Question

The cost of $9$ chairs and $3$ tables is $₹306$ while the cost of $8$ chairs and $2$ tables is $₹246$. Then the cost of $6$ chairs and $1$ table is:

• A. $₹164$
• B. $₹165$
• C. $₹166$
• D. $₹186$

Answer 1

The correct option is B

$₹165$

Explanation for the correct option:

Step 1: Writing a linear equation for the given variables

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

The cost of $9$ chairs and $3$ tables is $₹306$,

$$\begin{gathered} \Rightarrow 9x+3y=306 \\ \Rightarrow 3x+y=102 \\ \Rightarrow y=102-3x...\left(1\right) \end{gathered}$$divide by $3$

The cost of $8$ chairs and $2$ tables are$₹246$,

$$\begin{gathered} \Rightarrow 8x+2y=246 \\ \Rightarrow 4x+y=123...\left(2\right) \end{gathered}$$divide by $2$

Step 2: Finding $x$ and $y$

Substituting equation $\left(1\right)\text{in}\left(2\right)$,

$$\begin{gathered} \Rightarrow 4x+102-3x=123 \\ \Rightarrow x+102=123 \\ \Rightarrow x=123-102 \\ \Rightarrow x=21 \end{gathered}$$

Applying $x=21$ to find $y$

$$\begin{gathered} y=102-(3\times 21) \\ =102-63 \\ \therefore y=39 \end{gathered}$$

Thus, the cost of one chair is$₹21$ and the table is$₹39$.

Step 3: Finding the cost

Therefore for $6$ chairs and $1$ table, the cost is

$$\begin{gathered} =6x+y \\ =(6\times 21)+39 \\ =126+39 \\ =165 \end{gathered}$$

Cost of $6$ chairs and $1$ table is $₹165$

Hence, the correct answer is Option B.