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At present, Sourav's age is $3$ years more than the square of his son Ravi's age. When Ravi grows to his father's present age, Sourav's age would be $6$ years less than $13$ times the present age of Ravi. Find present ages of Ravi and Sourav.
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Let the present age of Ravi be 'r' years
and the present age of Sourav be 's' years
Therefore, $s = 3 + r^2$ --- (1)
Ravi grows to father's present age in $(s - r)$ years.
$\therefore$ father's age after $(s - r)$ years = $(2s - r)$ years
and Ravi's age after $(s - r)$ years = 's' years
Therefore, $2s - r = 13r - 6$ or $s = 7r - 3$ --- (2)
Using (1) and (2),
$r^2 - 7r + 6 = 0$
$\Rightarrow (r - 6)(r - 1) = 0$
$\Rightarrow r = 6, 1$
Ignoring $r = 1$ as $s \neq 4$
r = $6$
Hence $s = 39$
and the present age of Sourav be 's' years
Therefore, $s = 3 + r^2$ --- (1)
Ravi grows to father's present age in $(s - r)$ years.
$\therefore$ father's age after $(s - r)$ years = $(2s - r)$ years
and Ravi's age after $(s - r)$ years = 's' years
Therefore, $2s - r = 13r - 6$ or $s = 7r - 3$ --- (2)
Using (1) and (2),
$r^2 - 7r + 6 = 0$
$\Rightarrow (r - 6)(r - 1) = 0$
$\Rightarrow r = 6, 1$
Ignoring $r = 1$ as $s \neq 4$
r = $6$
Hence $s = 39$