Question

4 chairs and 3 tables cost ₹ 2100 and 5 chairs and 2 tables cost ₹ 1750. Find the cost of a chair.

• A. ₹ 130
• B. ₹ 100
• C. ₹ 200
• D. ₹ 150

Answer 1

The correct option is D ₹ 150

Let $x$ denote the cost of a chair and $y$ denote the cost of a table.

$\Rightarrow 4x+3y=2100...\left(1\right)$

​$and5x+2y=1750...\left(2\right)$

On multiplying equation (1) by 2 and equation (2) by 3 to make the coefficients of y equal, we get

$\Rightarrow 8x+6y=4200....\left(3\right)$

$\Rightarrow 15x+6y=5250...\left(4\right)$

On subtracting equation (3) from (4), we get

$7x=1050$

$\Rightarrow x=150$

On substituting this value of $x$ in equation (1), we get

$4\left(150\right)+3y=2100$

$\Rightarrow 3y=1500$

$\Rightarrow y=500$

Thus, $x=150andy=500$

$\therefore$The cost of a chair is ₹150.