Ages (past–future relation): In 10 years A will be twice as old as B was 10 years ago. A is now 9 years older than B. Find B's present age.
Verbal Reasoning
Problems on Ages
Difficulty: Medium
Choose an option
-
A38 years
-
B39 years
-
C40 years
-
D41 years
-
E37 years
Answer
Correct Answer: 39 years
Explanation
Introduction / Context:This problem couples a forward shift in A's age with a backward reference to B's age, a common pattern in timeline-based age equations.
Given Data / Assumptions:
- A = B + 9 (A is currently 9 years older).
- In 10 years, A + 10 = 2 * (B − 10).
Concept / Approach:Use substitution. Express A in terms of B from the age difference, substitute into the future–past relation, and solve a single linear equation for B.
Step-by-Step Solution:
1) From difference: A = B + 9. 2) Future–past relation: (B + 9) + 10 = 2 * (B − 10). 3) Simplify: B + 19 = 2B − 20 → 19 + 20 = 2B − B → B = 39. 4) Optional: A = B + 9 = 48.Verification / Alternative check:Check condition: In 10 years A = 58; B was 10 years ago = 29. Twice of 29 is 58 → satisfied.
Why Other Options Are Wrong:Plugging them back violates the given equation.
Common Pitfalls:Misplacing the 10-year shift across different persons; ensure “A + 10” pairs with “B − 10.”
Final Answer:39 years