Take 5 parts out of 100 from £107 13s. 4¾d.
Answer, £5. 7. 8 and ³/₂₀ of a farthing.
£56 3s. 2d. is equally divided among 32 persons. How much does the share of 23 of them exceed that of the rest?
Answer, £24. 11. 4½ ½.
246. It is usual, in mercantile business, to mention the fraction which one sum is of another, by saying how many parts out of a hundred must be taken from the second in order to make the first. Thus, instead of saying that £16 12s. is the half of £33 4s., it is said that the first is 50 per cent of the second. Thus, £5 is 2½ per cent of £200; because, if £200 be divided into 100 parts, 2½ of those parts are £5. Also, £13 is 150 per cent of £8. 13. 4, since the first is the second and half the second. Suppose it asked, How much per cent is 23 parts out of 56 of any sum? The question amounts to this: If he who has £56 gets £100 for them, how much will he who has 23 receive? This, by 238, is 23 × ¹⁰⁰/₅₆ or ²³⁰⁰/₅₆ or 41¹/₁₄. Hence, 23 out of 56 is 41¹/₁₄ per cent.
Similarly 16 parts out of 18 is 16 × ¹⁰⁰/₁₈, or 88⁸/₉ per cent, and 2 parts out of 5 is 2 × ¹⁰⁰/₅, or 40 per cent.
From which the method of reducing other fractions to the rate per cent is evident.
Suppose it asked, How much per cent is £6. 12. 2 of £12. 3? Since the first contains 1586d., and the second 2916d., the first is 1586 out of 2916 parts of the second; that is, by the last rule, it is ¹⁵⁸⁶⁰⁰/₂₉₁₆, or 54¹¹³⁶/₂₉₁₆, or £54. 7. 9½ per cent, very nearly. The more expeditious way of doing this is to reduce the shillings, &c. to decimals of a pound. Three decimal places will give the rate per cent to the nearest shilling, which is near enough for all practical purposes. For instance, in the last example, which is to find how much £6·608 is of £12·15, 6·608 × 100 is 660·8, which divided by 12·15 gives £54·38, or £54. 7. Greater correctness may be had, if necessary, as in the [Appendix].
EXERCISES.
How much per cent is 198¼ out of 233 parts?—Ans. £85. 1. 8¾.