The sum of the weights of a father and a son is $85$ kg. The weight of the son is $\frac{1}{4}$ of the weight of the father. Find their weights.

Let the wight of the father be F and the weight of the son be S.

According to this question,

F+S=85 ---(1)

Also mentioned that father is 4 times heavier then his son.

i.e, S=F/4

or S=F/4=0----(2)

Therefore,

father's weight will be 4S

Thus, 4S+S=85

$\Rightarrow 5S=85$

$S=85/5$

$\therefore S=17$

Therefore F=85-17=68.

Weight of the father is 68 kg and weight of son is 17 kg.