Question

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

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

Answer 1

The correct option is B Rs. $165$

Let the cost of one chair and one table be Rs. $x$ and Rs.$y$ respectively.
$\therefore 9x+3y=306$ ...(i)
$8x+2y=246$ ...(ii)
Now multiply (i) with 2 and multiply (ii) with 3 and subtract (ii) from (i) we get,
$(18x+6y)-(24x+6y)=612-738=-126$
$\Rightarrow -6x=-126\Rightarrow x=21$
Thus from (1), $9\times 21+3y=306\Rightarrow 3y=306-189=117\Rightarrow y=39$
$\therefore$ Cost of (6 chair $+$ 1 table)
$=6\times 21+1\times 39=$ Rs. $165$.