12. Three persons share £1000: B=2 A-£50, C=2 B+£30. Find the share of each.

13. Divide £4000 among four persons, so that A's share= B +£40, C's 2 B+£70, D's= } B—£20. What does each man get?

What

14. A sum of £91. 10s. was distributed among 15 men, 17 women and 8 children; each woman's share was three times as much as that of a child, and 13 of that of a man. did each man, each woman, and each child receive? 15. A detachment, consisting of five companies, compose a garrison, in which the duty requires 152 men per day. What number of men must each company furnish, according to their strength; the first company containing 108 men, the second 102 men, the third 96 men, the fourth 78 men, and the fifth 72 men.

16. A general laid a contribution of £140000 on four towns, to be paid according to the number of inhabitants contained in each the first had 50000, the second 70000, the third 80000, and the fourth 100000 inhabitants. What part must each town pay?

17. In a manufactory, each man receives 16s. 6d. per week, each woman 10s. 6d., and each boy 4s. 6d. The whole wages in a month, of 24 working days, are £1273. 10s., of which the men received £924, and the boys £76. 10s. How many men, women, and boys are working in the manufactory, and what is each person's wages?

18. Three corn factors freighted a ship; the first loaded 360 tons of corn, the second 200 tons, and the third 160 tons; on the voyage, during a storm, the sailors were obliged to throw overboard a part of the cargo, viz., 150 tons of the first factor, 90 of the second, and 30 of the third. How are they to settle accounts, so that the loss be shared according to each factor's load?

PROFIT AND LOSS.

301. In every mercantile transaction, some of the parties engaged may either gain or lose, or neither gain nor lose. Questions in which one of these three alternatives is to be determined, are classed under the head of Profit and Loss.

Ex. 1. Bought, 124 yards of cloth, at 15s. 6d., and sold it at 17s. 9d. What did I gain?

.1 yard is bought at 15s. 6d.,

..124 yards are bought for 124 × 15s. 6d., or £96. 2s.

And 1 yard is sold for 17s. 9d.,

.. 124 yards are sold for 124 × 17s. 9d., or £110. ls. Hence the gain=£110. 1s.—£96. 2s.=£13. 19s.

Or thus the gain per yard is 17s. 9d.—15s. 6d., or 2s. 3d; .. the gain on 124 yards is 124 × 2s. 3d., or £13. 19s. as before.

Ex. 2. If tea be bought at 4s. 6d., and sold at 6s. 2d. per lb, what is the gain per cent.?

on 4s. 6d., or 54d., the gain is 6s. 2d.-4s. 6d., or 1s. 8d., or 20d.,

Ex. 3 Bought, a horse for £66, and sold it again for £57. What did I lose per cent.?

Here the loss on £66 is £9,

Ex. 4. If coffee is bought at 3s. 4d. per lb., what must it be sold at to gain 24 per cent.?

Here we perceive that 100 are sold for 1244,

..3s. 4d. are sold for

31s. X 124

100

or 4s. 13d. nearly.

Ex. 5. Bought, velvet at 8s. 8d. per yard; but it getting damaged, I am compelled to sell it at a loss of 3911 per cent. What is the selling price per yard?

Here 100 are sold for 100-3911, or 6015,

.8s. 8d. worth, or 1 yard of velvet is sold for 104d. x 60

..

or 5s. 3d.

100

quantity of cloth, at 16s. 6d. What was the prime cost? 112 the prime cost is 100, 100 x 16s. 6d.

Ex. 6. Having sold a certain per yard, I gained 12 per cent. By the question, we see that for .. for 16s. 6d. the prime cost is

112

=

14s. 811d.

Ex. 7. By selling goods at 6s. 10d., I lost 18 per cent.

What did I buy them for?

It is evident that for 814 the prime cost is 100,

100 × 6s. 10d.

.. for 6s. 10d. the prime cost is

=8s. 443d.

811

Ex. 8. By selling cloth at 14s. per yard I gain 10 per cent. What did I gain per cent. by selling at 17s.

1st method: Here 110 cost 100,

.. 14s. worth, or 1 yard cost

100 x 14s.

110

per yard?

ΤΙ

=1109. = 12,318.;

2nd method: When sold for 14s., I get 110 out of 100,

.. when sold for 17s. I get

110 × 17

14

or 1334 out of 100.

