Question

Five years ago, A's age was four times the age of B. Five years hence, A's age will be twice the age of B. Find their present ages.

• A. Present age of $A=29$ years and that of $B=11$ years
• B. Present age of $A=25$ years and that of $B=10$ years
• C. Present age of $A=65$ years and that of $B=20$ years
• D. Present age of $A=40$ years and that of $B=10$ years

Answer 1

The correct option is B Present age of $A=25$ years and that of $B=10$ years

Let the present age of A be $y$ and of B is $x$

So according to $1^{st}$condition

$\Rightarrow$$4(x-5)=y-5$

$\Rightarrow$$4x-20=y-5$

$\Rightarrow$$y=4x-15$.....$\left(i\right)$
Now according to $2^{nd}$ condition

$\Rightarrow$$5+y=2(x+5)$
$\therefore 5+(4x-15)=2(x+5)$

$\therefore x=10$

now from eq. $\left(i\right)$ we get,

$\Rightarrow$$y=25$

$\therefore$ $y=25$ and $x=10$