(7) How many articles at 8s. 10d. will cost £1 1s. 64d. more than 5580 articles at 5s. 33d.?

(8) A wes B £1602, but becoming bankrupt, A pays each of his creditors 18s. Od. in the pound: what will B löse ?

(9) In one week 4512 passengers travelled on the Great Eastern Railway, and the average sum paid was 13s. 7μd., what were the total receipts for this week?

(10) A railway cost £3248000: in one year the profits were £2 16s. 104d., and the next £1 19s. 11d. on every £100 invested: what was the difference between the whole profits of these two years ?

(11) How much more will 13 cwt. 16 lbs. at £1 2s. 1d. per cwt, cost, than 22 cwt, 2 qrs. 10 lbs. at £1 7s. 3d. per cwt?

(12) What will be the cost of 29 m. 3 fur. 6 po. of wire at 78. 93d. per mile ?

(13) A proprietor sold 1193 oxen for £19 9s. 94d. each, and after having paid away £3964 16s. 5d. he spent the remainder in purchasing sheep at £1 18 64d. each: how many sheep did he buy ?

(14) A man who has 22 qrs. 4 bus. 8 gals. of corn to sell is offered £50 for it, he refuses the offer, and sells the corn a week after at 45s. 6d. per qr.; what did he gain by the delay ?

(15) If 7 cwt. 32 lbs, of new lead at £1 13s. 9d. per cwt. be exchanged for 11 cwt. 1 qr. of old lead at £1 2s. 9d. per cwt., what sum of money ought to be paid with the new lead ?

3 po.

(16) What would the rent of 13 ac. 3 rds. 33 p at £16 5s. per acre ?

of land

(17) The planting of a rood of ground cost £3 5s. 4d, : what will be the cost of planting 13 ac. 3 rds. 331 ps. P

(18) A rents 204 acs. 1rd. 20 ps. at £4 11s. 6d. per acre, and B rents 225 acs. 2 rds. 12 ps. at £6 2s. 6d. per acre, B's land produces half as much again as A's: which has the best bargain?

Examination Papers.

(1) What number taken from a million and eighty will leave the sum of seven thousand nine hundred and four, and six thousand eight hundred and eighty?

(2) Show, by making three examples, that if each of two numbers be multiplied by a third number and the products added, the same number is obtained as when the sum of the two numbers is multiplied by the third.

(3) The smaller of two numbers is contained 5423 times in 3270069, and the larger is contained 33 times in 63393. How much greater is one number than the other?

(4) A purse and its contents are worth £20 3s. 63d., and 7 times the contents + 4 times the value of the purse is £117 Os. 6d. Find their respective values.

(5) Three persons having a sugar loaf weighing 48 lbs. wish to divide it equally among them, but they have only a 7 lb. weight and a 4 lb. weight: how can the distribution be made?

(6) If divisor and dividend be multiplied by the same number, what difference is made in the quotient and what in the remainder?

Divide £387 17s. 6d. by 16%.

(7) Write down the table of time, and show how to determine when a year is leap-year.

(8) Explain the relation between the units of length, surface, and solidity used in England.

(9) A race course is 1826 yds. round. There were 15 horses in a race twice round the course. How many inches did they run altogether?

(10) Divide 40 lbs. into 4 parts which will serve to weigh any number of lbs. up to 40.

(11) Three fields, which contain altogether 29 ac. 15 po., were left to three brothers. The eldest took the largest field, and paid to his brothers £36 13s. 4d. The second son took the second field, and received £10 16s. 8d. of the sum paid by the eldest. The land was valued at £16 per acre. What was the size of each field?

(12) A person buys 28 bags of linseed, each weighing 3 cwt. 18 lbs., at £2 4s., and pays for carriage 2s. 2d. per bag. He retails it at 54d. per lb. What is his profit ?

(13) A grocer mixes 48 lbs. of tea, which cost him 2s. 8d. a lb. with a certain quantity at 2s. 6d. a lb. He sells the whole for £16 1s. 6d., and gains by the transaction £2 3s. 6d. How much tea did he sell?

(14) The water in a cistern 3 ft. long, 2 ft. 6 in. wide, and 2 ft. deep, exactly fills a number of bottles of equal size. Each bottle weighed 1 lb. 7 oz. when empty, and 8 drs. less than 9 lbs. when full. How many were there? (15) A manufacturer's profits average £147 10s. 8d. per week. He 20 pays persons at the rate of 1 guinea a week, 10 at 18s. 9d. per week, and 3 at 12s. 74d. per week. For rent and machinery he pays £1872 11s. 9d. a year. What is his yearly income ?

(16) What must 12345679 be multiplied by to give 888888888 ?

(17) What number is that from which if you deduct 27568 the remainder will be 3149 times 1538?

(18) Victoria was 49 years old in 1868, and the Duke of Wellington was 50 years old in 1819. In what year was the Duke of Wellington three times as old as the queen

?

