2023 · Q28
The age of Q exceeds the age of P by 3 years. The age of R is twice the age of P and the age of Q is twice the age of S. Further, the age difference of R and S is 30 years. What is the sum of the ages of P and Q?
Elementary MathematicsRatio and Proportion
- A35 years
- B38 years
- C39 years
- D45 years
Explanation
Let P's age be p; then Q = p + 3, R = 2p and S = (p + 3)/2. The condition |R − S| = 30 gives |(3p − 3)/2| = 30; the negative branch yields a negative age, so (3p − 3)/2 = 30, p = 21, q = 24. Thus P + Q = 45 years (D).