The average of the ages of a man and his daughter is 34 years. If the respective ratio of their ages four years from now is 14 : 5,what is daughter's present age ?

Explanation:-

Average age of man and his daughter = 34 years
Their total age = (34 × 2) years = 68 years
Let man's age be x years,
Then daughter age = (68 - x) years
$$\eqalign{ & \therefore \frac{{x + 4}}{{68 - x + 4}} = \frac{{14}}{5} \cr & \Rightarrow 5\left( {x + 4} \right) = 14\left( {72 - x} \right) \cr & \Rightarrow 5x + 20 = 1008 - 14x \cr & \Rightarrow 19x = 988 \cr & \Rightarrow x = 52 \cr}$$
∴ Daughter's present age
= (68 - 52) years
= 16 years