15 chairs and 19 tables cost ₹5,300 and 19 chairs and 19 tables cost ₹5,700. What is the cost of 12 chairs and 13 tables?

Correct option is B

Given:
15 chairs and 19 tables cost ₹5,300
19 chairs and 19 tables cost ₹5,700
Required: Cost of 12 chairs and 13 tables
Solution:
Let the cost of one chair = ₹x
Let the cost of one table = ₹y
15x + 19y = 5300...............(1)
19x + 19y = 5700..............(2)
Subtract Equation 1 from Equation 2:
(19x + 19y) − (15x + 19y) = 5700 − 5300
=> 4x = 400 => x = 100
Substitute x = 100 into Equation 1:
15 × 100 + 19y = 5300
=> 1500 + 19y = 5300
=> 19y = 3800 => y = 200
Cost of 12 chairs and 13 tables= 12 × 100 + 13 × 200 = 1200 + 2600 = ₹3800