Question

I am three times as old as my son. 5 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. 45 years, 15 years
• B. 40 years, 10 years
• C. 60 years, 25 years
• D. 50 years, 20 years
• E. None of these

Answer 1

The correct option is A 45 years, 15 years

Let, that I am x years old and my son is y years old. Then, according to the first condition of the problem,
x = 3y ....... (1)
Five years later, my age = (x + 5) years and my son's age = (y + 5) years.
Then, according to the second condition of the problem,
$x+5=2\frac{1}{2}(y+5)$ ........ (2)
Putting x = 3y from (1), we get
$3y+5=2\frac{1}{2}(y+5)\Rightarrow 3y+5=\frac{5}{2}(y+5)$
$\Rightarrow 6y+10=5y+25$
$\Rightarrow 6y-5y=25-10$
$\Rightarrow y=15$
Putting y = 15 in (1) in (2), we get x = 3(15) = 45
Hence, I am 45 years old and my son is 15 years old, at present.