Two numbers A and B are in the ratio 3:5. When 20 is added to each number, their ratio becomes 5:7. If 10 is subtracted from each original number, find the sum of the two resulting numbers.

ATQ, Let the two original numbers A and B be 3x and 5x. According to the question, when 20 is added to each number, the new ratio becomes 5:7. So, the new numbers are 3x + 20 and 5x + 20. Now, their ratio is 5:7. So, 7 × (3x + 20) = 5 × (5x + 20). 21x + 140 = 25x + 100. 25x − 21x = 140 − 100. 4x = 40. x = 40 ÷ 4 = 10. Now, the first original number = 3x = 3 × 10 = 30. The second original number = 5x = 5 × 10 = 50. Now, 10 is subtracted from each original number. First resulting number = 30 − 10 = 20. Second resulting number = 50 − 10 = 40. Required sum = 20 + 40 = 60.