Each one of ^@A^@ and ^@B^@ has some money. If ^@A^@ gives ^@$ 9 | Math Question and Answer

Answer:

$A$ has $$ 186$ and $B$ has $$ 102.$

Step by Step Explanation:

Let us assume $A$ and $B$ have $$ x$ and $$ y$ respectively.
$A$ gives $$ 90$ to $B$ and then $B$ will have twice the money left with $A$ .

Money with $A$ = $ $(x - 90)$
Money with $B$ = $ $(y + 90)$ $\begin{aligned} \therefore \space & 2(x - 90) = (y + 90) \\ \implies & 2x - 180 = y + 90 \\ \implies & 2x - y = 270 && \ldots (1) \end{aligned}$
$B$ gives $$ 30$ to $A$ and then $A$ will have thrice as much as is left with $B$ .

Money with $A$ = $ $(x + 30)$
Money with $B$ = $ $(y - 30)$ $\begin{aligned} \therefore \space & x + 30 = 3(y - 30) \\ \implies & x + 30 = 3y - 90 \\ \implies & x - 3y = -120 && \ldots (2) \end{aligned}$
On multiplying $(1)$ by $3$ we get $\begin{aligned} & 6x - 3y = 810 && \ldots (3)\end{aligned}$ Now, subtracting $(2)$ from $(3),$ we get $\begin{aligned} & 5x = 930 \\ \implies & x = 186 \end{aligned}$
Now, substituting $x = 186$ in $(1),$ we get $\begin{aligned} & 2(186) - y = 270 \\ \implies & y = 372 - 270 = 102 \end{aligned}$
Hence, $A$ has $$ 186$ and $B$ has $$ 102.$

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