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PROFIT AND LOSS.
PROFIT and Loss refers to calculations of the profits or losses of merchants in buying and selling goods.
The price at which a merchant buys his goods, is termed the cost price, and that at which he sells them, the selling price.
When they are sold for more than they cost, there is a profit on the transaction ; and when sold for less, there is a loss.
The profit or loss is calculated on the cost price, and is usually stated at so much per cent.
The method of working questions of Profit and Loss, will be seen from the following examples :
I. TO ASCERTAIN THE TOTAL PROFIT OR Loss IN SELLING A
QUANTITY OF GOODS—THE RATES AT WHICH THEY WERE
BOUGHT AND SOLD BEING GIVEN. Example. A merchant purchased 7 tons of iron rods, at £10, 178. 9d. per ton, and sold them again at 16s. 4 d. per cwt.; how much did he gain on the whole ?
The prices at which the goods
were bought and Sold 7 tons = 140 cwt. at £0 16 41 = £114 12 6
sold are calcuBought 7 tons ... 10 17 9 = 76 4 3 lated, and the Total gain, £38 8
amount of the 3
one is then deducted from that of the other.
II. TO ASCERTAIN THE PROFIT OR Loss per cent.—THE COST AND
SELLING PRICE BEING GIVEN. Example.--If indigo be bought at 3s. a lb. and sold at 3s. 9d. a lb. what is the gain per cent. ?
Here the gain upon 38. is 9d.; and S. d. £ £
to find the gain per cent. state
the question as in Simple Pro3 : 9 :: 100: 25 Ans.
portion : "If 3s. gain 9d. what will £100 gain ?'
NOTE.—This question, and the examples under Rules III. and IV. are stated in the order in which the meaning may be expressed in words, according to the rule in Simple Proportion, given at page 59. The examples under Ru are stated according to the rule in Simple Proportion, page 56.
III. TO ASCERTAIN THE Selling PRICE—THE COST, AND THE PROFIT
OR LOSS PER CENT. BEING GIVEN. Example 1; where there is a profit.- I bought a quantity of tea at 2s. 6d. a lb.; at what price must I sell it per lb. in order to gain 10 per cent. ?
Goods costing £100 must, at this rate, be sold for £110, to gain 10 per cent.;
and therefore, to find what £ £ s. d. S. d. goods costing 2s. 6d, must 100 : 110 :: 2 6 : 2 9 Ans.
be sold for, to gain the same percentage, state the question thus: - If £100 sells for £110, what will
28. 6d. sell for ?'. . . Example 2; where there is a loss.—What is the selling price of a pound of tea, if it has cost me 2s. 6d. and I have lost 10 per cent. in selling it ?
Goods costing £100 must, at this rate, be sold for £90, to lose 10 per cent.;
and therefore, to find what £ £ $. d. S. d. goods costing 28. 6d. must 100 : 90 :: 2 26 : 2 3 Ans. be sold for, to lose the
same percentage, state the question thus:- If $100 is sold for £90, what will 2s. 6d. be sold for?'
IV. TO ASCERTAIN THE Cost PRICE—THE SELLING PRICE, AND THE
PROFIT OR LOSS PER CENT. ON THE COST BEING GIVEN. Example 1; where there is a profit.-What is the cost price of a yard of cloth, which I sold for 16s. and thereby gained 10 per cent. on the cost ?
Goods sold for £110 will,
at this rate, cost £100; £ £ s. d. S.
therefore, to find what
goods sold for 16s. 6d. will 110 : 100 :: 16 6 : 15 Ans.
cost, state the question thus:- If £110 cost $100,
what will 16s. 6d. cost ? Example 2 ; where there is a loss. What is the cost price of a yard of cloth, which I sold for 18s. and thereby lost at the rate of 10 per cent. on the cost ?
Goods sold for £90 will
at this rate, cost €100; £ £ s. £
therefore, to find what
goods sold for 188. cost, 90 : 100 :: 18 : 1 Ans.
state the question thus:
will 18s. cost?' NOTE.-In questions of profit and loss, it must be remembered that the calculations are made on the cost price, and not on the selling price of the goods.
