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 ?
A. 10 years
B. 12 years
C. 18 years
D. Cannot be determined
E. None of these
Answer: Option E
Solution(By Examveda Team)
Average age of man and his daughter = 34 yearsTheir 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
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Comments ( 2 )
Related Questions on Problems on Ages
A. 2 times
B. $$2\frac{1}{2}\,{\text{times}}$$
C. $$2\frac{3}{4}\,{\text{times}}$$
D. 3 times
A. 4 years
B. 8 years
C. 10 years
D. None of these
A. 14 years
B. 19 years
C. 33 years
D. 38 years
Let man=m and daughter=d, then
According to the first condition,
Average=(m+d)/2
34=( m+d)/2
m+d= 68 ----------eq(1)
According to the second condition,
(m+4)/(d+4)= 14/5-------eq(2)
by solving both equations simultaneously, we get daughter's age=16
Answer