Question

$2$ tables and $3$ chairs together cost $₹2000$ whereas $3$ tables and $2$ chairs together cost $₹2500$(. Find the total cost of $1$ table and $5$ chairs

• A. $Rs.1800.00$
• B. $Rs.1700.00$
• C. $Rs.900.00$
• D. $Rs.1500.00$

Answer 1

The correct option is B $Rs.1700.00$

Let the cost of a table be $₹x$ and that of a chair be \(₹ y\). Then, $2x+3y=2000$
and, $3x+2y=2500$
This system of equations may be written as
$2x+3y-2000=0$
$3x+2y-2500=0$
By using cross-multiplication, we get

$\frac{x}{3x-2500-2\times -200}=\frac{-y}{2\times -2500-3\times -2000}=\frac{1}{2\times 2-3\times 3}$

$\Rightarrow \frac{x}{-7500+4000}=\frac{y}{-1000}=\frac{1}{-5}$

$\Rightarrow x=\frac{-3500}{-5}=700$ and $y=\frac{-1000}{-5}=200$

$\therefore$ Cost of a table $=₹700$ and, cost of a chair $₹=200$
Hence, cost of one table and $5$ chairs $=₹(x+5y)=₹1700$.