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 ?

Answer: Option E

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
$$\begin{array}{rl}& \therefore \frac{x+4}{68-x+4}=\frac{14}{5}\\ & \Rightarrow 5\left(x+4\right)=14\left(72-x\right)\\ & \Rightarrow 5x+20=1008-14x\\ & \Rightarrow 19x=988\\ & \Rightarrow x=52\end{array}$$
∴ Daughter's present age
= (68 - 52) years
= 16 years

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Alternate Solution :
According to question,
After 4 years, the total age of man & daughter is
= [(34 × 2) + 4 + 4]
= 76 years
After 4 years their age ratio is 14 : 5 (given)
So, 4 years after the daughter age will be
= 76 × $$\frac{5}{19}$$
= 20 years
∴ Daughter present age
= 20 - 4
= 16 years