Subject: General Aptitude · Chapter: Problems on Ages · Exam: 2003 · Marks: · Difficulty:
The age of a man 10 years ago was thrice the age of his son. 10 years hence, the man's age will be twice the age of his son. The ratio of their present ages is
(a)5 : 2
(b)7 : 3
(c)9 : 2
(d)13 : 4
Answer
Answer (as printed): B
Explanation
Let son's age 10 years ago be $x$ years. Then, man's age 10 years ago $=3 x$ years. Son's present age $=(x+10)$ years, Man's present age $=(3 x+10)$ years. $$\begin{aligned} & (3 x+10)+10=2(x+10+10) \\ & \Rightarrow 3 x+20=2(x+20) \\ & \Rightarrow 3 x+20=2 x+40 \\ & \Rightarrow x=20 \end{aligned}$$ Ratio of present ages of man and the son $$=\frac{3 x+10}{x+10}=\frac{3 \times 20+10}{20+10}=\frac{70}{30}=7: 3 .$$
Explanation as extracted from the printed page; notation may be imperfect.