Question

$2$ tables and $3$ chairs cost Rs.$2000$.Where as $3$ tables and $2$ chairs cost Rs.$2500$.Find the total cost of $1$ table and $5$ chairs.

Answer 1

Let the cost of a table be Rs.$x$ and that of a chair be Rs.$y$.Then

$2x+3y=2000$ ........$\left(1\right)$

$3x+2y=2500$ ........$\left(2\right)$

Multiplying equation $\left(1\right)$ by $3$ and $\left(2\right)$ by $1$, we get

$6x+9y=6000$ .........$\left(3\right)$

$6x+4y=5000$ .........$\left(4\right)$

Subtracting $\left(4\right)$ from $\left(3\right)$ we get

$6x+4y-6x-9y=5000-6000$

$\Rightarrow -5y=-1000$

$\Rightarrow y=\frac{-1000}{-5}=200$

$\therefore y=200$

Put $y=200$ in $\left(3\right)$ we get

$2x+3\times 200=2000$

$\Rightarrow 2x=2000-600=1400$

$\Rightarrow x=\frac{1400}{2}=700$

So,Cost of a table$=$Rs.$700$ and cost of a chair $=$Rs.$200$

Hence cost of $1$ table and $5$ chairs$=1\times 700+5\times 200=700+1000=$Rs.$1700$