, eighty thousand, eight hundred and eight; seven millions, eight hundred and forty-nine thousand, six hundred and thirty; four hundred and eighteen thousand, two hundred and fifty-four.

6. Ten millions and one; twenty millions, two hundred and twenty thousand and twenty-two; ninety-two millions, five hundred and sixty-eight thousand, nine hundred and eighty-seven; thirty millions, one hundred and eighty thousand and seventy.

7. Two thousand five hundred and sixty millions, five hundred and thirty thousand, two hundred; eight hundred millions, three hundred and nine thousand, five hundred and sixty; nine thousand seven hundred and thirty-eight millions, four hundred and thirteen thousand, two hundred and eight.

8. Seven thousand and seventy millions, four hundred and twenty-three; nine hundred and eighty-seven millions, six hundred and fifty-four thousand, three hundred and twenty-one; five thousand seven hundred and seven millions, sixtyeight thousand and eighty.

9. One hundred billions, one hundred and ninety-eight thousand seven hundred millions, ten thousand and ninety; forty-eight thousand seven hundred and twenty-six billions, eight hundred and seventy thousand six hundred and thirtyfour millions, one hundred and three thousand, two hundred and sixty-four.