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  4. A father's present age is 6 times his son's present age. Thirty years hence the father's age will be ten years less than twice the son's age. After how many years will the son's age be half of the father's present age?

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Q. A father's present age is 6 times his son's present age. Thirty years hence the father's age will be ten years less than twice the son's age. After how many years will the son's age be half of the father's present age?

Pair of Linear Equations in Two Variables

Solution:

Let the present ages of father and son be $f$ and $s$, respectively.
Then, $f=6 s$
The second condition gives,
$f+30=2(s+30)-10 \Rightarrow f=2 s+20$
$\therefore 6 s-2 s=20$
$\Rightarrow s=5 \text { and } f=30$
( $\because$ from Eq. (1))
Half the father's present age is 15 . After 10 years, the son's age will be 15 .