Question

5 chairs and 4 tables together cost ₹ 5,600, while 4 chairs and 3 tables together cost
₹ 4,340. Find the cost of a chair and that of a table.

Answer 1

Let the cost of a chair be ₹ x and that of a table be ₹ y. Then
$$\begin{gathered} 5x+4y=5600.....\left(i\right) \\ 4x+3y=4340.....\left(ii\right) \end{gathered}$$
Multiplying (i) by 3 and (ii) by 4, we get
$$\begin{gathered} 15x-16x=16800-17360 \\ \Rightarrow -x=-560 \\ \Rightarrow x=560 \end{gathered}$$
Substituting x = 560 in (i), we have
$$\begin{gathered} 5\times 560+4y=5600 \\ \Rightarrow 4y=5600-2800 \\ \Rightarrow y=\frac{2800}{4}=700 \end{gathered}$$
Hence, the cost of a chair and that of a table are respectively ₹ 560 and ₹ 700.