Seven chairs and three tables together cost ₹7400, three chairs and five tables together cost ₹5400. The total cost (in ₹) of 1 chair and 2 tables is:
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 2000
Let a chair cost \(c\) and a table \(t\) rupees. The two statements give two equations, and making the \(t\) terms equal lets one of them be removed by subtraction.
The two equations:
\(7c+3t=7400\) (1)
\(3c+5t=5400\) (2)
Finding \(c\) (5 × (1) minus 3 × (2), the \(t\) terms cancel):
\(35c+15t=37000\) and \(9c+15t=16200\)
\(26c=20800\)
\(c=800\)
Finding \(t\) (from (1)):
\(3t=7400-5600=1800\)
\(t=600\)
Cost of 1 chair and 2 tables: \(800+2\times600=\) ₹2000