## Answer & Solution

Answer:** Option E**

Solution:

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

**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