The ages of Ajay and Vijay are in the ratio 9 : 5 . After eight years the ratio of their ages will be 13 : 9. What is the difference between their present ages? अजय और विजय की आयु में 9 : 5 का अनुपात है। आठ वर्षो बाद उनकी आयु का अनुपात 13 : 9 हो जाएगा। उनकी वर्तमान आयु के बीच क्या अंतर है?

Let present ages be 9x and 5x. After 8 years: (9x+8)/(5x+8) = 13/9. Cross-multiplying: 81x + 72 = 65x + 104, so 16x = 32 and x = 2. Present ages are 18 and 9, difference = 9. Wait - that gives 9, not 8. Let me recalculate: (9x+8)/(5x+8) = 13/9. 9(9x+8) = 13(5x+8). 81x + 72 = 65x + 104. 16x = 32. x = 2. Ages: 9×2=18, 5×2=10. Difference = 8 years. Option A is correct. Option C (9 years) is a common error from mis-solving.