Question

In the given 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

Hint: In this question, we will assume the price of 1 chair to be equal to Rs. x and the price of 1 table to be equal to Rs. y. After that, we will try to form linear equations in x and y using the given conditions. On solving the equations we will get the values of x and y using which we can find the cost of 2 tables and 2 chairs.

Complete step-by-step answer:

Let us assume that the price of each chair be = Rs x
And, the price of each table be = Rs y

Since, it is given that the price of two tables and two chairs cost Rs. 700. So, we can write the following equation:
$3x+2y=700.........\left( 1 \right)$
It is also given that the price of 5 chairs and 3 tables is Rs. 1100. So, we can write the following equation for this:
\[5x+3y=1100..........\left( 2 \right)\]

On multiplying equation (1) by 5 and equation (2) by 3 and then subtracting equation (1) from equation (2), we get:
$\begin{align}
  & 3\left( 5x+3y \right)-5\left( 3x+2y \right)=3\times 1100-5\times 700 \\
 & \Rightarrow 15x+9y-15x-10y=3300-3500 \\
 & \Rightarrow -y=-200 \\
 & \Rightarrow y=200 \\
\end{align}$
So, the value of y is = Rs. 200

On substituting the value of y in equation (1), we get:
$\begin{align}
  & 3x+2\times 200=700 \\
 & \Rightarrow 3x=700-400 \\
 & \Rightarrow 3x=300 \\
 & \Rightarrow x=\dfrac{300}{3} \\
 & \Rightarrow x=100 \\
\end{align}$

So, the value of x is Rs. 100.
Now, we have to find the sum of 2 tables and 2 chairs.
Since, price of 1 chair is = Rs x = Rs. 100
So, the price of 2 chairs = $2\times Rs100=Rs.200$
And, the price of 1 table is = Rs y = Rs. 200
So, the price of 2 tables is = $2\times Rs.200=Rs.400$

Therefore, the total price of 2 tables and 2 chairs is = Rs. 200 + Rs. 400 = Rs. 600
Hence, option (c) is the correct answer.

Note: Students should note here that the linear equations formed must be correct. One can also use other methods like cross multiplication methods to find the solution of equations.