Difficulty: Medium
Correct Answer: 39
Explanation:
Introduction / Context:
This age problem relates future and past ages of two people, A and B. You must form simultaneous equations by carefully translating the statements into algebra and then solve for the present age of B.
Given Data / Assumptions:
Concept / Approach:
Translate the sentence about ages into an equation. B was b - 10 years old ten years ago. A will be (b + 9) + 10 years old ten years from now. The condition is that this future age of A equals two times that past age of B. Form a linear equation, solve it, and interpret the result.
Step-by-Step Solution:
Let B s present age = b.
Then A s present age = b + 9.
Ten years from now, A s age = (b + 9) + 10 = b + 19.
Ten years ago, B s age = b - 10.
Given: A s age in 10 years = 2 times B s age 10 years ago.
So b + 19 = 2(b - 10).
b + 19 = 2b - 20.
Bring terms together: 19 + 20 = 2b - b.
39 = b.
Hence B s present age is 39 years.
Verification / Alternative check:
Check the condition with b = 39. B was 39 - 10 = 29 years old 10 years ago. In 10 years, A will be (39 + 9) + 10 = 58 years old. Twice B s age 10 years ago is 2 * 29 = 58 years, which matches exactly. Thus the solution is correct.
Why Other Options Are Wrong:
If b = 19 or 29 or 49, substituting in the condition will not make the future age of A equal to twice B s past age. For example, with b = 29, A s future age would be 29 + 9 + 10 = 48 while twice B s age 10 years ago would be 2 * 19 = 38, which does not match.
Common Pitfalls:
The main difficulty is handling the time shifts correctly. Many learners mistakenly use b - 10 instead of b + 10 for future ages or mix up who is older by 9 years. Carefully label each age with its time reference, and build the equation step by step to avoid confusion.
Final Answer:
The present age of B is 39 years.
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