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5. A yearly income of £500 has to be divided among three persons in the ratio of 3:7:9, after the income tax of one shilling in the pound has been paid. How much will each receive ? 6. Find the square roots of

237,45 and 47829.69. 7. If by selling eggs at a ponny each, I gain 20 per cent., what was the cost price of twenty dozen eggs ?

8. Find the compound interest on £500 for four years at 5 per cent. per annum.

9. În a town the rateable value of which is £95,000, the amount charged on the rates for the purpose of education is £3240. 158. Find to the nearest penny the amount paid for education by a man whose property has a rateable value of £70.

10. The difference between the incomes derived by investing a certain sum in 5 per cent. stock at £160 and 3 per cent. stock at £125 was £13. What was the sum invested ?

XX. SEPTEMBER, 1906.

1. Find the cost of 2345 articles at £2. 28. 2 d. each.

2. Divide 6o by 318, and .025 by 27. Multiply ·060253 by 3.62.

3. Reduce £5. 148. 4d. to a decimal of £7. 4. Find the G.C.M. of 22100 and 18759. . 5. Find correct to the nearest penny the simple interest on £550. 168. 9d. for 5 years at 4 per cent. per annum.

6. A train is travelling at 70 miles an hour, find how many inches it travels in one second.

7. A man buys apples at 3£d. a dozen and sells them at 5 for twopence. How much per cent. profit does he make ?

8. Find the true discount, correct to the nearest penny, on £155. 108. due in 8 months, interest being charged at 5 per cent. per annum.

9. What sum must be invested in 4 per cent. stock at 105 in order to produce an income of £156 after deducting income tax of 6d. in the pound ?

10. A quadrangle which is 35 yards long and 29 yards 1 foot wide, has a gravel path 7 ft. wide all round it and a rectangular plot of grass in the middle. How much will it cost to returf the grass plot with sods, 3 ft. by 1 ft., at 2d. a sod; and to put gravel down on the path at 18. 6d. a square yard ?

11. A person invested £772. 10s. in 21 per cent. consols at 90. He afterwards sold out at 93} and invested the proceeds in 45 per cent. stock at 103. What addition is thereby made to his income?

ALGEBRA

I. MICHAELMAS TERM, 1901. 1. Find the value of

[a? — (b-c)]? –[B2 – (a-c)2]-[c? – (ab)?], when

d=3, b= -2, c=1, and resolve into factors 22—(a + b)x+ab, x2 + 4x — 21, 1684–1,

a? +62 – 02- 2 ab. 2. Multiply

223 — 322 y + 4xy? - yu by 202 + 3xy-y?, and give the 4th power of 2a-b. 3. Divide

26 — 2 25 + 6x4 – 3x3 + 3x2 + 7x + 4 by 22 – 3+ 4. 4. Find the G.C. M. of

4203 – 80— +2 and 4.0,3 – 12 x2 – 19x + 12. 5. Find the L. C. M. of

23 yo, xoy + y4, 22 + xy + yo, x2y2-y4. 6. Simplify:

al + b2 a_72
a? 72 a2 + 22

a+b a-bi
a bato

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9. A ballot-box contains black balls and white balls, 125 in all. If there were twice as many black balls and half as many white balls, the whole number would be 40 less. How many black balls are in the box ?

10. Two trains start at the same time, one from Exeter at the rate of 50 miles an hour, and one from London at 55 miles an hour. If the distance between London and Exeter is 194 miles, how far from Exeter will they meet?

II. HILARY TERM, 1902. 1. Find the value of

203 + Y'? + 23 + xy2 + x2y +xz2 + ? 2 + yz2 + yaz when x = 2, y = -1, z = 3, and resolve into factors

22 + (ab)x - ab, 202 -- X – 30,

2502 – 9y, 12+c2-a2 + 2 bc. 2. Multiply

24 + 32o y + 822y2 8y4 by 22 – 3 xy + y, and express in the simplest form (ab)8 (a2 - 2ab-62).

3. Divide
10.806 ye – 27x++ 4?y* – 9x2y6 — 2 xy6

by 5x2y wy2 + 2 y3. 4. Find the G.C. M. of

Q2 + 4x + 3 and 26 + 5 x? + 6. 5. Find the L. C. M. of 5(22 - 2xy), 10(xy + 2 y), 15(wya494),

20(@+ + 42-y?).

6. Simplify:
(1) G + - 2) 6 + + 2) =-6 –2);

-1 6+1)
ab +1 -!+ ab-í
a +1

a(6-1)
ab - 1+ ab + 1
7. Find the square root of
(1) 1624 — 24 23 – 31 x2 + 30% +25;

2 , 79 10.
(2) 402 — 20x + 5-50+

1

m2 8. Solve the equations :

(2) 38–11 _ 97 -- 7 _ 5(8—1)
(2)

111 – 38.
*16-- 2 = 8 - 4 ;
(3) 2+ 6y=28,

5x + 174 = 274. 9. A person spent £14. 118. 8d. on tulips, buying three consignments each containing the same number of bulbs. For the first he paid at the rate of ninepence a dozen, for the second at the rate of fifteen-pence, and for the third at the rate of eighteen-pence. How many were there in each consignment ?

10. On a division being taken at a general meeting of a Club, if the supporters of the motion had been increased by 50 from the other party the Ayes would have been twice the number of the Noes, but if the opponents of the motion had received 80 from the other side the Noes would have been twice the number of the Ayes.

Find the number of members who voted on each side in the division.

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