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. 87 Ans. 174 Ans. 58 Ans. : : or : : : or : : 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 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. EXAMPLE. Selling price = £3: 3:0 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. EXAMPLE. £207 Ans. £. £. 64 1503 £. = £23:9:81. 64 £. s. d. £23 981= selling price. 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 ? 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. £= £. 7 X 4 X 120 : : 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 £100 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 £1 2s. Od.? As £14 £11) £120 Produce of £100 110 x 120 11 X 12 X 4 ... produce of £100 = £. = -£. 11 5 = £105 : 12:0 : Def. Fellowship is the Rule, by which the gain, loss, or liability in a joint concern may be equitably apportioned to each of the partners, according to the amount of their contributions to the general stock, or the advantages reaped by each from the concern. It is called Simple or Compound Fellowship, according as the times for which each partner has been engaged are the same or not. I. TO DETERMINE THE AMOUNT OF GAIN OR LOSS BELONGING TO EACH PARTNER IN A JOINT CONCERN, THE TIMES OF ENGAGEMENT OF ALL BEING THE SAME. Rule. Find the ratio of the whole gain or loss to the whole stock and multiply by it each partner's stock. The result will be each partner's share. EXAMPLE. A and B trade together, A puts into the general fund £1450 10s. Od. B puts in £2560 15s. Od.; they gain £1050 13s. Od. ; what is the share of each? A's stock.... = £1450.5 4011,25)1050.650(.261926 B's stock.... = £2560.75 802250 II. TO DETERMINE THE SHARE OF GAIN OR LIABILITY OF EACH PARTNER IN A CONCERN, ACCORDING TO THE NUMBER OF SHARES HELD BY EACH. Rule. Divide the whole liability by the whole number of shares, and multiply the result by the number of shares, which each partner holds. The results are the liabilities or gains of each partner. EXAMPLES 1. A, B, C, purchase shares in a concern; A pays for 8 shares, B for 12, C for 15; they gain £735 : 15: 0; determine each partner's share of the gain. Whole No. of shares = 8 + 12 + 15 = 35. £. d. £21 0 51= gain of 1 share. S. £. 8. d. 21 0 57 8 £. 8. d. 12 £. $. d. 15 168 354 A's gain 252 5 14 B's gain 315 6 54 C's gain 2. A and B rent a pasture for £70; A puts in 150 sheep, B 200 sheep, how much ought each to pay towards the rent? No. of shares = 150 + 200 = 350 1 = Rent belonging to 1 share 350 5 111. TO DETERMINE THE SHARE OF GAIN OR LOSS BELONGING TO EACH PARTNER IN A CONCERN, THE TIMES FOR WHICH EACH HAS BEEN ENGAGED NOT BEING THE SAME. Rule. Express all the times and stocks in terms of the same unit, multiply each partner's stock by the units in the time; add the products; divide the whole gain or loss by the sum, and multiply by each product separately. The results will be the shares required. EXAMPLES 1. A, B, and C trade together; A advanced £850 for 12 months, B £1000 for 9 months, C £ 1500 for 6 months; they gain £1250; what is the share of each? K |