Question

The age of a father $10$ years ago was thrice the age of his son. $10$ years hence, the father's age will be twice that of his son. The ratio of their present ages is

• A. $8:5$
• B. $7:3$
• C. $9:5$
• D. $5:2$

Answer 1

The correct option is B $7:3$

Let son's age $10$ years ago be $x$ years.
Then, father's age $10$ years ago $=3x$ years.
Son's age now $=(x+10)$ years
Father's age now $=(3x+10)$ years

According to question,
$(3x+10)+10=2\left[\right(x+10)+10]$
$\Rightarrow 3x+20=2x+40$
$\Rightarrow x=20$
Ratio of present ages of father and son $=\frac{3x+10}{x+10}=\frac{70}{30}=7:3$