15 chairs and 3 tables cost ₹7,800 and 14 chairs and 6 tables cost ₹9,200. What is the cost of 17 chairs and 18 tables?

Correct option is C

Given:

15 chairs and 3 tables cost ₹7,800.

14 chairs and 6 tables cost ₹9,200.

We need to find the cost of 17 chairs and 18 tables.

Solution:

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

From the given condition;

15x + 3y = 7800.......(1)

14x + 6y = 9200........(2)

Subtracting 2$$\times$$​ (1) - (2) 

​$$30x + 6y = 15600 \\\underline{-14x - 6y = -9200} \\ 16x \quad =\quad 6400 \\ \ \\x = 400$$​​

Substituting x = 400 into the first equation to find y:

15(400) + 3y = 7800

3y = 7800 - 6000 = 1800

y = 600

Now,  the cost of 17 chairs and 18 tables:

= 17x + 18y = 17(400) + 18(600)

= 6800 + 10800 = ₹17600