PRICING GOODS. 5. Premium on £840 atp.c. 135 6. Amount to cover premium and £1200 atp.c., also premium. 7. Amount to cover premium and £1850 at 2s. 9d. per £100, also premium. 8. Amount to cover premium and £7000 at 3s. 4d. per £100, also premium. 9. Amount to cover premium and £6450 at 1p.c., also premium. 10. Amount to cover premium and £20000 at 5 p.c., also premium. Profit and Loss and the Pricing of Goods. 13. Questions in Profit and Loss are solved by the principles of proportion. Their solution involves the constant use of percentages. The chief point to be observed in all questions of theory is to reckon on the cost price unless the selling price is specially involved. The Pricing of Goods is a very important branch of the subject. 1°. To find gain or loss p.c., given cost price and selling price. 3°. To mark goods so as to ensure a given p.c. profit after a given discount. (1) Find selling price so as to gain the given p.c. Multiply this by 100 100-given discount (2) Multiply cost price by 100+ given p.c. profit 100-given p.c. disct. Note. By discounting the selling price of an article a loss may be sustained without suspecting it-this arises from the fact that the profit is thus discounted as well as the original price. Ex. An article costs 58. and is marked so as to realise 60 p.c. profit -but a discount on the selling price of 45 p.c. is allowed, is there a loss? Selling price 5s.+10% of 5s. = 58. + 38. = 8s. 45 p.c. on 8s.=3.6s. on 5s., i.e. 12 p.c. .. actual selling price is 4.4s., a loss of gs. Example 1. Find gain p.c. by selling for 11td. what cost 83d. 114d. - 8 d. 24d. 250 82 -1000=200=284 p.c. Example 2. Find selling price of an article which cost 2s. 91d. so as to gain 20 p.c. after deducting 10. 120 x 33.25d. 12 × 33·25=33·25 +11.083=44·333d. Example 3. Find selling price of article costing 3s. 24d. so as to gain 12 p.c. 38*5d. x1:12=385 3.85 ⚫770 43.120d. EXAMPLES. 1. Find gain or loss p.c. by selling article at 64d. for 9d., 73d. for 6d., 10d. for Is., 25s. for 30s., £15. 15s. for £20., £5. 178. 43d. for £7. 10s. 2. Find selling price of article at 103d. so as to gain 5 p.c., 1s. 5d. gain 7 p.c., 3s. 7d. gain 10 p.c., 1s. 52d. gain 15 p.c., 58. 11d. gain 20 p.c., £3. 5s. 93d. gain 24 p.c., £11. 10s. 6d. gain 40 p.c. 3. Find selling price of articles at these prices to gain the given p.c. after deducting the given discounts. (1) 7 d. 15 p.c. 5 p.c. (2) 1s. 91d. 10 p.c. 5 p.c. (3) 3s. 11d. 25 p.c. 10 p.c. (4) 5s. 6d. 18 p.c. 5 p.c. (5) 228. 11 d. 12 p.c. p.c. (6) 178. 103d. 20 p.c. 7 p.c. (7) £3. 5s. 9d. 40 p.c. 25 p.c. (8) £8. 88. 60 p.c. 20 p.c. (9) £25. 7s. 6d. 15 p.c. 2 p.c. (10) £30. 4s. 6d. 25 p.c. 125 p.c. MARKING GOODS. 137 4. To mark Goods bought by the dozen, score, gross, hundred, thousand, so as to gain a given p.c. (6) Use Denomination-changes (for dozens s. as d., for score £ as s., for gross s. as d. twice) and multiply by 100+ given p.c. This principle may be extended to any quantities convenient for such changes, e.g. for 12 score consider £ as d., for 80 dozen consider £ as f., etc. The chief Methods of Solution are these: (1) Directly-multiplying cost price (e.g.) for dozens by 105 and dividing by 12, for score by 105 and dividing by 2, for gross by 105 and dividing by 144, for hundreds by 0105, for thousands by 00105. The methods of approximation apply-more particularly the method adopted in compound interest for any year. Example 1. Find selling price of each article in a dozen costing 17s. 8d. so as to gain 6 p.c. Example 2. Find single selling price of 100 costing £25. 178. 8d. so as to gain 7 p.c. (2) By considering shillings pence etc. and then multiplying cost price so changed by 1·05 (e.g.). Example. Find selling price of each in a score at £12. 7s. 81d. 80 as to gain 8 p.c. (3) By aliquotising the fractions given above. Thus for dozens the fraction 100+ given p.c. 1200 20 p.c., for 25 p.c., for 5 p.c., etc., and these can easily be aliquotised when necessary. 100+ given p.c. 144 can be ali of the result taken for gross. Similarly the fraction quotised and Thus also the fraction advantageously aliquotised. 100 can often be Example. Mark goods at 5s. 9d. per dozen so as to gain 10 p.c. 120 ==0- (12) (10). 69 575 6.325d. 6d. or 64d. Mark goods so as to gain following p.c. 1. Dozens at 22s. 91d., 36s. 7d., 25s. 7d., 19s. 10 d., 478. 61d. so as to gain 5, 7, 16, 20, 24 p.c. respectively. 2. Score at 63s. 7d., 85s. 9d., 115s. 10d., 79s. 4d., £3. 16s. 91d. so as to gain 13, 21, 18, 25, 35 p.c. respectively. 3. Gross at £12. 9s. 101d., £15. 18s., £21. 6s., £94. 7s. 10d., £38. 9s. 6d. so as to gain 10, 15, 20, 25, 60 p.c. respectively. 4. Hundreds at £112. 9s. 61d., £256. 78. 81⁄2d., £97. 8s. 10‡d. so as to gain 5, 12, 15 p.c. respectively. 5. Thousands at £320. 7s. 101d., £640, £850 so as to gain 8, 14, 24, p.c. respectively. 6. Articles at 61d. (5 p.c.), 3s. 11d. (22 p.c.), 1s. 11⁄2d. (7 p.c.), 2s. 71⁄2d. (24 p.c.), 1s. 6d. (16 p.c.), 5s. 9d. (26 p.c.), 2s. 01d. (25 p.c.), 1s. 11 d. (24 p.c.), 2s. 44d. (30 p.c.). 7. Dozens at 10s. 6d. (5 p.c.), 9s. 5d. (12 p.c.), 11s. 4d. (17 p.c.), 24s. 7d. (40 p.c.), 17s. 101d. (10 p.c.). 8. Score at 55s. 6d., 73s. 101⁄2d., 96s. 81d. to gain 5, 7, 13 p.c. respectively. 9. Gross at £12. 9s. 71d., £16, £40. 7s. 10d. to gain 16, 24, 32 p.c. respectively. 10. Hundreds at £64. 8s. 7d., £20. 9s. 5d. to gain 10 p.c. and 15 p.c. respectively. 5. To price goods bought in any quantity so as to gain a given p.c. Add to total cost required gain p.c., found by any of the percentage methods. Divide by quantity expressed in unit whose price is required-using Division-approximation to any desired accuracy (farthings, eighths, or sixteenths of a penny). |