in the same form as the price, or it may be expressed as a per

From (1) and (2) we deduce

na shillings new price = n shillings old price.

Suppose that the change given in the form of a percentage is 10 per cent. advance.

Ex. 1.-Find the value of the wheat crop grown on 89 acres, when the average yield is 31 bushels per acre, and the price of wheat is 6s. 3d. per bushel.

25 shillings

=

4 bushels,

Ex. 2.-What do eggs cost per dozen when 12 fewer in a shilling's worth raises the price 2d. per dozen?

Here we have an equation in which the unit is the same on the two sides; it can therefore be solved on general principles, independently of the unit. It reduces to the quadratic equation x2 + 2x 24 0;

hence x = 4 or 6.

=

It is the positive value which is the answer

to our question; hence the answer is 4 pence per dozen.

Ex. 3.-A and B together spend a shilling on 65 apples, A's costing six a penny, and B's 20 per cent. more.

How many did

20 pence additional = 100 pence by 4,

penny additional = penny by A, penny = 6 apples,

Price paid by A,

1 penny

=

5 apples.

6

5

And B

from which x = 30. Hence A bought 30 apples, and B 35.

Ex. 4.—If 3 ducks be worth 4 chickens, and 2 geese be worth

7 ducks, find the value of a goose when a pair of chickens can be bought for 3s. 9d.

Ex. 5.-There are two coins such that 15 of the first and 14 of the second have the same value as 45 of the first and 6 of the second. What is the ratio of the value of the first coin to that of the second?

Let V denote the first coin, and V' the second. Then we have 15 V+ 14 V' = 45 V + 6 V',

Thus 4 of the second coin are equivalent (in value) to 15 of the first.

Ex. 6.-Find the cost of electric lighting for 13 weeks, with sixty lamps burning on an average eight hours per day, the rate of charge being 21d. per lamp per hour.

EXERCISE II.

1. Find the value of a steel hammer weighing 225 tons at the rate of 1 lbs. for 3d.

2. Find the value of 1000 lbs. pimento sold at 31 d. per lb.

3. Three thousand workmen strike because an advance of one halfpenny per hour is not conceded. Find the additional sum which would be required weekly to concede the demand, taking a working day to consist of nine hours.

4. A burner consuming 4 cubic feet of gas per hour is used on an average 6 hours per day during a year. Required the cost at 48. 6d. per 1000 cubic feet.

5. If, for this country, we have on an average eighteen letters per head per annum, find the average number of letters for a month; and also the revenue for the month, taking the average postage at one penny halfpenny per letter. The population is 35,262,762.

6. Find the value of 215 tons 17 cwt. 3 qrs. 9 lbs. of cast-iron at 97. 11s. 61d. per ton.

7. Calculate to the nearest farthing, by whatever process you consider the most convenient, the cost of 19 tons 19 cwt. 3 qrs. 27 lbs. of merchandise at 197. 19s. 11 d. per ton.

8. A farmer sold seven oxen and twelve cows for 2501. He sold three more oxen for 50%. than he did cows for 30. Required the price of each.

9. If 21 men in 27 days receive 1417. 15s. in wages, how many men must work 21 days to earn 1577. 10s. ?

10. If it cost 617. 18s. 5d. to keep 2 horses for 11 months, how long can 3 horses be kept for 591. 2s. 11⁄2d. ?

11. How far ought 4 cwt. to be carried for 11s. 10d. when the carriage of 17 cwt. for 52 miles cost 8s. 4d.?

12. If 64 cwt. carried 40 miles cost 10s. 8d., what will 80 cwt. carried 63 miles cost?

13. A reduction of 20 per cent. in the price of beef would enable a purchaser to obtain 6 lbs. more for a sovereign. What is the reduced price?

14. What are ashes per 100 loads when 8 more loads for a sovereign lower sthe price a penny a load?

15. What are eggs selling at when, if they be raised threepence the dozen, one would get four fewer in a shilling's worth?

16. A reduction of 30 per cent. in the price of eggs would enable a purchaser to obtain 54 more for a guinea. What may the present price be?

17. A reduction of 10 per cent. in the price of iron would enable a purchaser to obtain one hundredweight more for a sovereign. What is the present price? 18. "There is not one of those countries where they don't pay 30 to 40 per cent. more for sugar than you would pay in England." Find the approximate foreign price when the home price is 5d. per lb.

19. In a mixed excursion train of 1000 passengers, the fares in the three classes are in the ordinary proportion of 4, 3, 2; and the corresponding receipts are 521.,

B

577., and 617. respectively. Required the fare and the number of passengers in each class.

20. A gets half of B's money, and then B gets half of A's; B then has 20 per cent. more than A. What relative sums had they at first?

21. How many lbs. of butter at 1s. 3 d. per lb. must a farmer give to a grocer for 8 lbs. of sugar at 5id. per lb.?

22. A farmer sold on one day 2 oxen and 3 sheep for 347. 10s,, 4 oxen and 5 sheep for 677. 10s., and 6 oxen and 7 sheep for 100l. Is it possible that all the oxen were sold at one price, and all the sheep at one price?

23. 14 tons 3 cwt. copper at 921. 15s. per ton; 12 tons 12 cwt. spelter at 35s. 10d. per cwt. ; 3 tons 5 cwt. tin at 78s. 9d. per cwt. Coal consumed, 14 tons at 14s. 3d. Loss of metal in casting. Labour equal to one man for 31 days at 48. 9d. Other expenses reckoned at 1257. What is the cost per ton to the nearest shilling?

SECTION III.-PROFIT AND LOSS.

ART. 23.-Profit and Loss. A merchant both buys and sells. Suppose that a grocer buys at the rate of

from these two rates we deduce a third, viz. :—

n pence receipt = m pence cost.

(1)

(2)

(3)

Again, from (1) and (2) we deduce the rate of profit or loss; it has three forms depending on the three quantities involved in the

(nm) pence profit or loss = n pence receipt.

(4)

(5)

(6)

If n is greater than m we have profit, if n is less than m we have loss.

=

Observe-The sign in these equivalences means for every. When the number on the right-hand side of the equivalence is 1, it need not be expressed.