Question

$3$ chairs and $2$ tables cost $Rs.700$ while $5$ chairs and $3$ tables cost $Rs.1100$. What is the cost of $2$ chairs and $2$ tables?

• A. $Rs.300$
• B. $Rs.500$
• C. $Rs.600$
• D. $Rs.400$

Answer 1

The correct option is C $Rs.600$

We take the cost of one chair $=Rs.x$ and that of a table $=Rs.y$

Then, in the first case, total cost $=3x+2y$ and in the second case, total cost $=5x+3y.$

Also, the cost of 2 chairs+the cost of 2 tables $=2x+2y.$

So, by the given the given conditions,

$3x+2y=700$ ...........(i) &

$5x+3y=1100$ ..........(ii).

$\left(i\right)\times 5⟶15x+10y=3500$ ......(iii)

$\left(ii\right)\times 3⟶15x+9y=3300$ .........(iv).

$\left(iii\right)-\left(iv\right)⟶y=200$

Substituting $y=200$ in (i),

$3x+2\times 200=700⟹3x=300⟹x=100$

So, the cost of 2 chairs+the cost of 2 tables $=2x+2y$

$=2(x+y)=Rs.2(100+200)=Rs.600$