Question

Three chairs and two tables cost $Rs.1850$. Five chairs and three tables cost $Rs.2850$. Find the total cost of one chair and one table

• A. $Rs.800$
• B. $Rs.850$
• C. $Rs.900$
• D. $Rs.950$

Answer 1

The correct option is B $Rs.850$

Let the cost of one chair and one table be x and y

cost of $3$ chairs and $2$ tables is $Rs.1850$ (Given)

$\therefore$ $3x+2y=1850$ $⟶{eq}^n\left(i\right)$

cost of $5$ chairs and $3$ tables is $Rs.2850$

$\therefore$ $5x+3y=2850$ $⟶{eq}^n\left(ii\right)$

Multiplying ${eq}^n\left(i\right)$ by $3$, we get

$9x+6y=5550$ $⟶{eq}^n\left(iii\right)$

Multiplying ${eq}^n\left(ii\right)$ by $2$, we get

$10x+6y=5700$ $⟶{eq}^n\left(iv\right)$

Subtracting ${eq}^n\left(iii\right)$ from $\left(iv\right)$, we have

$10x+6y-9x-6y=5700-5550$

$\Rightarrow$ $x=150$

Substituting the value of x in ${eq}^n\left(i\right)$, we get

$3\times 150+2y=1850$

$\Rightarrow$ $2y=1850-450$

$\Rightarrow$ $y=700$

Hence, the cost of $1$ chair and $1$ table is $Rs.150$ and $Rs.700$ rspectively.

$\therefore$ total cost of one chair and one table $=x+y=700+150=850$

Hence, total cost of one chair and one table is $Rs.850.$