Question

# The sum of present ages of the father and his son is $45$ years. $5$ years ago, the age of the father is $6$ times that of the son. What is the present age of son?

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Hint: Use all the given conditions. Here first we find $5$ years ago of son and father by assuming their present age and equate it to the given condition.

Let the present age of father be = $x$ years
And the present age of son be = $y$ years
Given that sum of their present ages = $45$ years
$\Rightarrow x + y = 45 \to (1)$
$5$ Years ago, age of the father = $x - 5$ years
$5$ Years ago, age of the son = $y - 5$ years
Given the condition is that, $5$ Years ago the age of a father is $6$ times that of his son.
So,
$\Rightarrow (x - 5) = 6(y - 5) \\ \Rightarrow (x - 5) = 6(y - 30) \\ \Rightarrow 6y - x = - 5 + 30 \\ \Rightarrow 6y - x = 25 \to (2) \\$
Now on adding equation $(1)$ and $(2)$ we get
$\Rightarrow x + y + 6y - x = 45 + 25 \\ \Rightarrow 7y = 70 \\ \Rightarrow y = 10 \\$
Here we have consider that present age of son as $y$ years
Therefore the present age of a son is $10$ years.

Note: Here we have to find the $5$ years ago age of son and father, here ago means before present age where we have to subtract the present age, 5 i.e. $(x - 5)$.