Question

I am three times as old as my son. Five years later, I shall be two and a half times as old as my son. How old am I and how old is my son?

• A. My present age is 45 years and my son's present age is 15 years
• B. My present age is 60 years and my son's present age is 20 years
• C. My present age is 75 years and my son's present age is 25 years
• D. None of these

Answer 1

The correct option is A My present age is 45 years and my son's present age is 15 years

Let 's suppose I am $x$ years old and my son is $y$ years old
According to the first condition
$\Rightarrow x=3y....eq1$

$5$ years later I shall be $(x+5)$ and son will be $(y+5)$

According to the second comdition
$\Rightarrow x+5=2\frac{1}{2}(y+5)$

$\Rightarrow x+5=\frac{5}{2}(y+5)\Rightarrow 2x+10=5y+25$

$\Rightarrow 2x-5y=\mathrm{15....}eq2$

put the value of $x$ from eq1
$\Rightarrow 2\times 3y-5y=15\Rightarrow 6y-5y=15\Rightarrow y=15$

put $y=15$ in eq1
$\Rightarrow x=3\times 15=45$

Hence, I am 45 years old
Son is 15 years old.