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 ?
Correct Answer: None of these
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
=
= 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
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
=
= 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