Data Sufficiency Question 67
- What is the sum of the present ages of father and the son?
I. Father’s present age is thrice son’s present age
II. After 6 years the ratio of father’s age to the son’s age will be $12: 5$
III. The difference between the father’s age and the son’s age is equal to twice the son’s age.
(1) I and III
(2) II alone
(3) II and either I or III
(4) I and either II or III
(5) None of these
Show Answer
Correct Answer: 67. (3)
Solution: 67. (3) I. $F=3 S$
III. $\mathrm{F}-\mathrm{S}=2 \mathrm{~S} \Rightarrow \mathrm{F}=2 \mathrm{~S}$
So, Statements I and III are equivalent.
II. $\frac{F+6}{S+6}=\frac{15}{5} \Rightarrow \frac{3 S+6}{S+6}=\frac{15}{5}$
$15 \mathrm{~S}+30=12 \mathrm{~S}+72$
$\Rightarrow 3 \mathrm{~S}=42$
$\therefore \mathrm{S}=14$
$\mathrm{F}+\mathrm{S}=45=4 \times 14$
$=56$ years
So, II and either I or III are Sufficient.
BETA
