Ratio of age of Sanjay and Arjun 6 years ago was (4:5), ratio of their age 9 years hence becomes (9:10). Find the sum of their present age. (in years)

Let present ages be S and A. Six years ago: (S-6)/(A-6) = 4/5, so 5S-30 = 4A-24, or 5S-4A = 6. Nine years hence: (S+9)/(A+9) = 9/10, so 10S+90 = 9A+81, or 10S-9A = -9. Solving: From first eq, S = (6+4A)/5. Substituting in second: 10(6+4A)/5 - 9A = -9, which gives 12+8A-9A = -9, so A = 21. Then S = (6+84)/5 = 18. Present sum = 18+21 = 39 years. Option A (36) is too low, C (42) and D (45) are too high.