Two numbers A and B are in the ratio 8:13. When 30 is added to each number, their ratio becomes 9:14. If 20 is subtracted from each original number, find the sum of the two resulting numbers.

ATQ, Let the two original numbers A and B be 8x and 13x. According to the question, when 30 is added to each number, the new ratio becomes 9:14. So, the new numbers are 8x + 30 and 13x + 30. Now, their ratio is 9:14. So, 14 × (8x + 30) = 9 × (13x + 30). 112x + 420 = 117x + 270. 117x − 112x = 420 − 270. 5x = 150. x = 150 ÷ 5 = 30. Now, the first original number = 8x = 8 × 30 = 240. The second original number = 13x = 13 × 30 = 390. Now, 20 is subtracted from each original number. First resulting number = 240 − 20 = 220. Second resulting number = 390 − 20 = 370. Required sum = 220 + 370 = 590.