Question

Age of father $10$ years ago was three times the age of his son. After $10$ years, father's age is twice that of his son. The ratio of their present ages is?

• A. $11:7$
• B. $7:4$
• C. $9:5$
• D. $7:3$

Answer 1

Answer: (D)

$7:3$

Let the present age of the son be $x$ years and present age of father be $y$years.

It is given that $10$ years ago, father's age was three times the age of his son that is:

$y-10=3(x-10)\Rightarrow y-10=3x-30\Rightarrow y=3x-30+10\Rightarrow y=3x-20.....\left(1\right)$

Now, it is also given that after $10$ years, father's age is twice that of his son, that is:

$y+10=2(x+10)\Rightarrow y+10=2x+20\Rightarrow y=2x+20-10\Rightarrow y=2x+10.....\left(2\right)$

From equations 1 and 2, we get:

$3x-20=2x+10\Rightarrow 3x-2x=10+20\Rightarrow x=30$

Now, substitute the value of $x$ in equation 1 as shown below:

$y=(3\times 30)-20=90-20=70$

Therefore, the age of the son is $30$ years and father's age is $70$ years.

Ratio of their present ages is:

$\frac{70}{30}=\frac{7}{3}=7:3$

Hence, the ratio of their present ages is $7:3$.