The product of the ages of a father and his son is $180$ years. When the son becomes as old as his father is now, the sum of their ages will be $84$ years. Find their present ages.
My Attempt:
Let the present age of father be $x$ years and the present age of son be $y$ years.
According to question,
$x\times y= 180$
$y=\frac {180}{x}$.
But how should I get the other equation?
If $x$ is father's current age. Since the years passed would be $x-y$ for the age of son to reach his father's age, then son's age will be $x$ and age of father will be $x+(x-y)=2x-y$
Therefore,
$$3x-y=84$$
Hint: how many years does it take the son to reach his father's current age (depending on $x,y$)? The son is then $x$ years old. How old is the father at that time? Now use the sentence about $84$.
The son then has to be $x $ years of age. The time elapsed for this to take place is $x-y $ years. So the father should be of age $x+(x-y)=2x-y $ years. Thus we have, $$ \text {Father's age} +\text {Son's age} =84$$ $$\Rightarrow (2x-y)+(x)= 84 \tag {2} $$ Hope you can take it from here.