Question

Two years ago, Dilip was three times as old as his son and two years hence, twice his age will be equal to five times that of his son. Then the present age of Dilip is ___________.

• A. $14$ years
• B. $38$ years
• C. $32$ years
• D. $34$ years

Answer 1

Answer: (B)

$38$ years

Let age of Dilip and his son be $x,y$ respectively

Given,two years ago Dilip was three times as old as his son.

$\Rightarrow$age of Dilip was $x-2$ and his son was $y-2$.

$x-2=3(y-2)$

$2x=6y-8$...........(i)

Given, two years hence Dilip will be five times as old as his son.

$\Rightarrow$age of Dilip was $x+2$ and his son was $y+2$.

$2(x+2)=5(y+2)$

$2x=5y+6$...........(ii)

Equating (i) and (ii),we get

$6y-8=5y+6$

$y=6+8=14$

Substituting value of $y$ in (i)

$x=3y-4=3\left(14\right)-4=42-4=38$

$\therefore$ the age of Dilip is $38$ years.