(19) A farmer purchased 36 oxen for £848 10s. 3d. Four of them died, and he then sold the remainder so as to gain £33 15s. 4d. on the whole. At what price per head did he sell them?

(20) A quantity of lead weighs 12 tons 13 cwt. 25 lbs., and is made into sheets each weighing 2 cwt. 7 lbs. How many sheets will there be, and how much lead to spare?

(21) A cart wheel is 3 ft. in circumference. How far will it go in one revolution, and how many revolutions will it make in 10 m. 7 fur. 11 po.1 yd.?

(22) A man walked 78 miles in 20 hours. He walked at the rate of 4 m. 10 po. per hour for the first 6 hours, and 3 m. 7 fur. 20 po. per hour for the next 8 hours. Find his average rate for the remainder of the time.

(23) How many half-guineas are there in 588 halfsovereigns ?

(24) If 9 men and 12 boys do as much work in a week as 12 men would do, how many boys must assist 4 men that they may do in a certain time the work which 17 men and 16 boys can do in the same time ?

(25) How many gallons will a cistern hold which contains 277 cubic feet?

(26) What is the circumference in feet of a coachwheel which turns round 7850 times in 23 m. 5 fur.?

(27) Two persons having a gallon measure full of ale wish to divide it equally between them. They have two empty vessels, which contain respectively 5 pints and 3 pints. How may they measure exactly their shares with these vessels ?

(28) Divide 16,306 lbs. by 62, and 16,306 lbs. by 62 lbs., and state what is the difference between the two questions. (29) The product of two numbers, one of which is 149 more than the other, is added to 38,378, and it is found that the sum subtracted from a million leaves half a million. What are the numbers?

(30) A farmer sold a number of turkeys and four times as many geese for £7 8s. 6d. Each turkey was sold for half as much again as a goose, and all the geese were sold for £3 7s. 6d. more than the sum received for the turkeys. Find the number of turkeys and geese sold, and the price of each.

(31) The following errors were made in writing a bill. A O was mistaken for a 6 in the pence. £3 5s. was written instead of 3s. 5d. The amount of 12 dozen articles, at 41d. each, was set down as 4s. 6d. ; and in adding up the pence column, which amounted to 84 pence, 4 was set down and 8 was carried to the shillings. How much less was charged than ought to have been?

(32) A house agent collected a quarter's rent from 9 tenants. Eight of them paid respectively £11 3s. 4d., £12 17s. 6d., £13 9s. 4d., £8 15s. 8d., £24 9s. 6d., £15 15s. 3d., £10 12s. 6d., and 21 guineas. The ninth payment was equal to the sum of the first three less the fourth. The agent paid to the landlord £145 6s. 8d. What did he charge for collecting?

(33) Write out Wine Measure, and find how many hhds. there are in 2205 puncheons.

(34) Multiply 18,643 by 52,800, and explain each step of the process.

(35) Multiply 27,564 by 1944, and also by the numbers

4, 6, 9, and 9 in succession. Compare the results, and state the fact they illustrate.

(36) Why is multiplying a number by itself called squaring the number ?

(37) Why is multiplying together a number and its square called cubing the number?

(38) 30 yds. of flannel are bought, and three portions of it, measuring respectively 7 yds. 3 qrs., 15 yds. 3 nls. 2 in., and 5 yds. 3 nls. Îin., are sold. How much more is sold

than is left?

(39) The cost of 30 pieces of silk is £102 17s., at 7s. 94d. per English ell. How many yards did the piece contain ? (40) How many links must be taken away from 3 ms. 7 furs. 11 yds. that it may contain an exact number of chains ?

(41) How many yards of carpet, 3 qrs. wide, will have the same extent of surface as a rectangle 10 ft. wide and 16 ft. long?

(42) 84 yds of carpet, an ell wide, are required to cover a room 15 ft. long. What is its width?

=

=

(43) Divide £648 16s. 11 d. amongst 3 persons, A., B., and C., so that of A.'s of B.'s of C.'s portion. (44) How many bottles, each containing 13 of a pint, can be filled out of 1 pipe of wine?

(45) What is meant by the G. C. M. of two numbers? What difference is there between the G.C.M. and L.C.M.? Find the G.C.M. and L.C.M. of 1848, 3366, 396.

(46) Define a fraction, and from the definition of a fraction show that =

(47) Reduce to common denominators,, 1, 17. (48) Find the sum of ↓ ↓ ↓ ↓ ↓ ↓ J.

(49) What decimal is 1 lb. avoir. of 1 cwt.? (50) The assets of a company £2773125, and debts 5 millions: what is the debt on which they pay £2700? (51) How many times is 278. contained in of £4; P (52) Subtract of 7 poles from 283 square yards. (53) Divide of by of 11 of 11% of, and multiply the quotient by 61f of 7.