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Cost per cent. = (£913 + }) = £91} = £91.5
Amount of stock = £2675

91.5

13375

2675 24075

Product divided by 100 = £2447.625

Ans. £2447 : 12 : 6.

11.

TO FIND HOW MUCH STOCK CAN BE PURCHASED FOR A GIVEN SUM.

Rule. State a proportion thus: As the price of £100 is to the given sum, so is £100 to the answer.

EXAMPLE. Find what amount of stock may be purchased in the 33 per cents. at 873 for £3425. As £871

£3425

£100

Ans.
As £175

£6850

£100

Ans.
As £ 7

£1370

£ 20

Ans. 20

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III.

TO FIND WHAT INTEREST PER CENT. MAY BE OBTAINED BY

PURCHASING STOCK AT A GIVEN PRICE.

Rule. State a proportion thus: As the price of £100 stock is to £100, so is the interest on £100 stock to the answer.

EXAMPLE.
Find what rate of interest will be obtained by investing in the 31 per
cents. at 953.
As £95.375

£100
£3.25

Ans.
100

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95.375)325.000(3.4076£.

286 125

38875
38150

725
667

58
57

Ans. £3 : 8:18 nearly.

IV.

TO FIND IN WHICH OF TWO STOCKS IT IS MORE ADVANTAGEOUS

TO INVEST.

Rule. Compare the ratios of the interest on, to the price of, £100 stock, in each case. The stock to which the greater ratio belongs is the more advantageous.

EXAMPLE. In which is it more advantageous to invest, in the 31 per cents. at 913, or in the 31 per cents. at 925 ? 31 913

31 925
As 26
731

28

741
As
26 Х 741

28 Х 731
As 13 x 741

14 Х 731
As
9633

10234
... It is more advantageous to invest in the 3} per cents.

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or

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V. TO FIND WHAT ANNUAL INCOME MAY BE REALIZED BY INVESTING

A GIVEN SUM IN STOCK AT A GIVEN RATE.

Rule. State a proportion thus: As the price of £100 stock is to the given sum, so is the rate of interest to the answer,

EXAMPLE Find what income may be derived from investing £2865 in the 31 per cents. at 71. As £713 £2865

£3}

Ans.
As £71.625 : £2865

£3.5

Ans.
As £2.865 : £573

£.7

Ans. .7

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2.865)401.100(140£.

2865

11460
11460

Ans. £140.

VI. TO FIND WHAT SUM MUST BE INVESTED IN A GIVEN STOCK TO

PRODUCE A GIVEN INCOME.

Rule. State a proportion thus: As the înterest on £100 stock is to the amount of the income, so is the price of £100 stock to the answer.

EXAMPLE.
Find what sum must be invested in the 33 per cents. at 85% to produce an
income of £84.
As £3}

£84
£853

Ans.
As £3.5

£84

£85.375 : Ans. As £1

£12

£170.75 : Ans.

12

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VII.

TO FIND HOW MUCH OF A GIVEN STOCK MAY BE PURCHASED WITH

THE PROCEEDS OF THE SALE OF A GIVEN AMOUNT OF OTHER STOCK.

Rule. State a Proportion thus :-As the price of £100 of the new stock is to the price of £100 of the old stock, so is the amount of stock to the answer.

EXAMPLE.
A person transfers £8500 from the 31 per cents. at 87, to the 3 per cents.
at 82), how much of the latter stock does he hold ?
As 823

87
£8500

Ans.
As 165

174
£8500

Ans.
As 11

58
£1700

Ans.
58

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VIII. · TO FIND THE DIFFERENCE IN A PERSON'S INCOME BY TRANS

FERRING MONEY FROM ONE STOCK TO ANOTHER.

Rule. Multiply the new rate of interest by the former price per cent. and the former rate of interest by the new price per cent. ; divide the former product by the latter; the quotient is the ratio of the new, to the previous, income.

If the actual difference of income be required, find the difference between the above ratio and unity, and multiply the previous income by it.

EXAMPLE. A person transfers £30000 stock from the 3} per cents. at 92, to the 3 per cents. at 69, what is the difference in his income! Ratio of new income to previous one

3 x 92 184

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1.

TO FIND THE PROFIT OR LOSS PER CENT. BY SELLING AN ARTICLE

AT A CERTAIN GAIN OR LOSS ON THE PRIME COST.

Rule. As the prime cost is to £100, so is the gain or loss to the profit or loss per cent.

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EXAMPLE.
Find the profit per cent. on goods bought at £2: 14 : 0 and sold at £3: 3:0.

Selling price = £3: 3:0
Prime cost

= £2:14:0

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II.

TO FIND AT WHAT PRICE AN ARTICLE MUST BE SOLD TO GAIN OR

LOSE SO MUCH PER CENT.

Rule. As £100 is to the prime cost, so is the produce of £100 to the selling price required. Or work by Practice.

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EXAMPLE
Find what must be the selling price of an article which cost £20 : 17 : 6
to gain £124 per cent.
As £100

£20]
£112}

Ans.
207 X 1121
Ans. =

£.
100
167 X 225 167 X 9
£. =

£.
1600

64 1503

£. = £23:9:81.

64
Or thus by Practice-

£. d.
Prime cost = 20 17 6 = gain at £100 per cent.
121 = } of 100 2 12 24=gain at 124 per cent.

£23 9 82= selling price.

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III. TO FIND THE PRIME COST OF AN ARTICLE, BY SELLING WHICH

AT A CERTAIN PRICE A GIVEN GAIN OR LOSS PER CENT. IS MADE.

Rule. As the produce of £100 is to the selling price, so is £100 to the prime cost required.

EXAMPLE. By selling tea at 4s. 9d. per lb. a grocer gains 8 per cent. what was the prime cost?

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IV. GIVEN THAT BY SELLING GOODS AT A CERTAIN PRICE A CERTAIN

GAIN OR LOSS IS MADE, TO FIND WHAT SHOULD HAVE BEEN THE SELLING PRICE TO HAVE MADE ANOTHER GAIN OR LOSS.

Rule. As the first produce of £100 is to the required produce, so is the first selling price to the selling price required.

EXAMPLE. By selling goods at £1: 15 : 0 a gain of 20 per cent. is made, what should be the selling price to gain 284 per cent? As £120 £1284

£11

Ans. 1284 X 14

900 X 7 .: Ans. =

£=

£.
120

7 X 4 X 120
45
=- £= £1:17 : 6 Ans.
24

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V. GIVEN THAT BY SELLING GOODS AT A CERTAIN PRICE A CERTAIN GAIN OR LOSS IS MADE, TO FIND WHAT WILL BE THE GAIN OR LOSS WHEN THE SELLING PRICE IS ALTERED.

Rule. As the first selling price is to the second selling price, so the first produce of £J00 to the second produce of £100; the difference between which and £100 is the answer required.

EXAMPLE. By selling goods at £1 5s. Od. a gain of 20 per cent. is made, what will be the gain if the price fall to £l 2s. Od.? As £11 £11b

£120

Produce of £100

11 X 120 11 X 12 X 4 .. produce of £100 =

£. =

-£. 14

5
528
£.

= £105 : 12:0
5
.: Ans. = £5 : 12 : 0.

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