​Three chairs and two tables cost ₹1,850. Five chairs and three tables cost ₹2,850. Find the cost of two chairs and two tables.​​

Correct option is C

Given:

3 chairs + 2 tables = ₹1850

5 chairs + 3 tables = ₹2850

Solution:

Let the cost of 1 chair = x, and 1 table = y
From the given:

​$$3x + 2y = 1850 \quad \text{(1)} \\ 5x + 3y = 2850 \quad \text{(2)}$$​​

Multiply (1) by 3:

9x + 6y = 5550     (3)

Multiply (2) by 2:

10x + 6y = 5700    (4)

Now subtract (3) from (4):

(10x + 6y) - (9x + 6y) = 5700 - 5550

x = 150

Substitute x = 150 in (1):

3(150) + 2y = 1850

450 + 2y = 1850

2y = 1400

y = 700

Now find cost of 2 chairs + 2 tables:

2x + 2y = 2(150) + 2(700) = 300 + 1400 = ₹1700