The sum of the present ages of P & Q and R & Q is 64 years and 56 years,…
2025
The sum of the present ages of P & Q and R & Q is 64 years and 56 years, respectively. The ratio of the age of P after 12 years to the age of Q six years ago is 4 : X. If the age of R after 12 years is 32 years, then find X.
- A.
1
- B.
5
- C.
3
- D.
7
- E.
9
Attempted by 4 students.
Show answer & explanation
Correct answer: C
Concept
When ages are linked by sums and a known future/past value, set up one linear equation per stated relationship and solve them together. A person's age k years from now is (present age + k) and k years ago is (present age − k). A ratio of the form 4 : X means the two quantities, written in lowest terms, share the factor that turns 4 into the first quantity — so X is the second quantity scaled by the same factor.
Application
R after 12 years = 32, so R's present age = 32 − 12 = 20 years.
R & Q sum to 56, so Q's present age = 56 − 20 = 36 years.
P & Q sum to 64, so P's present age = 64 − 36 = 28 years.
P after 12 years = 28 + 12 = 40 years.
Q six years ago = 36 − 6 = 30 years.
Ratio (P after 12) : (Q six years ago) = 40 : 30 = 4 : 3, so X = 3.
Cross-check
Reduce 40 : 30 by dividing both by 10 to get 4 : 3; the first term matches the given 4, confirming the second term X = 3. Equivalently, 40/4 = 10 and 30/10 = 3, so X = 3.