Hence 1334-100=334-the gain per cent.

Ex. 9. By selling linen at 5s. per yard, I lost 16 per cent. What did I lose by selling it at 4s. 4d.?

2nd method: When sold for 5s. I get 84 out of 100,

84×4

.. when sold for 43s. I get

= 72 out of 100.

5

Hence, loss per cent. is 100-721, or 27},

Ex. 10. If 10 per cent. be gained by selling tea at 4s. 6d.

per lb., what must it be sold at to gain 36 per cent.?

1st method. 110 cost 100,

By the second part of the question, we have: 100 sold for 136,

..4s. worth, or 1 lb. of tea is sold for

22

511s., or 5s. 61d. 127

2nd method. if 100 sold for 110, I get 4s. 6d. per lb,,

.. if 100 sold for 136, I get

136 x 4s. 6d.
110

or 5s. 6d. 187.

Ex. 11. A person sold a horse for 70 guineas, and lost 15 per What should he have sold it at to gain 20 per cent.? Here, if 100 sold for 85, I obtain 70 guineas,

cent.

Ex. 12. By selling 514 cwt. of sugar, at 3 per cent. profit, I gained £80. 11s. What was it bought and sold at per cwt.? . 3 are gained by 100,

1. What must linen, which cost 9s. 44d. per yard, be sold for, to gain 16 per cent. ?

2. If paper, which cost £1. 6s. 6d. per ream, be sold at £1. 16s. 4d. per ream, what is the gain per cent. ?

3. Goods, bought at £171.25, were sold at £183.475. What is the whole gain, and how much per cent. ?

4. A draper bought 78 yards of cloth, at £1. 8s. 9d. per yard. and 147 yards of linen, at 3s. 3d. per yard. The whole was sold for £141. 9s. 0ąd. Find the gain, and also the gain per cent. ?

5. Bought, 87.9 yards of linen, at 6.4s. per yard; also, 698 yards, at 4.57s. per yard; and also, 78 yards, at 6.9s. per yard. The selling of the whole brought a profit of 34 per cent. The selling price of the whole is required.

6. Bought, goods at £1. 17s. 6d., and sold them at £1. 5s. 4d. Find the loss per cent. ?

7. What must goods, which cost £6. 10s. 6d. be sold at to gain 18 per cent.?

8. Find the selling price of goods, bought at £1. 6s. 74d., and sold so as to lose 10 per cent.

9. What is the prime cost of a cricket ball, which, when sold at 8s. 6d., brings a gain of 35 per cent.?

10. If I gain 20 per cent. by selling tea at 6s. 8d., how much is gained per cent. by selling it at 7s. 6d. ?

11. Bought, 56 pieces of stuff, at £6 per piece, and sold 20 pieces at £9, and 16 at £7. 10s. each. At what rate per piece must the remainder be sold, to gain 40 per cent. on the whole?

12. A grocer bought rice at £1. 15s. per cwt., and vermicelli at £1. 17s. 6d.; he sold the rice at 93d. per lb., and the vermicelli at 114d. per lb. Find the difference of the gains, also the profit per cent. on each.

13. The produce of some land is £99. 10s., which is an increase of 8 per cent. on the preceding year. What was the value of the produce then?

14. By selling goods at 1s. 10d. per lb., I gain 12 per cent. What is the cost price of 1 cwt.?

15. How much must an article, bought at £12. 16s. 6d. per cwt., be sold for to gain 24 per cent., and what quantity of it must be sold at that rate to make a profit of 100 guineas? 16. If 15 cwt. 1 qr. 2 lbs. of sugar cost £51. 19s. 8d., what must it be sold at per lb. to gain 15 per cent.?

17. If the brewing of 8741 gallons of ale cost £493. 10s., what must it be sold at per gallon to clear 125 per cent.?

18. If £27. 6s. be lost by the sale of 2 cwt. of raw silk, at £1. 18s. per lb., what was the prime cost, and what the loss per cent.?

19. I gained 253 per cent. by selling goods at 10d. What was the prime cost?

20. By selling some articles at 16s. 6d. I gained 25 per cent. What did I gain per cent. when selling the same articles at 18s. 4d.?