V. TO ASCERTAIN WHAT WILL BE THE PROFIT OR LOSS PER CENT.
AT A CERTAIN SELLING PRICE—THE PROFIT OR LOSS PER
CENT. AT ANOTHER SELLING PRICE BEING GIVEN. Example 1; where there is a profit.- What will be the percentage gained by selling sugar at £44 a ton, if 5 per cent. is gained by selling it at £42 a ton ? £ £ £
Here the sel42 : 44 :: 105 : 110
ling price, £42,
which includes Deduct, as the cost of £110,...... 100
a gain of 5 per The remainder is the percentage required, £10 viz. 10 per cent. gain. cent. ont
cent. on the cost, bears the
same proportion to £44, the other selling price, that £105-namely, £100 of cost and 5 per cent. added-bears to £100 of cost, with the required percentage added; therefore, state the question thus:--As $42 is to £44, so is £105 to $100 with the required percentage added.' The answer is £110, from which the cost, £100, is deducted, leaving £10 the required percentage. · Example 2; where there is a loss.—What will be the percentage lost by selling sugar at £38 a ton, if 10 per cent. is gained by selling it at £44 a ton ?
Here the sel44 : 38 :: 110 : 95
ling price, £44,
which includes The cost price of £95 is . ....... 100
a gain of 10 per The selling price deducted from the cost gives the required percentage
cent. bears the viz. 5 per cent. lost. ...
tion to £38, the other selling price, that £110-namely, £100 of cost, and 10 per cent, of gain added-will bear to £100, with the required loss per cent. deducted , therefore, state the question thus :- As £44 is to £38, so is £110 to £100, with the required percentage deducted. The answer is £95, which is deducted from $100, the cost price, and the remainder is the percentage required.
Exercises. 1. A person bought 137 cwts. of pearl sago, at £1, 14s. 91d. per cwt. and sold it again at 4 d. per lb. ; whether did he gain or lose, and how much on the whole ? Ans. £33, 7s. 102d. gain,
2. How much is gained per cent. by selling Muscatel raisins at 91s. 3d. per cwt. which were purchased at 77s. 9d. ? Ans. 17113
3. A bookseller bought a copy of an Encyclopædia for £22; at what price must he sell it, to gain 20 per cent, ? Ans. £26, 8s.
4. I have bought cloth at 15s. a yard, and lost 5 per cent. in selling it ; what was it sold for? . . . . Ans. 14s. 3d.
5. A merchant sold a chest of tea containing 84 lbs. for £25, 7s. and gained at the rate of 20 per cent.; what was the cost per lb. ? . . . . . . . . . Ans. 5s. 04d.
6. If 154 per cent. be lost by selling Stockholm tar at 15s. 4d. per barrel, what was the cost ? . . . Ans. 18s. 1 d. 148
7. If 15 per cent. be gained by selling hemp at £32, 15s. per ton, what is gained or lost per cent. by selling it at £30, 15s. 6d. ?
Ans. £8, 1s. 31d.1'gain. н
8. If 8 per cent. be gained by selling 736 yards of linen for £125, 10s.; at what rate must the yard be sold so as to gain 16 per cent. ? . . . . . . . Ans. 3s. 7 d. 179
9. By selling molasses at £1, 10s. per cwt. I gained 14 per cent. but the market falling, I was obliged to dispose of the remainder at £1, 2s. 6d. per cwt. ; what was the gain or loss per cent. at this
. . . . . . Ans. £14, 10s. loss.
SHARES, STOCKS. SHARES AND STOCKS are terms applied to the capital of Jointstock Companies, and to those large sums of money borrowed by Government, termed the National Debt.
The capital of joint-stock associations is raised among the partners, by shares fixed at a specified sum ; the shares may be £10 each, £50 each, or any other sum ; and some persons may hold ten shares, while others have fifty; and so on.
