ARITHMETIC.

Male Candidates.

The solution must in every instance be given at full length. A correct answer if unaccompanied by the solution or if not obtained by an intelligible method, will be considered of no value.

[This direction was repeated in the Arithmetic Paper for Female Candidates (p. 18), and in the Paper on Algebra and Mensuration (p. 20).

SECTION I.

1. Shew by a simple example that multiplication is nothing more than a shortened mode of addition. Express in figures

(a) One hundred and thirty thousand and thirteen ; (b) thirteen million one hundred and thirty-one thousand three hundred and thirteen. Find the quotient and the difference of these numbers.

SECTION II.

1. A manager's salary is at the rate of £2. 1s. 3d. per day. What will be the total amount which he has received at the end of 4 years of 365 days each?

2. A had 3,640 fourpenny pieces, B had 28,640 halfpence; which had the most money, and by how

much?

3. How much shall I have left out of £100, after buying 48 pairs of blankets at 12s. 6d. per pair, 3000 yards of calico at 48. 5d. per dozen yards, 936 reels of cotton at 158. per gross, and 15 yards of velvet at 9s. 11d. per yard?

SECTION III.

1. If 175 lbs. of standard gold be required to make 5,616 medals, what is the weight of each?

2. Out of an income of 2555 guineas it is desired to lay by £511; what must be saved and spent daily?

3. A lake which covers a space of one square mile in extent, is drained and converted into farm land. After reserving 9 acres 1 rood for roads, the remainder is equally divided among 12 proprietors; how much does each receive?

SECTION IV.

1. Find the cost of 30,030 articles at £15. 18s. 8d. each.

2. What will be the value of 60 lbs. of sugar at £28. 98. 4d. per ton?

3. A railway is constructed at a cost of £6,480 per mile. Its length is 15 mi. 3 fur. 4 poles. What is its total cost?

SECTION V.

1. Two fields are of equal area; one is 35 poles long and 25 poles broad, the other is 40 poles broad; give its length in terms of feet and inches.

2. A rate of 2s. 9d. in the £ on the rental of a parish produces £352; what is the total rental?

3. If the net income of an estate after paying all taxes be £534. 15s., and the gross income be £570. 8s., to how much in the £ did the taxes amount?

SECTION VI.

1. If I buy 3 tons of cheese at £71. 58. per ton, at what price per cwt. must I sell it so as to gain 20 per cent?

2. On the 1st of January, 1870, a contractor borrows a sum of money at £5 per cent. simple interest. At the end of a year the rate of interest is reduced to £44 per cent. The total amount of interest paid up to the end of 1875 is £1760. What was the sum borrowed? 3. A sum of money has doubled itself in 16 years at simple interest. What is the rate per cent.?

as a simple ratio.

2. A tradesman marks his goods with two prices, one for ready money and the other for credit of 6 months; what fixed proportion ought the two prices to bear to each other, allowing 5 per cent. simple interest?

3. A and B together can do a piece of work in 30 days, B by himself can perform the same in 70 days; in what time could A finish it by himself, and how much more of the work does A do than B?

SECTION VIII.

1. What decimal of a guinea is of 12s. 6d.? 2. How many paces of 2.16 feet are there in 3.25 of a mile ?

3. An estate is divided between two claimants in the ratio of 5 to 025; the money value of the smaller share is £238. 2s. ; express in guineas the corresponding value of the larger share.

SECTION IX.

1. If the value of £1 sterling varies from 25.15 francs to 26.75 francs, what is the corresponding variation in value of 100 guineas?

2. A B C D is a quadrilateral; A B-845 feet, B C 613 feet, CD-810 feet; A B is parallel to C D, and the angle at A is a right angle: find the area.

3. The wheels of a locomotive are 2 metres asunder, and the inner wheel describes the circumference of a circle whose radius is 120 metres; find the difference of the length of the paths of the wheels, having it given that the circumference of a circle equals 3.1416 its diameter.

SECTION X.

1. Define ratio and proportion. Shew that when four numbers are in proportion, the product of the means is equal to the product of the extremes.

2. Explain, as to a class, the object and the process of reducing fractions to a common denominator. Reduce to the least common denominator, 4, 1, 5, explaining the work.

3. State as precisely as possible your views as to the value of Mental Arithmetic simply as an Educational Instrument; explain how you would employ it for this purpose in the different classes of a mixed school of 120 children of from 7 to 14 years of age, and point out any faults which you have noticed in the ordinary treatment of this subject.

B

ARITHMETIC.

Female Candidates.

SECTION I.

1. Add together four thousand five hundred and ninety-eight; four hundred and sixty seven thousand and eight hundred; seventy-three thousand and nine hundred; seven hundred and twenty thousand; and four million forty-nine thousand and forty-five-from the sum take away three hundred and thirty-four thousand one hundred and forty-three; and divide the difference by three hundred and forty-five.

SECTION II.

1. Multiply 456978 by 789.
2. Divide 302129168 by 6704.

SECTION III.

1. How many days, hours and minutes in 505680 seconds?

2. How many ounces in 1 ton 7 cwt. 13 lbs. ?

1. Find the value of the sum of £453125, 1.14843753s. and ·71875d.

2. Subtract 90-41 from 300, and divide the difference by 62.

SECTION VI.

1. If of a ship be worth £36. 108. 74d., what share will be worth £125. 58. Od.?

2. A bankrupt has assets to the amount of £1020 and debts to the amount of £3225; what will his creditors receive in the £?