9. How many lbs. of coffee, at 1s. per lb., must be given for 5 cwt. 2 qrs. 14 lbs. at 6d. per lb. ?

10. Bartered, 82 cwt. of hops, at 30s. per cwt., for which I received £20 in money, and the rest in prunes at 5d. per lb. What quantity of prunes did I receive?

11. A grocer, with whom I bartered tea for sugar, raised his sugar from Is. to 1s. 1d. per lb. What ought I to have charged for the tea, which I sold for ready money at 5s. 6d. per lb. ?

12. A farmer bought of a draper 24 yards of cloth, at 9s. 4d. per yard; 30 yards of linen, at 3s. 9d. per yard; and 80 yards of printed calico, at 1s. 2d. per yard; for which he gave £13. 2s. 6d. in money and 32 cwt. of potatoes. Required, the value of the potatoes per cwt.

13. O has 1600 lbs. of coffee, at 1s. 5d. per lb., which he barters with P, for goods at 5d. and 8d. per lb., and to have money, and of each sort of goods an equal quantity. How much money, and how many lbs. of each kind of goods will he receive?

14. A merchant consigns 64 bales of cloth, at £86. 2s. 6d, per bale, to his agent, who, retaining 1 per cent. commission, sends him, in return, one-half of the value in sugar, at 44s. per cwt., and the other in rum, at 4s. 8d. per gallon. What quantity of each did he receive?

15. Bartered, 2400 dozen pairs of stockings, at £1. 10s. per dozen, for equal quantities of coal, at 8s., 10s. 6d. and 12s. 9d. per ton respectively, and received also £120 in money. many tons of each kind of coal had I?

How

16. How much does cloth cost per yard, if I receive 55 yards for 10 cwt. of sugar, at £3. 9s. 0ąd. per cwt. ?

17. A wants to exchange some land, at £22. 16 acres of other land, worth £175 per acre. of the first land must be given?

10s. per acre, for How many acres

TARE AND TRET.

308. When goods are weighed, together with the box, bag, barrel, &c., which contains them, the whole weight is called Gross Weight,

The allowance which the seller makes to the buyer for the weight of the box, bag, barrel, &c., which contains the goods bought, is called its Tare.

What remains after the tare is deducted from the gross weight is called Tare Suttle.

Tret is an allowance of 4lbs. on 104lbs. tare suttle, for waste, dust, &c.

After the deduction for tare and tret, what remains is called tret suttle.

Cloff is an allowance of 2lbs. in every 3 cwt. of tret suttle, given to retailers in order to turn the scales.

Net Weight is what remains after the allowances are deducted. Questions treating of these allowances are classed under the head of Tare and Tret.

Ex. 1. What is the net weight of 16 barrels of rice, each containing 3 cwt. 2 qrs. 21lbs., tare 20lbs. per cwt., tret 4lbs. per 104 lbs., and cloff 2lbs. for every 3 cwt.

The gross weight of 1 barrel is 3 cwt. 2 qrs. 21 lbs.,

..the gross weight of 16 barrels = 16×3 cwt. 2 qrs. 21 lbs., or 59 cwt.

And tare on 1 cwt.=20 lbs.,

..tare on 59 cwt.=59×20 lbs., or 1180 lbs., or 10 cwt. 2 qrs. 4 lbs.

..tare suttle=59 cwt.-10 cwt. 2 qrs. 4 lbs., or 48 cwt. 1 qr. 24 lbs.

Also, the tret on 104 lbs. is 4 lbs., ..the tret on 1 lb. is, or ;

.. the tret on 48 cwt. 1 qr. 24 lbs. is

1 cwt. 3 qrs. 12.77 lbs.

48 cwt. 1 qr. 24 lbs.

or

26

.. tret suttle 48 cwt. 1 qr. 24 lbs.-1 cwt. 3 qrs. 12.77 lbs. =46 cwt. 2 qrs. 11.22 lbs.

And the cloff on 3 cwt., or on 336 lbs. is 2 lbs..

.. the cloff on 1 cwt., or Tag ;

..the cloff on 46 cwt. 2 qrs. 11.22 lbs. is or 1 qr. 3.06 lbs.

46 cwt. 2 qrs. 11.22lbs.

168

..the net weight=46 cwt. 2 qrs. 11.22 lbs.—1 qr. 3.06 lbs., or 46 cwt. 1 qr. 8.15 lbs.

The mechanical part of this work is exhibited in the following scheme ;

Another method of obtaining the same result would be to find the net weight of 1 barrel, and multiply by the number of barrels.

Ex. 2, How much will 29 packs of wool cost, each weighing 3 cwt. 2 qrs. 25 lbs., tare 16 lbs. per cwt., tret and cloff as usual, at 3s. 9d. per lb. net?

..tare on 1 cwt. is 16 lbs., or †,

..tare on 1 pack, or 3 cwt. 2 qrs. 25 lbs.

or 2 qrs. 3.571 lbs.

