Two numbers M and N are in the ratio 7:9. When 24 is added to each number, their ratio becomes 5:6. If 12 is subtracted from each original number, find the sum of the two resulting numbers.

ATQ, Let the two original numbers M and N be 7x and 9x. According to the question, when 24 is added to each number, the new ratio becomes 5:6. So, the new numbers are 7x + 24 and 9x + 24. Now, their ratio is 5:6. So, 6 × (7x + 24) = 5 × (9x + 24). 42x + 144 = 45x + 120. 45x − 42x = 144 − 120. 3x = 24. x = 24 ÷ 3 = 8. Now, the first original number = 7x = 7 × 8 = 56. The second original number = 9x = 9 × 8 = 72. Now, 12 is subtracted from each original number. First resulting number = 56 − 12 = 44. Second resulting number = 72 − 12 = 60. Required sum = 44 + 60 = 104.