Question

$A$ and $B$ each has some money. If $A$ gives Rs. $30$ to $B$, then $B$ will have twice the money with $A$. But if $B$ gives Rs. $10$ to $A$, then $A$ will have thrice as much as is left with $B$. How much money does each have?

Answer 1

Let $A$ has money $=$ $Rs.x$

& $B$ has money $=$ $Rs.y$

Case $1:$ $2x=(y+30)2x=y+302x-y=30⟶\left(i\right)$

Case $2:$ $(x+10)=3(y-10)\Rightarrow x-3y=-40\Rightarrow 2x-6y=-80⟶\left(ii\right)$

On substracting $\left(ii\right)$ from $\left(i\right)$ we get $,$

$\therefore 2x-y-(2x-6y)=30-(-80)\Rightarrow -y+6y=30+80\Rightarrow 5y=110\therefore y=22$

On putting $y$ in $\left(i\right)$ we get $,$

$2x-y=30$

$\therefore x=26$

Hence $,$ $A$ has $Rs.26$ and $B$ has $Rs.22.$