4 years ago, the respective ratio between (\frac{1}{2}) of P’s age and four times of Q’s age was 5 : 12. Eight years hence (\frac{1}{2}) of P’s age will be less than Q’s age at that time by 2 years. What is Q’s present age?

Let P's present age = P, Q's present age = Q. 4 years ago: (P-4)/2 : 4(Q-4) = 5 : 12. So (P-4)/(8Q-32) = 5/12, giving 12(P-4) = 5(8Q-32), so 12P-48 = 40Q-160, or 12P = 40Q-112. 8 years hence: (P+8)/2 = (Q+8) - 2 = Q+6. So (P+8)/2 = Q+6, giving P+8 = 2Q+12, or P = 2Q+4. Substituting: 12(2Q+4) = 40Q-112, so 24Q+48 = 40Q-112, giving 160 = 16Q, so Q = 10. Option C is correct.