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?
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.
Complete step-by-step answer: 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. $(x - 5)$.