4 tables and 3 chairs, together, cost ₹ 2250 and 3 tables and 4 chairs cost ₹ 1950. Find the cost of 2 chairs and 1 table.


Given:

4 tables and 3 chairs, together, cost ₹ 2250 and 3 tables and 4 chairs cost ₹ 1950.

To do:

We have to find the cost of 2 chairs and 1 table.

Solution:

Let the cost of 1 table and 1 chair be $x$ and $y$ respectively.

According to the question,

$4x + 3y = 2250$.....(i)

$3x + 4y = 1950$.....(ii)

Multiplying equation (i) by 4 on both sides, we get,

$4(4x+3y)=4(2250)$

$16x+12y=9000$.....(iii)

Multiplying equation (ii) by 3 on both sides, we get,

$3(3x+4y)=3(1950)$

$9x+12y=5850$.....(iv)

Subtracting equation (iv) from equation (iii), we get,

$(16x+12y)-(9x+12y)=9000-5850$

$16x-9x+12y-12y=3150$

$7x=3150$

$x=\frac{3150}{7}$

$x=450$

Substituting $x=450$ in equation (ii), we get,

$3(450)+4y=1950$

$1350+4y=1950$

$4y=1950-1350$

$4y=600$

$y=\frac{600}{4}$

$y=150$

$\Rightarrow 2y=2(150)=300$

$x=450$ and $2y=300$

$x+2y=450+300=750$

The cost of 2 chairs and 1 table is Rs. 750.  

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Updated on: 10-Oct-2022

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