3 cwt. 2 qrs. 25 lbs.

=

7

..tare suttle=3 cwt. 2 qrs. 25 lbs.—2 qrs. 3.571 lbs.=3 cwt.

0 qr. 21.428 lbs.

Tret is of the tare suttle, or 13.747 lbs.

3 cwt. 0 qr. 21.428 lbs.

26

..Tret suttle=3 cwt. 0 qr. 21.428 lbs.-13.747 lbs.=3 cwt. 0 qr. 7.681 lbs.

Cloff is of 3 cwt. 0 qr. 7.681 lbs., or =2.045 lbs.

3 cwt. 0 qr. 7.681 lbs.

168

..net weight per pack=3 cwt. 0 qr. 7.681 lbs.-2.045 lbs.= 3 cwt. 0 qr. 5.635 lbs.

..net weight of 29 packs=29×3 cwt. 0 qr. 5.635 lbs., or 88 cwt. 1 qr. 23.434 lbs.

168)3 0 7.6813=tret suttle 2.0457cloff

29×3 0 5.6356-88 cwt. 1 qr. 23.434 lbs.=net weight.

Now, 1 lb. cost 3s. 9d.,

..23.434 lbs. cost 23.434 x 3s. 9d.=87.8775s.

Also, 1 qr.=28 × 3s. 9d. ....

And 88 cwt. = 88 x 112 x 3s. 9d.=36960s.

= 105s.

37152.8775s.

Therefore, 29 packs of wool cost £1857. 12s. 10.530d.

Or. 1 lb. cost 3s. 9d.,

..88 cwt. 1 qr. 23.434 lbs., or 9907.434 lbs, cost 9907.434 X 3s. 9d.= £1857. 12s. 10.53d.

309. EXERCISES.

1. What is the net weight of 144 cwt. 2 qrs. 10 lbs. gross, tare 16 lbs. per cwt.?

2. What is the net weight of 36 bags, each 4 cwt. 1 qr. 14 lbs. gross, tare 18 lbs. per cwt., and tret as usual?

3. In 48 hhds. or sugar, each 10 cwt. 2 qrs. 20 lbs., how much net weight, allowing 16 lbs. per cwt., tare, tret, and cloff as usual?

4. Bought, 3 packs of wool, No. 1 weighing 3 cwt. 3 qrs. 21 lbs. ; No. 2, 4 cwt. 0 qr. 8 lbs.; No. 3, 3 cwt. 3 qrs. 14 lbs. ; tare, 30 lbs. per pack; tret 8 lbs. for every 20 stones. What will the whole amount to, at 10s. 8d. per stone.

5. At the rate of 8 lbs. per cwt. the tare of some goods is 119 lbs. Required the net weight.

6. The net weight of some goods is 13 cwt. 3 qrs. 7 lbs., and the tare is 8 lbs. per cwt. Find the gross weight.

7. The tare on some goods comes to 119 lbs. at the rate of 8lbs. per cwt. What was the gross weight?

8. The tare of 14 cwt. 3 qrs. 14 lbs. is 119 lbs. What is it per cwt. ?

9. When the tare is at 8 lbs. per cwt., and subtracted from the gross weight, the net weight is 13 cwt. 3 qrs. 7 lbs. Find the tare.

10. The gross weight of 4 bags of pepper, bought at 1s. 6d. per lb. net, is 14 cwt. 3 qrs. 12 lbs., tare 14 lbs. per bag. What is the cost?

11. A buys 11 cwt. 1 qr. 20 lbs. gross, of sugar, at the rate of 8d. per lb., and pays £36. 8s. 2d. How much was allowed for the tare, and what was it per cent. ?

12. What must be paid for six bags of rice, weighing 15 cwt. 1 qr. 4 lbs. gross, if 3 qrs. 16 lbs. net weight cost £2. 18s. 6d., tare of the gross?

EXCHANGE.

310. When it is required to find how much of the money of one city or country is equivalent to a given sum of money of another, the term applied to such a conversion is Exchange.

In every country, the mint fixes a precise weight and purity for its currency; for instance, in England and France the mint regulations, value £1 to be equal to 25 francs, 20 centimes, and this is said to be the par of exchange between the two countries. Therefore, when transactions between London and Paris are conducted on this footing, the exchange is at par. But it happens continually that £1 in London buys more or less than 25.20 francs in Paris; in the first case, the exchange is in favour of London, and in the second, against, Now, the sum of money of one country, given at any particular time, in exchange for a fixed sum of money of another, is called the course of exchange.

The circumstances which produce variation in the course of exchange depend on the state of trade, and the value of the coins of any country, which seldom correspond to their mint standard.

It happens that in cities or countries, which carry on considerable commercial transactions, the debts of the one are nearly equal to the debts of the other. In England there are always a considerable number of merchants indebted to America, for instance, and likewise about the same number in this country to whom America is indebted. Therefore, when A of England has a payment to make to B of America, he does not effect it in