Question

$A$ and $B$ each has some money. If $A$ gives $Rs30$ to $B$ then $B$ will have twice the money left with $A$. But, if $B$ gives $Rs10$ to $A$ then $A$ will have thrice as much as is left with $B$. How much money does each have?

• A. $62,34$
• B. $60,34$
• C. $60,36$
• D. $62,30$

Answer 1

The correct option is A $62,34$

Let money that $A$ has be $x$ and money that $B$ has be $y$

Case

(1) $2(x-30)=(y+30)$

$\Rightarrow 2x-60=y+30$

$\Rightarrow 2x-y-90=0$ (1)

Case (2)

$x+10=3(y-10)$

$\Rightarrow x=10=3y-30$

$\Rightarrow x-3y+40=0$

$\Rightarrow 2x-6y+80=0$ (2)

Subtraction (2) From (1)

$(2x-6y)-(2x-y)=0-0$ $\to -5y+170=0$

$\Rightarrow 5y=170$

$\Rightarrow y=\frac{170}{5}$

$\Rightarrow y=34$

Putting $y=34$ in (1)

$2x-y-90=0$

$\Rightarrow 2x-3y=90$

$\Rightarrow 2x-34=90$

$\Rightarrow 2x=90+34$

$\Rightarrow 3x=124$

$\Rightarrow x=62$

Therefore money that $A$ and $B$ had are $62$ & $34$ respectively