Subject: General Aptitude · Chapter: Ratio and Proportion · Exam: · Marks: · Difficulty:
The present ages of a mother and her son are in the ratio 11 : 5. When the son becomes as old as his mother is now, then the ratio of his father's age to that of his mother is 19 : 17. When the son becomes as old as his father is now, then the sum of his father's age and his age will be 170 years. What is the father's present age?
(a)52 years
(b)60 years
(c)65 years
(d)70 years
Answer
Answer (as printed): C
Explanation
Let the present ages of the mother, son and father be $11 x$, $5 x$ and $y$ years respectively. Then, the son will become as old as his mother is now, after $(11 x-5 x)=6 x$ years. After $6 x$ years, father's age $=(y+6 x)$ years; mother's age $=(11 x+6 x)$ years $=17 x$ years. $\therefore \frac{y+6 x}{17 x}=\frac{19}{17} \Rightarrow y+6 x=19 x \Rightarrow y=13 x$. Again, the son will become as old as his father is now, after $(y-5 x)=(13 x-5 x)=8 x$ years. After $8 x$ years, father's age $=(y+8 x)$ years $=21 x$ years; son's age $=(5 x+8 x)$ years $=13 x$ years. $\therefore 21 x+13 x=170 \Rightarrow 34 x=170 \Rightarrow x=5$. Hence, father's present age $=y=13 x=(13 \times 5)$ years = 65 years.
Explanation as extracted from the printed page; notation may be imperfect.