Question:
The ratio of the present ages of a father and his son is 2:1. If the ratio 10 years ago was 5:2, then the present age of the son is
The ratio of the present ages of a father and his son is 2:1. If the ratio 10 years ago was 5:2, then the present age of the son is
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Cross-multiplying ratios is the fastest way to solve age problems involving two different points in time.
Updated On: Jul 3, 2026
- 30
- 25
- 24
- 32
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The Correct Option is A
Solution and Explanation
Step 1: Concept
Set up linear equations representing the ages at different time periods.
Step 2: Meaning
Let present ages be $2x$ and $x$. Ten years ago, ages were $2x - 10$ and $x - 10$.
Step 3: Analysis
$\frac{2x - 10}{x - 10} = \frac{5}{2} \Rightarrow 2(2x - 10) = 5(x - 10) \Rightarrow 4x - 20 = 5x - 50 \Rightarrow x = 30$.
Step 4: Conclusion
Since $x$ is the present age of the son, the son is 30 years old. Final Answer: (A)
Set up linear equations representing the ages at different time periods.
Step 2: Meaning
Let present ages be $2x$ and $x$. Ten years ago, ages were $2x - 10$ and $x - 10$.
Step 3: Analysis
$\frac{2x - 10}{x - 10} = \frac{5}{2} \Rightarrow 2(2x - 10) = 5(x - 10) \Rightarrow 4x - 20 = 5x - 50 \Rightarrow x = 30$.
Step 4: Conclusion
Since $x$ is the present age of the son, the son is 30 years old. Final Answer: (A)
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