EXERCISES.

1. The sum of £95. is due as follows: £25. in 6 months; £30. in 7 months; and £40. in 10 months; at what time ought the whole to be paid at once?

2. The sum of £120. was to have been paid as follows: £45. at 4 months; £60. at 9 months; and the rest at 12 months; but the debtor agrees to pay the whole at once. quired the average time.

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3. A debt is to be paid thus; one half at 8 months; one fourth at 12 months; and the balance at 15 months. Required the time of paying the whole.

4. A owes B £560. of which £60. is to be paid ready money, and the rest in 5 payments of £100. each, every 3 months. Required the equated time for paying the whole.

5. Bought goods payable as follows: £50. the 1st of May; £64. the 4th of June; £86. the 1st August; and £90. the 5th of September. Required the mean time for paying the whole.

6. A sells for B a parcel of goods. The following is a state of the sales: £110. due 1st of March; £108. 15s. due the 25th ditto; £107. 12s. April 10th: £217. 14s. May 2d; £218. 7s. the 29th ditto; £110. 12s. 6d. July 4th; and £110. 11s. 6d. due November 10th. They wish to settle accounts; required the mean time.

VARIETIES

IN PROPORTION*,

PROFIT AND LOSS.

MERCHANTS have found it necessary, in estimating their profits and losses, to have some common standard by which the gain

*This rule may be considered merely as a variety in Proportion, most of the questions being solved by that excellent rule.

or loss actually made, or proposed to be made, on any article of trade, may be tried or expressed, and the standard which has been fixed upon, by universal consent, for this purpose, is, the centum, or hundred, almost every gain or loss which arises from the sale or purchase of goods being stated at so much per cent. This rule, therefore, explains the methods of calculating the gain or loss, per cent. on the purchase or sale of any article of merchandise.

CASE I.

WHEN THE BUYING AND selling priCES ARE GIVEN, TO FIND THE GAIN OR LOSS PER CENT.

RULE.

As the buying price is to the gain or loss on it; so is 100 to the gain or loss, per cent.

EXAMPLE I.

Bought cloth at 3s. 4d. per yard, and sold it at 4s. per yard. Required the gain per cent.

Sold indigo for 9s. 7d. per lb., which cost 10s. 5d. per .; what was the loss per cent.?

125) 10 x 100 = 1000(8 per cent, loss.

1000

EXERCISES.

1. If 2d. be gained on each shilling, prime cost, what is the gain per cent.?

2. Bought barley at 30s. per boll, which, having received damage, was sold again for 27s. per boll; what was the loss per

cent.?

3. Bought 3 tons of hemp, for £245. 19s. 6d. and sold the whole, immediately, for £295. 19s. 6d.; what was gained per cent. by the transaction?

4. Bought cotton cloth at 2s. 10d per yard, ready money, and sold it at 3s. 6d. per yard, at 6 months credit. Required the gain per cent.

CASE II.

TO FIND THE PRICE AT WHICH AN ARTICLE SHOULD BE SOLD, TO GAIN OR LOSE SO MUCH PER CENT.

RULE.

1. As 100 is to 100 plus the gain, or minus the loss, so is the prime cost to the gain or loss per cent.

2. Take parts of the prime cost for the rate per cent; add the result, in the case of gain, but deduct it, when there is loss,

EXAMPLE.

Bought sugar at 1s. 3d. per lb.; what must it be sold for, lb. to gain 15 per cent.?

per

per

EXERCISES.

1. Bought cotton at 3s. 4d. per lb.; at what must it be sold lb. to gain 20 per cent.?

2. Gained 20 per cent on sugar, which was bought for 75s, per cwt; at what was it sold per cwt.?

3. A quantity of flax was bought for £63. per ton, which was sold at 10 per cent loss; what was the selling price?

4. The prime cost and charges of 640 lb. of Bohea tea amounted to £84. 13s. 4d.; what must it be sold at per lb. in order to gain 174 per cent.?

5. Bought cloth at 18s. per yard; at what must it be sold to clear 20 per cent and allow 8 months credit?

6. Bought sugar at 65s. per cwt., at 4 months credit; at what must it be sold, per cwt. to gain 163 per cent., and allow 6 months credit?

CASE III.

TO FIND THE PRIME COST, WHEN THE SELLING PRICE AND GAIN OR LOSS, PER CENT, ARE GIVEN.

RULE.

As 100 plus the gain per cent, or minus the loss per cent, is to 100; so is the selling price to the prime cost.

EXAMPLE I.

Sold 12 cwt. of sugar for £43. 15s. by which I gained 20 per cent.; what was the prime cost?

EXAMPLE II.

By selling cloth at 9s. 7d. per yard, I lost 8 per cent.; what was the prime cost?

1. Sold 500 lb. of indigo for £135. by which I cleared 15 per cent.; what did it cost me per lb.?

2. Sold a quantity of cotton wool at £13. 6s. per cwt., by which I lost at the rate of 5 per cent. Required the prime cost, per lb.

3. Received £18. Is. 14d. for a piece of cloth, by which I gained 1s. 6d. per yard, being at the rate of 12 per cent. Required the length of the piece and the prime cost, per yard.

CASE IV.

TO FIND A PROPORTIONAL RATE PER CENT ON AN ADVANCED PRICE.

RULE.

As the price, whose rate per cent is given, is to the other price, so is 100 with the gain added, or loss subtracted, to a fourth number; which, if greater than 100, shows the gain, and, if less, the loss per cent.

EXAMPLE I.

Sold nutmegs at 15s. per lb. by which I gained 5 per cent., the price of the remainder was afterwards raised to 18s. 6d. per Ib.; how much was that per cent.?

then 18 x 7 1294 — 100 = 29 per cent. Ans.

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