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The age of a father 10 years ago was thrice the age of his son. 10 years hence , the father's age will be twice that of his son. The ratio of their present age is = ?

The age of a father 10 years ago was thrice the age of his son. 10 years hence , the father's age will be twice that of his son. The ratio of their present age is = ? Correct Answer 7 : 3

Let son's age 10 years ago be $$x$$ years
Then, father age 10 years ago = 3$$x$$ years
Son's age now = ($$x$$ + 10) years,
Father age now = (3$$x$$ + 10) years
$$\eqalign{ & \left( {3x + 10} \right) + 10 = 2\left \cr & \Rightarrow 3x + 20 = 2\left( {x + 20} \right) \cr & \Rightarrow 3x + 20 = 2x + 40 \cr & \Rightarrow x = 20 \cr} $$
Ratio of present ages of father and son
$$\eqalign{ & {\text{ = }}\frac{{3x + 10}}{{x + 10}} \cr & = \frac{{3 \times 20 + 10}}{{20 + 10}} \cr & = \frac{{70}}{{30}} \cr & = \frac{7}{3} \cr & = 7:3 \cr} $$

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