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A simple application is to add the proportional sums, and take each proportion as a fraction of the total sum.

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A company is formed to which A contributes £100, B £120, C £150 and D £130, and the profits at the end of the year are £150. What share should each receive?

Here £100+120+150+130=total £500.

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Ex. Divide 70 guineas between A B & C, so that the sums each will receive shall be in the proportion of 7, 8, and 9. Áns. A £21,, 8, 9; B £24,, 10,, 0; C £27, 11,, 3.

Divide £20 among 7 men, 14 women, and 21 boys, so that each man will receive 3 times as much as each boy, and each woman half as much as a man and boy would earn together. Ans. Man's share 178. 1d.; woman's share 11s. 54d.; Boy's share 58,, 8 d.

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Divide £100 among A B C D so that A receives half as much as C and D together; B half the share of C; and C half as much again as D. Ans. A £22, 4, 54; B £33,, 6 8; C £16,, 13,, 4; D £27 „, 15,, 63.

PERCENTAGES.

A percentage is an estimate of increase or decrease, compared with 100 as the standard.

Soap is bought at 3 d. per lb., and sold at 44d. per lb. What is the gain per cent. ?

Here-selling price, 44d.-cost price, 3 d. d. gain.

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If goods are bought at £1,, 10 0, and sold at £1,, 12,, 0, what is the gain per cent. ? Ans. 63 per cent.

If I sell an article at 5s., and gain 15 per cent. on my outlay, what is the prime cost? Ans. 4s.,, 4 d.

If a person sells 40 articles for the same money which he paid for 50, what is the gain per cent. on his outlay. Ans. 25 per

cent.

If a tradesman uses for an oz. weight, one which only weighs 15 drams, what does he gain per cent. by his dishonesty? Ans. 63 per cent.

PRESENT WORTH & DISCOUNT.

If A owes B £100, to be paid at the end of a year, with interest at the rate of 5 per cent., it is clear that if the debt be paid at once, B should receive less than £100, viz.: that sum of money put out to interest would amount to £100 at the end of the year.

The sum which B should receive now is called the Present Worth, and the sum to be subtracted from the £100, on account. of the immediate payment of the debt, and which is the Simple Interest on the Present Worth, is termed the True Discount.

Bankers and merchants as a rule discount bills and notes of hand, when the credit of the person promising payment is satisfactory by charging the Interest on the whole sum. In this way the discount deducted is greater than that explained above, since the holder of the bill is a loser by the transaction. The Bankers' discount on a bill of £105, due at the end of a year, at 5 per cent., will be £5 5s., being the interest calculated on the total debt, £105, whereas the true discount is £5. The Banker is therefore the gainer by 5s., the interest on the true discount.

NOTE. Three days of grace after a bill falls nominally due, before it is legally due, are always allowed in Great Britain and Ireland; also if a bill falls nominally due on the 31st of any month which has only 29 or 30 days, it is considered nominally due on the last day of such month, and legally due on the 3rd of the following month. Bills falling legally due on Sunday, are paid in Great Britain on the Saturday, but in Ireland on the Monday. When a bill is payable on demand, the days of grace are disallowed.

Ex. (a) Find the present worth of £840 due 1 year hence at 5 per cent. per annum.

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Ex. (b) What is the present value of £196 ls. 9d. due 5 years hence at 43 per cent.

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Ex. (c) Find the true discount upon a bill for £251 158. 3d., drawn March 17th, at 3 months, discounted May 31st, at 6 per cent.

Int. on 100£ for 365 days=£6

March 17

April

May 31

June

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17 17 Amt. of 100£ for 20 days=£100%

Days of Grace 3 Disct. on £100-£2

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In finding the Banker's. discount on the above bill, we ascertain the interest in the usual manner for £251 15 3 to 18; the true discount being 16s.,,

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be 16s.
banker gains therefore

6d.

1188

1825d.

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6d., the

Ans.

6 due 3 yrs. hence at 4 p.c. per ann, £507 10 0

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