2. Simplify the fraction 37037

428571

3. Express as a recurring decimal the value of

4. Calculate the cost of 27 tons 1 cwt. 3 qrs. 4 lb. of coal at 288. a ton, and also the net cost if 2 per cent. discount is allowed for cash.

5. Find the amount of £8000 which is allowed to accumulate for three years at 4 per cent. per annum compound interest.

6. Excursion tickets are issued at the rate of a single fare and a quarter for the double journey. Find the cost of eight and a half such tickets for a journey for which the single fare is 38. 8d.

7. The area of a rectangular field is 20 acres, and the length of one side is 800 yards. Find the length of the other side, and the cost of fencing the whole field at 64d. per linear foot.

8. Assuming that a cubic foot of water weighs 1000 oz., find the depth of a rectangular tank, the area of whose base is 28 square feet and which contains a ton of water.

9. Divide £1087. 2s. 6d. among 2 sons, 3 daughters, and one grandchild, so that the shares of a son, a daughter, and a grandchild may be in the ratio of 3:2:1.

10. Find the income obtained by investing £525.16s. 8d. in Bank of England Stock at 315 paying 9 per cent. How much money would have to be invested in 2 per cent. Consols at 90 in order to obtain the same income?

XII. SEPTEMBER, 1904.

1. (1) Multiply 06351 by 039 and divide the result by .00013.

(2) Divide nine thousand one hundred and fiftythree million fifty-three thousand and one by three million fifty thousand and one.

2. (1) Simplify

(2) If A is fraction is A of C?

13

of 23 of B, and C is 13 of B, what

4.155

3. (1) Reduce to a decimal fraction 2+3 of 277

(2) Reduce 3 cubic yds. 13 ft. 864 in. to the decimal of 3 cubic yds.

4. Find the true discount on £565 due four months hence at 3 per cent. per annum.

5. Find the cube of 4.41 and extract the square root of the result.

6. A man has £7925 stock in three per cents. He sells out at 96 as much of this stock as will realize £4200, and keeping the remainder in three per cents., he invests the proceeds of the sale in five per cents. at 105. Find the change in his income.

7. Three men can mow a certain field in 6 days. At the end of the second day one of them falls ill, and the other two finish the work after mowing 9 days from the time when they began. How long would the third man have taken to mow the whole field by himself?

8. How many times will a wheel, whose circumference is 8 feet, revolve in a journey of 24 miles 2 furlongs 24 poles 4 feet?

9. A tradesman, who is selling off, states that he will make a reduction of 20 per cent. from the marked price. At what price will he mark goods, for which he wishes to receive 11s. 8d.?

10. Find, by Practice, the cost of 27 cwt. 3 qrs. 21 lb. at £365. 68. 8d. per cwt.

11. There is a walled garden 105 yards long and 95 yards wide. A path 3 feet wide has to be made round it, on the inside, so as to leave a border, 4 feet wide, between it and the wall. How many square yards will the path cover?

XIII. MICHAELMAS TERM, 1904.

1. Find by Practice the value of 1684 articles at £1. 168. 10d. each.

7

2. Simplify (1) 1-3+31-21 +12 and (2) 13158.

3. (1) Divide 003 by 01, and multiply the result by .002.

(2) Reduce 418 to a vulgar fraction, and to a recurring decimal.

(3) If I spent .82 of the money in my purse, and find that I have 3 shillings left, what had I to start with? 4. A gentleman has an estate 23 miles long by 11 miles broad; find the extent of his acreage. He is apportioning 20 acres for allotments of 16 poles each; find the number of allotments.

5. In a constituency there were 9453 voters on the register. At an election 1301 abstained from voting, and the successful candidate had a majority of 86 votes. What number of votes did each candidate receive?

6. In the year 1903 there were 22992 marriages in Ireland. The number was equal to 5.21 per thousand of the population. Find to the nearest unit the number of the population.

7. There is a square garden, in which there are 400 linear yards of footwalks, 3 feet wide; the flower-garden contains five times as much space as the footwalks, and the vegetable-garden contains twice as much as the flower-garden. Find the length of the side of the garden.

8. A testator left property which realized £130500. His instructions were that it should be apportioned to his relatives, to charitable institutions, to the University, to the foundation of scholarships, to minor legacies in the proportion of 13:7:5:3: 1. Divide his estate.

9. A person received a legacy of £1000 which he invested in Canadian Pacific Railway Stock at 80. When the Stock rose to 138, he sold out, and invested the proceeds in 3 per cent. Debentures at 75. Find his income, and the market value of his capital, when, subsequent to his purchase, the Debentures rose to par.

10. If a sum of money has to be put out at interest for three years, find whether it is more profitable to invest it at 3 per cent. Simple Interest or at 3 per cent. Compound Interest.

11. A woman bought two parcels of eggs, the same number in each parcel. The first she bought at 1d.

each, but the second at 3 for 2d. She then mixed them all together and sold them at 13d. a dozen. Find her gain per cent.

12. A garrison has supplies of food, sufficient to maintain 20000 men for 48 days, at the rate of 12 oz. per man per day. To what number must the garrison be reduced that the supplies may last for 72 days at the rate of 10 oz. per man per day?

XIV. HILARY TERM, 1905.

1. (1) Multiply £2904. 178. 34d. by 805.

(2) Divide 18972 tons 13 cwt. 2 qrs. 12 lb. by 348. 2. Find: (1) The L. C. M. of 63, 196, 238, 2601. (2) The square root of 2.140369.

3. Simplify:

1+

4. A clerk has an income of £100 a year. Lodgings cost him 118. a week, food 28. a day, clothing 308. a month, books 88. 4d. a month, insurance £1. 188. Counting the year at 52 weeks but 365 days, what sum has he left for incidental expenses, and how much (to the nearest halfpenny) does it allow him a day?

5. (1) Express as a decimal, 13901 as a vulgar fraction.

(2) Find the value of 1.09 of 7.3 of 27 yds. 1 ft. 6 in. 6. If a train is running at the rate of 45 miles an hour, find the distance that it runs in a second, and express it as the decimal of a furlong and of a mile.

7. Find the present value of £1875. 178. 6d., due 18 months hence at 5 per cent. per annum.

8. If timber is purchased at 5d. per square foot, how many square feet must be sold for 128. 6d. to gain 25 per cent. profit?

9. In a town, of which the rateable value amounts to £105000, the School Committee requires £4156. 58. Find to the nearest penny the amount of school-rate paid by a person whose house has a rateable value of £66. 138. 4d.

10. If 7 cows and 10 sheep together cost £119. 68. 8d., and 4 cows and 12 sheep together cost £75, what will be the cost of one cow and one sheep respectively?

11. A marsh which covered a space of one mile in length and three-quarters of a mile in breadth was drained and turned into farm land. Roads took up 4 acres of the reclaimed land; four neighbouring proprietors divided the remainder in parcels proportional to 3:4:45. How many acres did each receive?

12. A and B each received £1000. A invested his money in a mortgage at 4 per cent. B placed his money in Grand Trunk of Canada Stock, buying in at 9. This Stock paid no dividend, but after 18 years stood at 183, when B sold out. On each of his transactions he paid a brokerage of per cent. Find (1) the amount of Stock which B purchased, and (2) whether, at the end of the 18 years, A's or B's investment proved to have been the more profitable.

10625 (2)

36125.

2. (1) Multiply 4.025

by .0000004.

by .007 and divide the result

(2) Express 0571428 as a vulgar fraction, and as a decimal.

3. I bought a third part of a steamer, and then sold 375 of my share to a friend. Two months afterwards I bought from a fellow shareholder, who owned a half of