(7) Here, 400 × 12: number required × 2 :: 5 : 15; whence, the number required (9) Here, 4.35 × 5.75 : 49.3 × 18.4 :: 6d. : x, 49.3 × 18.4 × 6 5442.72 or, x= (10) Here, 10.164 × 4.5 8.4 × x :: 142.2: 505.6, 12 5 whence, x = 20 × 12 × 3, and x = 20 × 12 × 3 × 5 = 300 12 men. (12) or, 12 × 10 x × 4: 300 x 300: 600 × 10, 3 x 32; whence, x = 2 men. (13) 3 × 10 × 5 : x × 12 × 2 :: 150 × 240: 192 × 300, (14) 7 × 35 × 12 : 12 × 43 × 10 :: 245 × 8 × 11⁄2 (15) 27 × 14 × 10:1 of 24 × 45 × x :: 1 : (16) Since, 21216 ÷ 26 each gun, when there are 4 = 816 shots to be fired from men to a gun, we have 48 816 1: 17 hours; and when there are 5 men to a gun, we have whence, the excess = 17-15=113 5 (17) Since and 3 5 (18) 120×3×12 : x×9×15 :: 90 × 2 × 4:150× 6 × 41 ; whence, x = 180 men. (19) Since 6 × 3 × 14=252, and 10 × 5 × 9 = 450, we have 252 × x : 450 × 1 :: 15 : 101⁄2 ; whence, x = the ratio of the work of a man to that of a boy. Also, 1 man reaps 15 acres in 18 days: therefore 1 acres in 1 day whence, 4 men and 7 boys reap in 1 day (20) The number of hours from 12 o'clock on Monday to a quarter past 10 on the Saturday morning, is 1181 whence, we have 24 1181: 3 min. 10 sec. : x; = or, the gain in the proposed time 15 min. 367 sec.: 40 min. 36 sec. (21) The number of hours from the noon of Tuesday to 6 o'clock on Friday morning being 66, and 10 min. + 7 min. = 17 minutes being the separation in 24 hours, we have, 24: 66: 17 : x; which gives x 48 min. 7 sec., the difference required. (22) Here, 3 × 62s. 8d. : 5 × 50s. :: 1s. 3d. : x; whence, x = 1s. 7d. f., the price required. PAGE 135. SIMPLE INTEREST. All these examples are solved by the immediate application of the Rule: but many useful abbreviations of the processes will soon be learned by a little practice. The observation contained in Article (143), will now be briefly illustrated by means of Ex. (3) of this set, in the following Questions. (1) If £325. 16s. 8d. in 3 years, amount to £374. 6s. Old.: what is the rate per cent. per annum? Here, the interest in 3 years = £48. 19s. 44d. : therefore, the interest in 1 year = £13. 19s. 91d. f.: whence, £325. 16s. 8d. : £100 :: £13. 19s. 91d. } f. : x ; £4. 5s. 41, the rate per cent. per annum. and x = = (2) If £325. 16s. 8d. at 44 per cent. per annum, amount to £374. 6s. 04d.: find the number of years. Here, £48. 19s. 44d. is the interest of £325. 16s. 8d., when the interest of £100 for 1 year is £4. 5s.: whence, we have £100 × 1 : £325. 16s. 8d. × x :: £4. 5s. : £48. 19s. 41d.; which gives x = 3 years. (3) The amount of a certain sum in 3 years at 41 per cent. per annum, is £374. 6s. 04d.: what is the sum? At 41 per cent. per annum, £100 in 34 years amounts to £114. 17s. 6d. whence, we have £114. 17s. 6d. £374. 6s. 01d. :: 100 x; and therefore, x = £325. 16s. 8d. (4) Find the sum whose simple interest at 44 per cent. per annum, amounts in 34 years, to £48. 19s. 41d. Here, £14. 17s. 6d. : £48. 19s. 41d. :: 100 : x; from which, x = £325. 16s. 8d. In these four instances, are included directly or indirectly, all the varieties that can occur; and for the sake of acquiring a readiness in questions of this kind, it may be desirable for the student to diversify some of the other examples given under this head, in the same way as we have just done. PAGE 138. COMPOUND INTEREST. Merely for the sake of explaining what is meant by the remark made at the end of these examples, we shall give the solutions of those numbered (4), (5) and (6). (4) The rate of 5 per cent. = whence, we have £. S. 5 1 in the pound; 100 20 5. 63 = amount in 3 19 years: £881. 4. 10% amount in 4 years. (5) Since 2 per cent. for a half year 1 = we " 50 £584. 195004 = amount in 14 years: |