The original sum fixed upon for a share is called par; thus, if the shares be £10 each, then £10 is par. If they rise in value, a £10 share may become worth £12; in which case it is said to be £2 above par ; or it may fall in value, and be worth only £9, in which case it is said to be £1 below par.
GOVERNMENT STOCKS are usually called the funds: they take their special designations from the rate of interest paid on them; thus, the 3 per cents. mean that stock on which an annual dividend is paid of £3 per cent.; and so on. The usual practice in buying and selling these, is to offer shares nominally of £100 par, at from £80 to $90, or upwards, each; and the market-price of these fluctuates according to the abundance or scarcity of money, and other circumstances.
The persons who negotiate the sale and purchase of stocks are termed brokers. and the charge they make for their trouble is called brokerage, or commission. Questions as to stocks, &c. are wrought by Simple Proportion.
Example.--A person invested a certain sum in the 3 per cents. when they were selling at £94%; what rate per cent. had he for his money?
Here, by paying £943, he receives a yearly sum of £3-that is, £3 is the in
terest of £943-therefore state the ques942 : 100 :: 3 : 3.47 Ans. tion as in Simple Proportion, thus : If
£947 yields £3 of interest, what will £100
yield ' Note.In calculating the value of stocks, the sum paid for brokerage is added to the value of stock when bought, but deducted from it when sold. The brokerage in the following exercises is supposed to be at the rate of 1-8th per cent.
Exercises. 1. How much would a person pay for £1500 in the 3 per cents. when the selling price is 911 per cent. ? . . Ans. £1368, 15s.
2. A gentleman sold £2100 of the 34 per cents. at 964 per cent. ; required the nett proceeds, . . Ans. £2018, 12s. 6d.
3. What rate of interest does a person obtain by purchasing shares in a railway at £72, the annual dividend being 7 per cent. and the original value of a share £50 ? . . Ans. 43. per cent. PARTNERSHIP. PARTNERSHIP is the rule for ascertaining the share of profit. or loss belonging to each partner of a company, in proportion to his share of the joint capital.
Simple Partnership is that in which each partner employs his capital for the same period of time.
Compound Partnership is that in which each partner employs his capital for different periods of time.
I. SIMPLE PARTNERSHIP.
RULE.—Add together the different shares, and state and work the question as in Simple Proportion, for each partner, thus—'If the whole capital gain so much (namely, the total profit), what will each partner's capital gain ?'
Example.—Three partners, A, B, C, invested in business £300, £500, and £1200 respectively, and their total profit in a year was £400; what is each partner's share of the profit ? A. £300
Here we B. 500
the capital of C. 1200
all the part£2000 : £400 :: £300 : £60 A's share, ners, and 500 : 100 B's ,
then, to find
A's share of 1200 : 240 C's ,
profit, state £400 Total profit.
the question thus: If the
whole capital, £2000, gain £400, what will £300, A's share, gain?' It is then calculated as in Simple Proportion. B and C's shares are found in the same way.
NOTE.—The question is stated according to the rule in Simple Proportion, given at page 59.
Exercises. 1. Three merchants, A, B, and C, form a joint-capital, of which A contributes £700; B, £350; and C, £1000. At the end of a year their gain is found to be £500. What is each partner's share of the profit ?
Ans. A's share, £170, 14s. 7 d. 18;
B's, £85, 7s. 32d. ; C's, £243, 18s. 0 d. 14 2. A, B, C, and D purchase a ship: A pays for 6 shares; B for 5 ; C for 3; and D for 4. They receive of nett freight for a voyage to Jamaica, £364, 17s. 6d. How much of this sum ought each to receive ? Ans. A, £121, 12s. 6d.; B, £101, 7s. 1d.;
Ć, £60, 16s. 3d.; D, £81, 1s. 8d. 3. Three merchants, L, M, and N, continue in trade for a year, with a joint-stock of £3500. At the end of that time, L's share of the gain was £125; M's, £240; and N's, £135. What was each partner's stock ?
Ans. L's stock, £875; M's, £1680; N's, £945.